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Mar 14

Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

View-Consistent Hierarchical 3D Segmentation Using Ultrametric Feature Fields

Large-scale vision foundation models such as Segment Anything (SAM) demonstrate impressive performance in zero-shot image segmentation at multiple levels of granularity. However, these zero-shot predictions are rarely 3D-consistent. As the camera viewpoint changes in a scene, so do the segmentation predictions, as well as the characterizations of "coarse" or "fine" granularity. In this work, we address the challenging task of lifting multi-granular and view-inconsistent image segmentations into a hierarchical and 3D-consistent representation. We learn a novel feature field within a Neural Radiance Field (NeRF) representing a 3D scene, whose segmentation structure can be revealed at different scales by simply using different thresholds on feature distance. Our key idea is to learn an ultrametric feature space, which unlike a Euclidean space, exhibits transitivity in distance-based grouping, naturally leading to a hierarchical clustering. Put together, our method takes view-inconsistent multi-granularity 2D segmentations as input and produces a hierarchy of 3D-consistent segmentations as output. We evaluate our method and several baselines on synthetic datasets with multi-view images and multi-granular segmentation, showcasing improved accuracy and viewpoint-consistency. We additionally provide qualitative examples of our model's 3D hierarchical segmentations in real world scenes. The code and dataset are available at https://github.com/hardyho/ultrametric_feature_fields

When Does Bottom-up Beat Top-down in Hierarchical Community Detection?

Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.

Persistent homology of the cosmic web. I: Hierarchical topology in ΛCDM cosmologies

Using a set of LambdaCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

Unsupervised Semantic Segmentation of 3D Point Clouds via Cross-modal Distillation and Super-Voxel Clustering

Semantic segmentation of point clouds usually requires exhausting efforts of human annotations, hence it attracts wide attention to the challenging topic of learning from unlabeled or weaker forms of annotations. In this paper, we take the first attempt for fully unsupervised semantic segmentation of point clouds, which aims to delineate semantically meaningful objects without any form of annotations. Previous works of unsupervised pipeline on 2D images fails in this task of point clouds, due to: 1) Clustering Ambiguity caused by limited magnitude of data and imbalanced class distribution; 2) Irregularity Ambiguity caused by the irregular sparsity of point cloud. Therefore, we propose a novel framework, PointDC, which is comprised of two steps that handle the aforementioned problems respectively: Cross-Modal Distillation (CMD) and Super-Voxel Clustering (SVC). In the first stage of CMD, multi-view visual features are back-projected to the 3D space and aggregated to a unified point feature to distill the training of the point representation. In the second stage of SVC, the point features are aggregated to super-voxels and then fed to the iterative clustering process for excavating semantic classes. PointDC yields a significant improvement over the prior state-of-the-art unsupervised methods, on both the ScanNet-v2 (+18.4 mIoU) and S3DIS (+11.5 mIoU) semantic segmentation benchmarks.

Retro-FPN: Retrospective Feature Pyramid Network for Point Cloud Semantic Segmentation

Learning per-point semantic features from the hierarchical feature pyramid is essential for point cloud semantic segmentation. However, most previous methods suffered from ambiguous region features or failed to refine per-point features effectively, which leads to information loss and ambiguous semantic identification. To resolve this, we propose Retro-FPN to model the per-point feature prediction as an explicit and retrospective refining process, which goes through all the pyramid layers to extract semantic features explicitly for each point. Its key novelty is a retro-transformer for summarizing semantic contexts from the previous layer and accordingly refining the features in the current stage. In this way, the categorization of each point is conditioned on its local semantic pattern. Specifically, the retro-transformer consists of a local cross-attention block and a semantic gate unit. The cross-attention serves to summarize the semantic pattern retrospectively from the previous layer. And the gate unit carefully incorporates the summarized contexts and refines the current semantic features. Retro-FPN is a pluggable neural network that applies to hierarchical decoders. By integrating Retro-FPN with three representative backbones, including both point-based and voxel-based methods, we show that Retro-FPN can significantly improve performance over state-of-the-art backbones. Comprehensive experiments on widely used benchmarks can justify the effectiveness of our design. The source is available at https://github.com/AllenXiangX/Retro-FPN

RAPiD-Seg: Range-Aware Pointwise Distance Distribution Networks for 3D LiDAR Segmentation

3D point clouds play a pivotal role in outdoor scene perception, especially in the context of autonomous driving. Recent advancements in 3D LiDAR segmentation often focus intensely on the spatial positioning and distribution of points for accurate segmentation. However, these methods, while robust in variable conditions, encounter challenges due to sole reliance on coordinates and point intensity, leading to poor isometric invariance and suboptimal segmentation. To tackle this challenge, our work introduces Range-Aware Pointwise Distance Distribution (RAPiD) features and the associated RAPiD-Seg architecture. Our RAPiD features exhibit rigid transformation invariance and effectively adapt to variations in point density, with a design focus on capturing the localized geometry of neighboring structures. They utilize inherent LiDAR isotropic radiation and semantic categorization for enhanced local representation and computational efficiency, while incorporating a 4D distance metric that integrates geometric and surface material reflectivity for improved semantic segmentation. To effectively embed high-dimensional RAPiD features, we propose a double-nested autoencoder structure with a novel class-aware embedding objective to encode high-dimensional features into manageable voxel-wise embeddings. Additionally, we propose RAPiD-Seg which incorporates a channel-wise attention fusion and two effective RAPiD-Seg variants, further optimizing the embedding for enhanced performance and generalization. Our method outperforms contemporary LiDAR segmentation work in terms of mIoU on SemanticKITTI (76.1) and nuScenes (83.6) datasets.

Global Features are All You Need for Image Retrieval and Reranking

Image retrieval systems conventionally use a two-stage paradigm, leveraging global features for initial retrieval and local features for reranking. However, the scalability of this method is often limited due to the significant storage and computation cost incurred by local feature matching in the reranking stage. In this paper, we present SuperGlobal, a novel approach that exclusively employs global features for both stages, improving efficiency without sacrificing accuracy. SuperGlobal introduces key enhancements to the retrieval system, specifically focusing on the global feature extraction and reranking processes. For extraction, we identify sub-optimal performance when the widely-used ArcFace loss and Generalized Mean (GeM) pooling methods are combined and propose several new modules to improve GeM pooling. In the reranking stage, we introduce a novel method to update the global features of the query and top-ranked images by only considering feature refinement with a small set of images, thus being very compute and memory efficient. Our experiments demonstrate substantial improvements compared to the state of the art in standard benchmarks. Notably, on the Revisited Oxford+1M Hard dataset, our single-stage results improve by 7.1%, while our two-stage gain reaches 3.7% with a strong 64,865x speedup. Our two-stage system surpasses the current single-stage state-of-the-art by 16.3%, offering a scalable, accurate alternative for high-performing image retrieval systems with minimal time overhead. Code: https://github.com/ShihaoShao-GH/SuperGlobal.

Image-to-Lidar Self-Supervised Distillation for Autonomous Driving Data

Segmenting or detecting objects in sparse Lidar point clouds are two important tasks in autonomous driving to allow a vehicle to act safely in its 3D environment. The best performing methods in 3D semantic segmentation or object detection rely on a large amount of annotated data. Yet annotating 3D Lidar data for these tasks is tedious and costly. In this context, we propose a self-supervised pre-training method for 3D perception models that is tailored to autonomous driving data. Specifically, we leverage the availability of synchronized and calibrated image and Lidar sensors in autonomous driving setups for distilling self-supervised pre-trained image representations into 3D models. Hence, our method does not require any point cloud nor image annotations. The key ingredient of our method is the use of superpixels which are used to pool 3D point features and 2D pixel features in visually similar regions. We then train a 3D network on the self-supervised task of matching these pooled point features with the corresponding pooled image pixel features. The advantages of contrasting regions obtained by superpixels are that: (1) grouping together pixels and points of visually coherent regions leads to a more meaningful contrastive task that produces features well adapted to 3D semantic segmentation and 3D object detection; (2) all the different regions have the same weight in the contrastive loss regardless of the number of 3D points sampled in these regions; (3) it mitigates the noise produced by incorrect matching of points and pixels due to occlusions between the different sensors. Extensive experiments on autonomous driving datasets demonstrate the ability of our image-to-Lidar distillation strategy to produce 3D representations that transfer well on semantic segmentation and object detection tasks.

A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Where We Are and What We're Looking At: Query Based Worldwide Image Geo-localization Using Hierarchies and Scenes

Determining the exact latitude and longitude that a photo was taken is a useful and widely applicable task, yet it remains exceptionally difficult despite the accelerated progress of other computer vision tasks. Most previous approaches have opted to learn a single representation of query images, which are then classified at different levels of geographic granularity. These approaches fail to exploit the different visual cues that give context to different hierarchies, such as the country, state, and city level. To this end, we introduce an end-to-end transformer-based architecture that exploits the relationship between different geographic levels (which we refer to as hierarchies) and the corresponding visual scene information in an image through hierarchical cross-attention. We achieve this by learning a query for each geographic hierarchy and scene type. Furthermore, we learn a separate representation for different environmental scenes, as different scenes in the same location are often defined by completely different visual features. We achieve state of the art street level accuracy on 4 standard geo-localization datasets : Im2GPS, Im2GPS3k, YFCC4k, and YFCC26k, as well as qualitatively demonstrate how our method learns different representations for different visual hierarchies and scenes, which has not been demonstrated in the previous methods. These previous testing datasets mostly consist of iconic landmarks or images taken from social media, which makes them either a memorization task, or biased towards certain places. To address this issue we introduce a much harder testing dataset, Google-World-Streets-15k, comprised of images taken from Google Streetview covering the whole planet and present state of the art results. Our code will be made available in the camera-ready version.

Learning Mesh Representations via Binary Space Partitioning Tree Networks

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

Point Cloud Mamba: Point Cloud Learning via State Space Model

Recently, state space models have exhibited strong global modeling capabilities and linear computational complexity in contrast to transformers. This research focuses on applying such architecture to more efficiently and effectively model point cloud data globally with linear computational complexity. In particular, for the first time, we demonstrate that Mamba-based point cloud methods can outperform previous methods based on transformer or multi-layer perceptrons (MLPs). To enable Mamba to process 3-D point cloud data more effectively, we propose a novel Consistent Traverse Serialization method to convert point clouds into 1-D point sequences while ensuring that neighboring points in the sequence are also spatially adjacent. Consistent Traverse Serialization yields six variants by permuting the order of x, y, and z coordinates, and the synergistic use of these variants aids Mamba in comprehensively observing point cloud data. Furthermore, to assist Mamba in handling point sequences with different orders more effectively, we introduce point prompts to inform Mamba of the sequence's arrangement rules. Finally, we propose positional encoding based on spatial coordinate mapping to inject positional information into point cloud sequences more effectively. Point Cloud Mamba surpasses the state-of-the-art (SOTA) point-based method PointNeXt and achieves new SOTA performance on the ScanObjectNN, ModelNet40, ShapeNetPart, and S3DIS datasets. It is worth mentioning that when using a more powerful local feature extraction module, our PCM achieves 79.6 mIoU on S3DIS, significantly surpassing the previous SOTA models, DeLA and PTv3, by 5.5 mIoU and 4.9 mIoU, respectively.

Clustering based Point Cloud Representation Learning for 3D Analysis

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc. Current studies put much focus on the adaption of neural networks to the complex geometries of point clouds, but are blind to a fundamental question: how to learn an appropriate point embedding space that is aware of both discriminative semantics and challenging variations? As a response, we propose a clustering based supervised learning scheme for point cloud analysis. Unlike current de-facto, scene-wise training paradigm, our algorithm conducts within-class clustering on the point embedding space for automatically discovering subclass patterns which are latent yet representative across scenes. The mined patterns are, in turn, used to repaint the embedding space, so as to respect the underlying distribution of the entire training dataset and improve the robustness to the variations. Our algorithm is principled and readily pluggable to modern point cloud segmentation networks during training, without extra overhead during testing. With various 3D network architectures (i.e., voxel-based, point-based, Transformer-based, automatically searched), our algorithm shows notable improvements on famous point cloud segmentation datasets (i.e.,2.0-2.6% on single-scan and 2.0-2.2% multi-scan of SemanticKITTI, 1.8-1.9% on S3DIS, in terms of mIoU). Our algorithm also demonstrates utility in 3D detection, showing 2.0-3.4% mAP gains on KITTI.

G3Reg: Pyramid Graph-based Global Registration using Gaussian Ellipsoid Model

This study introduces a novel framework, G3Reg, for fast and robust global registration of LiDAR point clouds. In contrast to conventional complex keypoints and descriptors, we extract fundamental geometric primitives, including planes, clusters, and lines (PCL) from the raw point cloud to obtain low-level semantic segments. Each segment is represented as a unified Gaussian Ellipsoid Model (GEM), using a probability ellipsoid to ensure the ground truth centers are encompassed with a certain degree of probability. Utilizing these GEMs, we present a distrust-and-verify scheme based on a Pyramid Compatibility Graph for Global Registration (PAGOR). Specifically, we establish an upper bound, which can be traversed based on the confidence level for compatibility testing to construct the pyramid graph. Then, we solve multiple maximum cliques (MAC) for each level of the pyramid graph, thus generating the corresponding transformation candidates. In the verification phase, we adopt a precise and efficient metric for point cloud alignment quality, founded on geometric primitives, to identify the optimal candidate. The algorithm's performance is validated on three publicly available datasets and a self-collected multi-session dataset. Parameter settings remained unchanged during the experiment evaluations. The results exhibit superior robustness and real-time performance of the G3Reg framework compared to state-of-the-art methods. Furthermore, we demonstrate the potential for integrating individual GEM and PAGOR components into other registration frameworks to enhance their efficacy. Code: https://github.com/HKUST-Aerial-Robotics/G3Reg

Refinement Module based on Parse Graph of Feature Map for Human Pose Estimation

Parse graphs of the human body can be obtained in the human brain to help humans complete the human pose estimation (HPE). It contains a hierarchical structure, like a tree structure, and context relations among nodes. Many researchers pre-design the parse graph of body structure, and then design framework for HPE. However, these frameworks are difficulty adapting when encountering situations that differ from the preset human structure. Different from them, we regard the feature map as a whole, similarly to human body, so the feature map can be optimized based on parse graphs and each node feature is learned implicitly instead of explicitly, which means it can flexibly respond to different human body structure. In this paper, we design the Refinement Module based on the Parse Graph of feature map (RMPG), which includes two stages: top-down decomposition and bottom-up combination. In the top-down decomposition stage, the feature map is decomposed into multiple sub-feature maps along the channel and their context relations are calculated to obtain their respective context information. In the bottom-up combination stage, the sub-feature maps and their context information are combined to obtain refined sub-feature maps, and then these refined sub-feature maps are concatenated to obtain the refined feature map. Additionally ,we design a top-down framework by using multiple RMPG modules for HPE, some of which are supervised to obtain context relations among body parts. Our framework achieves excellent results on the COCO keypoint detection, CrowdPose and MPII human pose datasets. More importantly, our experiments also demonstrate the effectiveness of RMPG on different methods, including SimpleBaselines, Hourglass, and ViTPose.

Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud

We present Point2SSM, a novel unsupervised learning approach for constructing correspondence-based statistical shape models (SSMs) directly from raw point clouds. SSM is crucial in clinical research, enabling population-level analysis of morphological variation in bones and organs. Traditional methods of SSM construction have limitations, including the requirement of noise-free surface meshes or binary volumes, reliance on assumptions or templates, and prolonged inference times due to simultaneous optimization of the entire cohort. Point2SSM overcomes these barriers by providing a data-driven solution that infers SSMs directly from raw point clouds, reducing inference burdens and increasing applicability as point clouds are more easily acquired. While deep learning on 3D point clouds has seen success in unsupervised representation learning and shape correspondence, its application to anatomical SSM construction is largely unexplored. We conduct a benchmark of state-of-the-art point cloud deep networks on the SSM task, revealing their limited robustness to clinical challenges such as noisy, sparse, or incomplete input and limited training data. Point2SSM addresses these issues through an attention-based module, providing effective correspondence mappings from learned point features. Our results demonstrate that the proposed method significantly outperforms existing networks in terms of accurate surface sampling and correspondence, better capturing population-level statistics.

P2Seg: Pointly-supervised Segmentation via Mutual Distillation

Point-level Supervised Instance Segmentation (PSIS) aims to enhance the applicability and scalability of instance segmentation by utilizing low-cost yet instance-informative annotations. Existing PSIS methods usually rely on positional information to distinguish objects, but predicting precise boundaries remains challenging due to the lack of contour annotations. Nevertheless, weakly supervised semantic segmentation methods are proficient in utilizing intra-class feature consistency to capture the boundary contours of the same semantic regions. In this paper, we design a Mutual Distillation Module (MDM) to leverage the complementary strengths of both instance position and semantic information and achieve accurate instance-level object perception. The MDM consists of Semantic to Instance (S2I) and Instance to Semantic (I2S). S2I is guided by the precise boundaries of semantic regions to learn the association between annotated points and instance contours. I2S leverages discriminative relationships between instances to facilitate the differentiation of various objects within the semantic map. Extensive experiments substantiate the efficacy of MDM in fostering the synergy between instance and semantic information, consequently improving the quality of instance-level object representations. Our method achieves 55.7 mAP_{50} and 17.6 mAP on the PASCAL VOC and MS COCO datasets, significantly outperforming recent PSIS methods and several box-supervised instance segmentation competitors.

Fast and Eager k-Medoids Clustering: O(k) Runtime Improvement of the PAM, CLARA, and CLARANS Algorithms

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not exist for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains and applications. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm that achieve an O(k)-fold speedup in the second ("SWAP") phase of the algorithm, but will still find the same results as the original PAM algorithm. If we relax the choice of swaps performed (while retaining comparable quality), we can further accelerate the algorithm by eagerly performing additional swaps in each iteration. With the substantially faster SWAP, we can now explore faster initialization strategies, because (i) the classic ("BUILD") initialization now becomes the bottleneck, and (ii) our swap is fast enough to compensate for worse starting conditions. We also show how the CLARA and CLARANS algorithms benefit from the proposed modifications. While we do not study the parallelization of our approach in this work, it can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100,200, we observed a 458x respectively 1191x speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets, and in particular to higher k.

Hyp-OW: Exploiting Hierarchical Structure Learning with Hyperbolic Distance Enhances Open World Object Detection

Open World Object Detection (OWOD) is a challenging and realistic task that extends beyond the scope of standard Object Detection task. It involves detecting both known and unknown objects while integrating learned knowledge for future tasks. However, the level of "unknownness" varies significantly depending on the context. For example, a tree is typically considered part of the background in a self-driving scene, but it may be significant in a household context. We argue that this contextual information should already be embedded within the known classes. In other words, there should be a semantic or latent structure relationship between the known and unknown items to be discovered. Motivated by this observation, we propose Hyp-OW, a method that learns and models hierarchical representation of known items through a SuperClass Regularizer. Leveraging this representation allows us to effectively detect unknown objects using a similarity distance-based relabeling module. Extensive experiments on benchmark datasets demonstrate the effectiveness of Hyp-OW, achieving improvement in both known and unknown detection (up to 6 percent). These findings are particularly pronounced in our newly designed benchmark, where a strong hierarchical structure exists between known and unknown objects. Our code can be found at https://github.com/tldoan/-HYP-OW-AAAI-2024-

The Impacts of Data, Ordering, and Intrinsic Dimensionality on Recall in Hierarchical Navigable Small Worlds

Vector search systems, pivotal in AI applications, often rely on the Hierarchical Navigable Small Worlds (HNSW) algorithm. However, the behaviour of HNSW under real-world scenarios using vectors generated with deep learning models remains under-explored. Existing Approximate Nearest Neighbours (ANN) benchmarks and research typically has an over-reliance on simplistic datasets like MNIST or SIFT1M and fail to reflect the complexity of current use-cases. Our investigation focuses on HNSW's efficacy across a spectrum of datasets, including synthetic vectors tailored to mimic specific intrinsic dimensionalities, widely-used retrieval benchmarks with popular embedding models, and proprietary e-commerce image data with CLIP models. We survey the most popular HNSW vector databases and collate their default parameters to provide a realistic fixed parameterisation for the duration of the paper. We discover that the recall of approximate HNSW search, in comparison to exact K Nearest Neighbours (KNN) search, is linked to the vector space's intrinsic dimensionality and significantly influenced by the data insertion sequence. Our methodology highlights how insertion order, informed by measurable properties such as the pointwise Local Intrinsic Dimensionality (LID) or known categories, can shift recall by up to 12 percentage points. We also observe that running popular benchmark datasets with HNSW instead of KNN can shift rankings by up to three positions for some models. This work underscores the need for more nuanced benchmarks and design considerations in developing robust vector search systems using approximate vector search algorithms. This study presents a number of scenarios with varying real world applicability which aim to better increase understanding and future development of ANN algorithms and embedding

Slow Perception: Let's Perceive Geometric Figures Step-by-step

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.

Distillation with Contrast is All You Need for Self-Supervised Point Cloud Representation Learning

In this paper, we propose a simple and general framework for self-supervised point cloud representation learning. Human beings understand the 3D world by extracting two levels of information and establishing the relationship between them. One is the global shape of an object, and the other is the local structures of it. However, few existing studies in point cloud representation learning explored how to learn both global shapes and local-to-global relationships without a specified network architecture. Inspired by how human beings understand the world, we utilize knowledge distillation to learn both global shape information and the relationship between global shape and local structures. At the same time, we combine contrastive learning with knowledge distillation to make the teacher network be better updated. Our method achieves the state-of-the-art performance on linear classification and multiple other downstream tasks. Especially, we develop a variant of ViT for 3D point cloud feature extraction, which also achieves comparable results with existing backbones when combined with our framework, and visualization of the attention maps show that our model does understand the point cloud by combining the global shape information and multiple local structural information, which is consistent with the inspiration of our representation learning method. Our code will be released soon.

Exploring the Potential of Encoder-free Architectures in 3D LMMs

Encoder-free architectures have been preliminarily explored in the 2D visual domain, yet it remains an open question whether they can be effectively applied to 3D understanding scenarios. In this paper, we present the first comprehensive investigation into the potential of encoder-free architectures to overcome the challenges of encoder-based 3D Large Multimodal Models (LMMs). These challenges include the failure to adapt to varying point cloud resolutions and the point features from the encoder not meeting the semantic needs of Large Language Models (LLMs). We identify key aspects for 3D LMMs to remove the encoder and enable the LLM to assume the role of the 3D encoder: 1) We propose the LLM-embedded Semantic Encoding strategy in the pre-training stage, exploring the effects of various point cloud self-supervised losses. And we present the Hybrid Semantic Loss to extract high-level semantics. 2) We introduce the Hierarchical Geometry Aggregation strategy in the instruction tuning stage. This incorporates inductive bias into the LLM early layers to focus on the local details of the point clouds. To the end, we present the first Encoder-free 3D LMM, ENEL. Our 7B model rivals the current state-of-the-art model, ShapeLLM-13B, achieving 55.0%, 50.92%, and 42.7% on the classification, captioning, and VQA tasks, respectively. Our results demonstrate that the encoder-free architecture is highly promising for replacing encoder-based architectures in the field of 3D understanding. The code is released at https://github.com/Ivan-Tang-3D/ENEL

A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Space

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

SAGS: Structure-Aware 3D Gaussian Splatting

Following the advent of NeRFs, 3D Gaussian Splatting (3D-GS) has paved the way to real-time neural rendering overcoming the computational burden of volumetric methods. Following the pioneering work of 3D-GS, several methods have attempted to achieve compressible and high-fidelity performance alternatives. However, by employing a geometry-agnostic optimization scheme, these methods neglect the inherent 3D structure of the scene, thereby restricting the expressivity and the quality of the representation, resulting in various floating points and artifacts. In this work, we propose a structure-aware Gaussian Splatting method (SAGS) that implicitly encodes the geometry of the scene, which reflects to state-of-the-art rendering performance and reduced storage requirements on benchmark novel-view synthesis datasets. SAGS is founded on a local-global graph representation that facilitates the learning of complex scenes and enforces meaningful point displacements that preserve the scene's geometry. Additionally, we introduce a lightweight version of SAGS, using a simple yet effective mid-point interpolation scheme, which showcases a compact representation of the scene with up to 24times size reduction without the reliance on any compression strategies. Extensive experiments across multiple benchmark datasets demonstrate the superiority of SAGS compared to state-of-the-art 3D-GS methods under both rendering quality and model size. Besides, we demonstrate that our structure-aware method can effectively mitigate floating artifacts and irregular distortions of previous methods while obtaining precise depth maps. Project page https://eververas.github.io/SAGS/.

Hierarchical Spatio-Temporal Representation Learning for Gait Recognition

Gait recognition is a biometric technique that identifies individuals by their unique walking styles, which is suitable for unconstrained environments and has a wide range of applications. While current methods focus on exploiting body part-based representations, they often neglect the hierarchical dependencies between local motion patterns. In this paper, we propose a hierarchical spatio-temporal representation learning (HSTL) framework for extracting gait features from coarse to fine. Our framework starts with a hierarchical clustering analysis to recover multi-level body structures from the whole body to local details. Next, an adaptive region-based motion extractor (ARME) is designed to learn region-independent motion features. The proposed HSTL then stacks multiple ARMEs in a top-down manner, with each ARME corresponding to a specific partition level of the hierarchy. An adaptive spatio-temporal pooling (ASTP) module is used to capture gait features at different levels of detail to perform hierarchical feature mapping. Finally, a frame-level temporal aggregation (FTA) module is employed to reduce redundant information in gait sequences through multi-scale temporal downsampling. Extensive experiments on CASIA-B, OUMVLP, GREW, and Gait3D datasets demonstrate that our method outperforms the state-of-the-art while maintaining a reasonable balance between model accuracy and complexity.

STAR: A First-Ever Dataset and A Large-Scale Benchmark for Scene Graph Generation in Large-Size Satellite Imagery

Scene graph generation (SGG) in satellite imagery (SAI) benefits promoting understanding of geospatial scenarios from perception to cognition. In SAI, objects exhibit great variations in scales and aspect ratios, and there exist rich relationships between objects (even between spatially disjoint objects), which makes it attractive to holistically conduct SGG in large-size very-high-resolution (VHR) SAI. However, there lack such SGG datasets. Due to the complexity of large-size SAI, mining triplets <subject, relationship, object> heavily relies on long-range contextual reasoning. Consequently, SGG models designed for small-size natural imagery are not directly applicable to large-size SAI. This paper constructs a large-scale dataset for SGG in large-size VHR SAI with image sizes ranging from 512 x 768 to 27,860 x 31,096 pixels, named STAR (Scene graph generaTion in lArge-size satellite imageRy), encompassing over 210K objects and over 400K triplets. To realize SGG in large-size SAI, we propose a context-aware cascade cognition (CAC) framework to understand SAI regarding object detection (OBD), pair pruning and relationship prediction for SGG. We also release a SAI-oriented SGG toolkit with about 30 OBD and 10 SGG methods which need further adaptation by our devised modules on our challenging STAR dataset. The dataset and toolkit are available at: https://linlin-dev.github.io/project/STAR.

SMERF: Streamable Memory Efficient Radiance Fields for Real-Time Large-Scene Exploration

Recent techniques for real-time view synthesis have rapidly advanced in fidelity and speed, and modern methods are capable of rendering near-photorealistic scenes at interactive frame rates. At the same time, a tension has arisen between explicit scene representations amenable to rasterization and neural fields built on ray marching, with state-of-the-art instances of the latter surpassing the former in quality while being prohibitively expensive for real-time applications. In this work, we introduce SMERF, a view synthesis approach that achieves state-of-the-art accuracy among real-time methods on large scenes with footprints up to 300 m^2 at a volumetric resolution of 3.5 mm^3. Our method is built upon two primary contributions: a hierarchical model partitioning scheme, which increases model capacity while constraining compute and memory consumption, and a distillation training strategy that simultaneously yields high fidelity and internal consistency. Our approach enables full six degrees of freedom (6DOF) navigation within a web browser and renders in real-time on commodity smartphones and laptops. Extensive experiments show that our method exceeds the current state-of-the-art in real-time novel view synthesis by 0.78 dB on standard benchmarks and 1.78 dB on large scenes, renders frames three orders of magnitude faster than state-of-the-art radiance field models, and achieves real-time performance across a wide variety of commodity devices, including smartphones. We encourage readers to explore these models interactively at our project website: https://smerf-3d.github.io.

Mass-Radius Relationships for Solid Exoplanets

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial-mass planets of all compositions we considered follow a generic functional form that is not a simple power law: log_{10} R_s = k_1 + 1/3 log_{10}(M_s) - k_2 M_s^{k_3} for up to M_p approx 20 M_{oplus}, where M_s and R_s are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form rho = rho_0 + c P^n. We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found that: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with sim~5% uncertainty water ice planets with gtrsim 25% water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super Earths'' based on the clear distinction in radii between planets with significant gas envelopes and those without.

MHS-VM: Multi-Head Scanning in Parallel Subspaces for Vision Mamba

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

SVDFormer: Complementing Point Cloud via Self-view Augmentation and Self-structure Dual-generator

In this paper, we propose a novel network, SVDFormer, to tackle two specific challenges in point cloud completion: understanding faithful global shapes from incomplete point clouds and generating high-accuracy local structures. Current methods either perceive shape patterns using only 3D coordinates or import extra images with well-calibrated intrinsic parameters to guide the geometry estimation of the missing parts. However, these approaches do not always fully leverage the cross-modal self-structures available for accurate and high-quality point cloud completion. To this end, we first design a Self-view Fusion Network that leverages multiple-view depth image information to observe incomplete self-shape and generate a compact global shape. To reveal highly detailed structures, we then introduce a refinement module, called Self-structure Dual-generator, in which we incorporate learned shape priors and geometric self-similarities for producing new points. By perceiving the incompleteness of each point, the dual-path design disentangles refinement strategies conditioned on the structural type of each point. SVDFormer absorbs the wisdom of self-structures, avoiding any additional paired information such as color images with precisely calibrated camera intrinsic parameters. Comprehensive experiments indicate that our method achieves state-of-the-art performance on widely-used benchmarks. Code will be available at https://github.com/czvvd/SVDFormer.

UniPose: Detecting Any Keypoints

This work proposes a unified framework called UniPose to detect keypoints of any articulated (e.g., human and animal), rigid, and soft objects via visual or textual prompts for fine-grained vision understanding and manipulation. Keypoint is a structure-aware, pixel-level, and compact representation of any object, especially articulated objects. Existing fine-grained promptable tasks mainly focus on object instance detection and segmentation but often fail to identify fine-grained granularity and structured information of image and instance, such as eyes, leg, paw, etc. Meanwhile, prompt-based keypoint detection is still under-explored. To bridge the gap, we make the first attempt to develop an end-to-end prompt-based keypoint detection framework called UniPose to detect keypoints of any objects. As keypoint detection tasks are unified in this framework, we can leverage 13 keypoint detection datasets with 338 keypoints across 1,237 categories over 400K instances to train a generic keypoint detection model. UniPose can effectively align text-to-keypoint and image-to-keypoint due to the mutual enhancement of textual and visual prompts based on the cross-modality contrastive learning optimization objectives. Our experimental results show that UniPose has strong fine-grained localization and generalization abilities across image styles, categories, and poses. Based on UniPose as a generalist keypoint detector, we hope it could serve fine-grained visual perception, understanding, and generation.

Light Schrödinger Bridge

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

ScaleDepth: Decomposing Metric Depth Estimation into Scale Prediction and Relative Depth Estimation

Estimating depth from a single image is a challenging visual task. Compared to relative depth estimation, metric depth estimation attracts more attention due to its practical physical significance and critical applications in real-life scenarios. However, existing metric depth estimation methods are typically trained on specific datasets with similar scenes, facing challenges in generalizing across scenes with significant scale variations. To address this challenge, we propose a novel monocular depth estimation method called ScaleDepth. Our method decomposes metric depth into scene scale and relative depth, and predicts them through a semantic-aware scale prediction (SASP) module and an adaptive relative depth estimation (ARDE) module, respectively. The proposed ScaleDepth enjoys several merits. First, the SASP module can implicitly combine structural and semantic features of the images to predict precise scene scales. Second, the ARDE module can adaptively estimate the relative depth distribution of each image within a normalized depth space. Third, our method achieves metric depth estimation for both indoor and outdoor scenes in a unified framework, without the need for setting the depth range or fine-tuning model. Extensive experiments demonstrate that our method attains state-of-the-art performance across indoor, outdoor, unconstrained, and unseen scenes. Project page: https://ruijiezhu94.github.io/ScaleDepth

Iterative Soft Shrinkage Learning for Efficient Image Super-Resolution

Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. However, prevailing SR models suffer from prohibitive memory footprint and intensive computations, which limits further deployment on edge devices. This work investigates the potential of network pruning for super-resolution to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. Two main challenges remain in applying pruning methods for SR. First, the widely-used filter pruning technique reflects limited granularity and restricted adaptability to diverse network structures. Second, existing pruning methods generally operate upon a pre-trained network for the sparse structure determination, hard to get rid of dense model training in the traditional SR paradigm. To address these challenges, we adopt unstructured pruning with sparse models directly trained from scratch. Specifically, we propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly initialized network at each iteration and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly. We observe that the proposed ISS-P can dynamically learn sparse structures adapting to the optimization process and preserve the sparse model's trainability by yielding a more regularized gradient throughput. Experiments on benchmark datasets demonstrate the effectiveness of the proposed ISS-P over diverse network architectures. Code is available at https://github.com/Jiamian-Wang/Iterative-Soft-Shrinkage-SR

SparseSSP: 3D Subcellular Structure Prediction from Sparse-View Transmitted Light Images

Traditional fluorescence staining is phototoxic to live cells, slow, and expensive; thus, the subcellular structure prediction (SSP) from transmitted light (TL) images is emerging as a label-free, faster, low-cost alternative. However, existing approaches utilize 3D networks for one-to-one voxel level dense prediction, which necessitates a frequent and time-consuming Z-axis imaging process. Moreover, 3D convolutions inevitably lead to significant computation and GPU memory overhead. Therefore, we propose an efficient framework, SparseSSP, predicting fluorescent intensities within the target voxel grid in an efficient paradigm instead of relying entirely on 3D topologies. In particular, SparseSSP makes two pivotal improvements to prior works. First, SparseSSP introduces a one-to-many voxel mapping paradigm, which permits the sparse TL slices to reconstruct the subcellular structure. Secondly, we propose a hybrid dimensions topology, which folds the Z-axis information into channel features, enabling the 2D network layers to tackle SSP under low computational cost. We conduct extensive experiments to validate the effectiveness and advantages of SparseSSP on diverse sparse imaging ratios, and our approach achieves a leading performance compared to pure 3D topologies. SparseSSP reduces imaging frequencies compared to previous dense-view SSP (i.e., the number of imaging is reduced up to 87.5% at most), which is significant in visualizing rapid biological dynamics on low-cost devices and samples.

OReX: Object Reconstruction from Planar Cross-sections Using Neural Fields

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs

Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in the structure of the graph Laplacian operator, the properties of the associated diffusion equation, and the characteristics of the convolutional models that discretise this equation. In this paper, we use cellular sheaf theory to show that the underlying geometry of the graph is deeply linked with the performance of GNNs in heterophilic settings and their oversmoothing behaviour. By considering a hierarchy of increasingly general sheaves, we study how the ability of the sheaf diffusion process to achieve linear separation of the classes in the infinite time limit expands. At the same time, we prove that when the sheaf is non-trivial, discretised parametric diffusion processes have greater control than GNNs over their asymptotic behaviour. On the practical side, we study how sheaves can be learned from data. The resulting sheaf diffusion models have many desirable properties that address the limitations of classical graph diffusion equations (and corresponding GNN models) and obtain competitive results in heterophilic settings. Overall, our work provides new connections between GNNs and algebraic topology and would be of interest to both fields.

DreamCraft3D: Hierarchical 3D Generation with Bootstrapped Diffusion Prior

We present DreamCraft3D, a hierarchical 3D content generation method that produces high-fidelity and coherent 3D objects. We tackle the problem by leveraging a 2D reference image to guide the stages of geometry sculpting and texture boosting. A central focus of this work is to address the consistency issue that existing works encounter. To sculpt geometries that render coherently, we perform score distillation sampling via a view-dependent diffusion model. This 3D prior, alongside several training strategies, prioritizes the geometry consistency but compromises the texture fidelity. We further propose Bootstrapped Score Distillation to specifically boost the texture. We train a personalized diffusion model, Dreambooth, on the augmented renderings of the scene, imbuing it with 3D knowledge of the scene being optimized. The score distillation from this 3D-aware diffusion prior provides view-consistent guidance for the scene. Notably, through an alternating optimization of the diffusion prior and 3D scene representation, we achieve mutually reinforcing improvements: the optimized 3D scene aids in training the scene-specific diffusion model, which offers increasingly view-consistent guidance for 3D optimization. The optimization is thus bootstrapped and leads to substantial texture boosting. With tailored 3D priors throughout the hierarchical generation, DreamCraft3D generates coherent 3D objects with photorealistic renderings, advancing the state-of-the-art in 3D content generation. Code available at https://github.com/deepseek-ai/DreamCraft3D.

Vision-based Situational Graphs Generating Optimizable 3D Scene Representations

3D scene graphs offer a more efficient representation of the environment by hierarchically organizing diverse semantic entities and the topological relationships among them. Fiducial markers, on the other hand, offer a valuable mechanism for encoding comprehensive information pertaining to environments and the objects within them. In the context of Visual SLAM (VSLAM), especially when the reconstructed maps are enriched with practical semantic information, these markers have the potential to enhance the map by augmenting valuable semantic information and fostering meaningful connections among the semantic objects. In this regard, this paper exploits the potential of fiducial markers to incorporate a VSLAM framework with hierarchical representations that generates optimizable multi-layered vision-based situational graphs. The framework comprises a conventional VSLAM system with low-level feature tracking and mapping capabilities bolstered by the incorporation of a fiducial marker map. The fiducial markers aid in identifying walls and doors in the environment, subsequently establishing meaningful associations with high-level entities, including corridors and rooms. Experimental results are conducted on a real-world dataset collected using various legged robots and benchmarked against a Light Detection And Ranging (LiDAR)-based framework (S-Graphs) as the ground truth. Consequently, our framework not only excels in crafting a richer, multi-layered hierarchical map of the environment but also shows enhancement in robot pose accuracy when contrasted with state-of-the-art methodologies.

DeepArchitect: Automatically Designing and Training Deep Architectures

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

Landscaping Linear Mode Connectivity

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

AutoKnots: Adaptive Knot Allocation for Spline Interpolation

In astrophysical and cosmological analyses, the increasing quality and volume of astronomical data demand efficient and precise computational tools. This work introduces a novel adaptive algorithm for automatic knots (AutoKnots) allocation in spline interpolation, designed to meet user-defined precision requirements. Unlike traditional methods that rely on manually configured knot distributions with numerous parameters, the proposed technique automatically determines the optimal number and placement of knots based on interpolation error criteria. This simplifies configuration, often requiring only a single parameter. The algorithm progressively improves the interpolation by adaptively sampling the function-to-be-approximated, f(x), in regions where the interpolation error exceeds the desired threshold. All function evaluations contribute directly to the final approximation, ensuring efficiency. While each resampling step involves recomputing the interpolation table, this process is highly optimized and usually computationally negligible compared to the cost of evaluating f(x). We show the algorithm's efficacy through a series of precision tests on different functions. However, the study underscores the necessity for caution when dealing with certain function types, notably those featuring plateaus. To address this challenge, a heuristic enhancement is incorporated, improving accuracy in flat regions. This algorithm has been extensively used and tested over the years. NumCosmo includes a comprehensive set of unit tests that rigorously evaluate the algorithm both directly and indirectly, underscoring its robustness and reliability. As a practical application, we compute the surface mass density Sigma(R) and the average surface mass density Sigma(<R) for Navarro-Frenk-White and Hernquist halo density profiles, which provide analytical benchmarks. (abridged)

TinySAM: Pushing the Envelope for Efficient Segment Anything Model

Recently segment anything model (SAM) has shown powerful segmentation capability and has drawn great attention in computer vision fields. Massive following works have developed various applications based on the pretrained SAM and achieved impressive performance on downstream vision tasks. However, SAM consists of heavy architectures and requires massive computational capacity, which hinders the further application of SAM on computation constrained edge devices. To this end, in this paper we propose a framework to obtain a tiny segment anything model (TinySAM) while maintaining the strong zero-shot performance. We first propose a full-stage knowledge distillation method with online hard prompt sampling strategy to distill a lightweight student model. We also adapt the post-training quantization to the promptable segmentation task and further reduce the computational cost. Moreover, a hierarchical segmenting everything strategy is proposed to accelerate the everything inference by 2times with almost no performance degradation. With all these proposed methods, our TinySAM leads to orders of magnitude computational reduction and pushes the envelope for efficient segment anything task. Extensive experiments on various zero-shot transfer tasks demonstrate the significantly advantageous performance of our TinySAM against counterpart methods. Pre-trained models and codes will be available at https://github.com/xinghaochen/TinySAM and https://gitee.com/mindspore/models/tree/master/research/cv/TinySAM.

Hier-SLAM++: Neuro-Symbolic Semantic SLAM with a Hierarchically Categorical Gaussian Splatting

We propose Hier-SLAM++, a comprehensive Neuro-Symbolic semantic 3D Gaussian Splatting SLAM method with both RGB-D and monocular input featuring an advanced hierarchical categorical representation, which enables accurate pose estimation as well as global 3D semantic mapping. The parameter usage in semantic SLAM systems increases significantly with the growing complexity of the environment, making scene understanding particularly challenging and costly. To address this problem, we introduce a novel and general hierarchical representation that encodes both semantic and geometric information in a compact form into 3D Gaussian Splatting, leveraging the capabilities of large language models (LLMs) as well as the 3D generative model. By utilizing the proposed hierarchical tree structure, semantic information is symbolically represented and learned in an end-to-end manner. We further introduce a novel semantic loss designed to optimize hierarchical semantic information through both inter-level and cross-level optimization. Additionally, we propose an improved SLAM system to support both RGB-D and monocular inputs using a feed-forward model. To the best of our knowledge, this is the first semantic monocular Gaussian Splatting SLAM system, significantly reducing sensor requirements for 3D semantic understanding and broadening the applicability of semantic Gaussian SLAM system. We conduct experiments on both synthetic and real-world datasets, demonstrating superior or on-par performance with state-of-the-art NeRF-based and Gaussian-based SLAM systems, while significantly reducing storage and training time requirements.

Diffusion-Based Hierarchical Multi-Label Object Detection to Analyze Panoramic Dental X-rays

Due to the necessity for precise treatment planning, the use of panoramic X-rays to identify different dental diseases has tremendously increased. Although numerous ML models have been developed for the interpretation of panoramic X-rays, there has not been an end-to-end model developed that can identify problematic teeth with dental enumeration and associated diagnoses at the same time. To develop such a model, we structure the three distinct types of annotated data hierarchically following the FDI system, the first labeled with only quadrant, the second labeled with quadrant-enumeration, and the third fully labeled with quadrant-enumeration-diagnosis. To learn from all three hierarchies jointly, we introduce a novel diffusion-based hierarchical multi-label object detection framework by adapting a diffusion-based method that formulates object detection as a denoising diffusion process from noisy boxes to object boxes. Specifically, to take advantage of the hierarchically annotated data, our method utilizes a novel noisy box manipulation technique by adapting the denoising process in the diffusion network with the inference from the previously trained model in hierarchical order. We also utilize a multi-label object detection method to learn efficiently from partial annotations and to give all the needed information about each abnormal tooth for treatment planning. Experimental results show that our method significantly outperforms state-of-the-art object detection methods, including RetinaNet, Faster R-CNN, DETR, and DiffusionDet for the analysis of panoramic X-rays, demonstrating the great potential of our method for hierarchically and partially annotated datasets. The code and the data are available at: https://github.com/ibrahimethemhamamci/HierarchicalDet.

Representing Long Volumetric Video with Temporal Gaussian Hierarchy

This paper aims to address the challenge of reconstructing long volumetric videos from multi-view RGB videos. Recent dynamic view synthesis methods leverage powerful 4D representations, like feature grids or point cloud sequences, to achieve high-quality rendering results. However, they are typically limited to short (1~2s) video clips and often suffer from large memory footprints when dealing with longer videos. To solve this issue, we propose a novel 4D representation, named Temporal Gaussian Hierarchy, to compactly model long volumetric videos. Our key observation is that there are generally various degrees of temporal redundancy in dynamic scenes, which consist of areas changing at different speeds. Motivated by this, our approach builds a multi-level hierarchy of 4D Gaussian primitives, where each level separately describes scene regions with different degrees of content change, and adaptively shares Gaussian primitives to represent unchanged scene content over different temporal segments, thus effectively reducing the number of Gaussian primitives. In addition, the tree-like structure of the Gaussian hierarchy allows us to efficiently represent the scene at a particular moment with a subset of Gaussian primitives, leading to nearly constant GPU memory usage during the training or rendering regardless of the video length. Extensive experimental results demonstrate the superiority of our method over alternative methods in terms of training cost, rendering speed, and storage usage. To our knowledge, this work is the first approach capable of efficiently handling minutes of volumetric video data while maintaining state-of-the-art rendering quality. Our project page is available at: https://zju3dv.github.io/longvolcap.

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales r. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade at a constant rate varepsilon_u; iii) On small scales, the even order moments of pairwise velocity Delta u_L follow a two-thirds law (-varepsilon_ur)^{2/3}, while the odd order moments follow a linear scaling langle(Delta u_L)^{2n+1}rangle=(2n+1)langle(Delta u_L)^{2n}ranglelangleDelta u_Lrangler; iv) The scale variation of the velocity distributions was studied for longitudinal velocities u_L or u_L^{'}, pairwise velocity (velocity difference) Delta u_L=u_L^{'}-u_L and velocity sum Sigma u_L=u^{'}_L+u_L. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; v) On small scales, u_L and Sigma u_L can be modeled by a X distribution to maximize the system entropy; vi) On large scales, Delta u_L and Sigma u_L can be modeled by a logistic or a X distribution; vii) the redshift variation of the velocity distributions follows the evolution of the X distribution involving a shape parameter alpha(z) decreasing with time.

LayerPano3D: Layered 3D Panorama for Hyper-Immersive Scene Generation

3D immersive scene generation is a challenging yet critical task in computer vision and graphics. A desired virtual 3D scene should 1) exhibit omnidirectional view consistency, and 2) allow for free exploration in complex scene hierarchies. Existing methods either rely on successive scene expansion via inpainting or employ panorama representation to represent large FOV scene environments. However, the generated scene suffers from semantic drift during expansion and is unable to handle occlusion among scene hierarchies. To tackle these challenges, we introduce LayerPano3D, a novel framework for full-view, explorable panoramic 3D scene generation from a single text prompt. Our key insight is to decompose a reference 2D panorama into multiple layers at different depth levels, where each layer reveals the unseen space from the reference views via diffusion prior. LayerPano3D comprises multiple dedicated designs: 1) we introduce a novel text-guided anchor view synthesis pipeline for high-quality, consistent panorama generation. 2) We pioneer the Layered 3D Panorama as underlying representation to manage complex scene hierarchies and lift it into 3D Gaussians to splat detailed 360-degree omnidirectional scenes with unconstrained viewing paths. Extensive experiments demonstrate that our framework generates state-of-the-art 3D panoramic scene in both full view consistency and immersive exploratory experience. We believe that LayerPano3D holds promise for advancing 3D panoramic scene creation with numerous applications.

Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Efficient Encoding of Graphics Primitives with Simplex-based Structures

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

Level-S^2fM: Structure from Motion on Neural Level Set of Implicit Surfaces

This paper presents a neural incremental Structure-from-Motion (SfM) approach, Level-S^2fM, which estimates the camera poses and scene geometry from a set of uncalibrated images by learning coordinate MLPs for the implicit surfaces and the radiance fields from the established keypoint correspondences. Our novel formulation poses some new challenges due to inevitable two-view and few-view configurations in the incremental SfM pipeline, which complicates the optimization of coordinate MLPs for volumetric neural rendering with unknown camera poses. Nevertheless, we demonstrate that the strong inductive basis conveying in the 2D correspondences is promising to tackle those challenges by exploiting the relationship between the ray sampling schemes. Based on this, we revisit the pipeline of incremental SfM and renew the key components, including two-view geometry initialization, the camera poses registration, the 3D points triangulation, and Bundle Adjustment, with a fresh perspective based on neural implicit surfaces. By unifying the scene geometry in small MLP networks through coordinate MLPs, our Level-S^2fM treats the zero-level set of the implicit surface as an informative top-down regularization to manage the reconstructed 3D points, reject the outliers in correspondences via querying SDF, and refine the estimated geometries by NBA (Neural BA). Not only does our Level-S^2fM lead to promising results on camera pose estimation and scene geometry reconstruction, but it also shows a promising way for neural implicit rendering without knowing camera extrinsic beforehand.

Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not hold for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains such as biology that require the use of Jaccard, Gower, or more complex distances. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm to achieve an O(k)-fold speedup in the second SWAP phase of the algorithm, but will still find the same results as the original PAM algorithm. If we slightly relax the choice of swaps performed (at comparable quality), we can further accelerate the algorithm by performing up to k swaps in each iteration. With the substantially faster SWAP, we can now also explore alternative strategies for choosing the initial medoids. We also show how the CLARA and CLARANS algorithms benefit from these modifications. It can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100, we observed a 200-fold speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets as long as we can afford to compute a distance matrix, and in particular to higher k (at k=2, the new SWAP was only 1.5 times faster, as the speedup is expected to increase with k).

Learning to Aggregate Multi-Scale Context for Instance Segmentation in Remote Sensing Images

The task of instance segmentation in remote sensing images, aiming at performing per-pixel labeling of objects at instance level, is of great importance for various civil applications. Despite previous successes, most existing instance segmentation methods designed for natural images encounter sharp performance degradations when they are directly applied to top-view remote sensing images. Through careful analysis, we observe that the challenges mainly come from the lack of discriminative object features due to severe scale variations, low contrasts, and clustered distributions. In order to address these problems, a novel context aggregation network (CATNet) is proposed to improve the feature extraction process. The proposed model exploits three lightweight plug-and-play modules, namely dense feature pyramid network (DenseFPN), spatial context pyramid (SCP), and hierarchical region of interest extractor (HRoIE), to aggregate global visual context at feature, spatial, and instance domains, respectively. DenseFPN is a multi-scale feature propagation module that establishes more flexible information flows by adopting inter-level residual connections, cross-level dense connections, and feature re-weighting strategy. Leveraging the attention mechanism, SCP further augments the features by aggregating global spatial context into local regions. For each instance, HRoIE adaptively generates RoI features for different downstream tasks. Extensive evaluations of the proposed scheme on iSAID, DIOR, NWPU VHR-10, and HRSID datasets demonstrate that the proposed approach outperforms state-of-the-arts under similar computational costs. Source code and pre-trained models are available at https://github.com/yeliudev/CATNet.

Remote sensing framework for geological mapping via stacked autoencoders and clustering

Supervised machine learning methods for geological mapping via remote sensing face limitations due to the scarcity of accurately labelled training data that can be addressed by unsupervised learning, such as dimensionality reduction and clustering. Dimensionality reduction methods have the potential to play a crucial role in improving the accuracy of geological maps. Although conventional dimensionality reduction methods may struggle with nonlinear data, unsupervised deep learning models such as autoencoders can model non-linear relationships. Stacked autoencoders feature multiple interconnected layers to capture hierarchical data representations useful for remote sensing data. We present an unsupervised machine learning-based framework for processing remote sensing data using stacked autoencoders for dimensionality reduction and k-means clustering for mapping geological units. We use Landsat 8, ASTER, and Sentinel-2 datasets to evaluate the framework for geological mapping of the Mutawintji region in Western New South Wales, Australia. We also compare stacked autoencoders with principal component analysis (PCA) and canonical autoencoders. Our results reveal that the framework produces accurate and interpretable geological maps, efficiently discriminating rock units. The results reveal that the combination of stacked autoencoders with Sentinel-2 data yields the best performance accuracy when compared to other combinations. We find that stacked autoencoders enable better extraction of complex and hierarchical representations of the input data when compared to canonical autoencoders and PCA. We also find that the generated maps align with prior geological knowledge of the study area while providing novel insights into geological structures.

Scale-Equalizing Pyramid Convolution for Object Detection

Feature pyramid has been an efficient method to extract features at different scales. Development over this method mainly focuses on aggregating contextual information at different levels while seldom touching the inter-level correlation in the feature pyramid. Early computer vision methods extracted scale-invariant features by locating the feature extrema in both spatial and scale dimension. Inspired by this, a convolution across the pyramid level is proposed in this study, which is termed pyramid convolution and is a modified 3-D convolution. Stacked pyramid convolutions directly extract 3-D (scale and spatial) features and outperforms other meticulously designed feature fusion modules. Based on the viewpoint of 3-D convolution, an integrated batch normalization that collects statistics from the whole feature pyramid is naturally inserted after the pyramid convolution. Furthermore, we also show that the naive pyramid convolution, together with the design of RetinaNet head, actually best applies for extracting features from a Gaussian pyramid, whose properties can hardly be satisfied by a feature pyramid. In order to alleviate this discrepancy, we build a scale-equalizing pyramid convolution (SEPC) that aligns the shared pyramid convolution kernel only at high-level feature maps. Being computationally efficient and compatible with the head design of most single-stage object detectors, the SEPC module brings significant performance improvement (>4AP increase on MS-COCO2017 dataset) in state-of-the-art one-stage object detectors, and a light version of SEPC also has sim3.5AP gain with only around 7% inference time increase. The pyramid convolution also functions well as a stand-alone module in two-stage object detectors and is able to improve the performance by sim2AP. The source code can be found at https://github.com/jshilong/SEPC.

Structural Multiplane Image: Bridging Neural View Synthesis and 3D Reconstruction

The Multiplane Image (MPI), containing a set of fronto-parallel RGBA layers, is an effective and efficient representation for view synthesis from sparse inputs. Yet, its fixed structure limits the performance, especially for surfaces imaged at oblique angles. We introduce the Structural MPI (S-MPI), where the plane structure approximates 3D scenes concisely. Conveying RGBA contexts with geometrically-faithful structures, the S-MPI directly bridges view synthesis and 3D reconstruction. It can not only overcome the critical limitations of MPI, i.e., discretization artifacts from sloped surfaces and abuse of redundant layers, and can also acquire planar 3D reconstruction. Despite the intuition and demand of applying S-MPI, great challenges are introduced, e.g., high-fidelity approximation for both RGBA layers and plane poses, multi-view consistency, non-planar regions modeling, and efficient rendering with intersected planes. Accordingly, we propose a transformer-based network based on a segmentation model. It predicts compact and expressive S-MPI layers with their corresponding masks, poses, and RGBA contexts. Non-planar regions are inclusively handled as a special case in our unified framework. Multi-view consistency is ensured by sharing global proxy embeddings, which encode plane-level features covering the complete 3D scenes with aligned coordinates. Intensive experiments show that our method outperforms both previous state-of-the-art MPI-based view synthesis methods and planar reconstruction methods.

A Robust and Efficient Boundary Point Detection Method by Measuring Local Direction Dispersion

Boundary point detection aims to outline the external contour structure of clusters and enhance the inter-cluster discrimination, thus bolstering the performance of the downstream classification and clustering tasks. However, existing boundary point detectors are sensitive to density heterogeneity or cannot identify boundary points in concave structures and high-dimensional manifolds. In this work, we propose a robust and efficient boundary point detection method based on Local Direction Dispersion (LoDD). The core of boundary point detection lies in measuring the difference between boundary points and internal points. It is a common observation that an internal point is surrounded by its neighbors in all directions, while the neighbors of a boundary point tend to be distributed only in a certain directional range. By considering this observation, we adopt density-independent K-Nearest Neighbors (KNN) method to determine neighboring points and design a centrality metric LoDD using the eigenvalues of the covariance matrix to depict the distribution uniformity of KNN. We also develop a grid-structure assumption of data distribution to determine the parameters adaptively. The effectiveness of LoDD is demonstrated on synthetic datasets, real-world benchmarks, and application of training set split for deep learning model and hole detection on point cloud data. The datasets and toolkit are available at: https://github.com/ZPGuiGroupWhu/lodd.

Solving High-Dimensional PDEs with Latent Spectral Models

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Arc-support Line Segments Revisited: An Efficient and High-quality Ellipse Detection

Over the years many ellipse detection algorithms spring up and are studied broadly, while the critical issue of detecting ellipses accurately and efficiently in real-world images remains a challenge. In this paper, we propose a valuable industry-oriented ellipse detector by arc-support line segments, which simultaneously reaches high detection accuracy and efficiency. To simplify the complicated curves in an image while retaining the general properties including convexity and polarity, the arc-support line segments are extracted, which grounds the successful detection of ellipses. The arc-support groups are formed by iteratively and robustly linking the arc-support line segments that latently belong to a common ellipse. Afterward, two complementary approaches, namely, locally selecting the arc-support group with higher saliency and globally searching all the valid paired groups, are adopted to fit the initial ellipses in a fast way. Then, the ellipse candidate set can be formulated by hierarchical clustering of 5D parameter space of initial ellipses. Finally, the salient ellipse candidates are selected and refined as detections subject to the stringent and effective verification. Extensive experiments on three public datasets are implemented and our method achieves the best F-measure scores compared to the state-of-the-art methods. The source code is available at https://github.com/AlanLuSun/High-quality-ellipse-detection.