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# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved
import torch
from torch.nn import functional as F
def squared_euclidean_distance_matrix(pts1: torch.Tensor, pts2: torch.Tensor) -> torch.Tensor:
"""
Get squared Euclidean Distance Matrix
Computes pairwise squared Euclidean distances between points
Args:
pts1: Tensor [M x D], M is the number of points, D is feature dimensionality
pts2: Tensor [N x D], N is the number of points, D is feature dimensionality
Return:
Tensor [M, N]: matrix of squared Euclidean distances; at index (m, n)
it contains || pts1[m] - pts2[n] ||^2
"""
edm = torch.mm(-2 * pts1, pts2.t())
edm += (pts1 * pts1).sum(1, keepdim=True) + (pts2 * pts2).sum(1, keepdim=True).t()
return edm.contiguous()
def normalize_embeddings(embeddings: torch.Tensor, epsilon: float = 1e-6) -> torch.Tensor:
"""
Normalize N D-dimensional embedding vectors arranged in a tensor [N, D]
Args:
embeddings (tensor [N, D]): N D-dimensional embedding vectors
epsilon (float): minimum value for a vector norm
Return:
Normalized embeddings (tensor [N, D]), such that L2 vector norms are all equal to 1.
"""
return embeddings / torch.clamp(embeddings.norm(p=None, dim=1, keepdim=True), min=epsilon)
def get_closest_vertices_mask_from_ES(
E: torch.Tensor,
S: torch.Tensor,
h: int,
w: int,
mesh_vertex_embeddings: torch.Tensor,
device: torch.device,
):
"""
Interpolate Embeddings and Segmentations to the size of a given bounding box,
and compute closest vertices and the segmentation mask
Args:
E (tensor [1, D, H, W]): D-dimensional embedding vectors for every point of the
default-sized box
S (tensor [1, 2, H, W]): 2-dimensional segmentation mask for every point of the
default-sized box
h (int): height of the target bounding box
w (int): width of the target bounding box
mesh_vertex_embeddings (tensor [N, D]): vertex embeddings for a chosen mesh
N is the number of vertices in the mesh, D is feature dimensionality
device (torch.device): device to move the tensors to
Return:
Closest Vertices (tensor [h, w]), int, for every point of the resulting box
Segmentation mask (tensor [h, w]), boolean, for every point of the resulting box
"""
embedding_resized = F.interpolate(E, size=(h, w), mode="bilinear")[0].to(device)
coarse_segm_resized = F.interpolate(S, size=(h, w), mode="bilinear")[0].to(device)
mask = coarse_segm_resized.argmax(0) > 0
closest_vertices = torch.zeros(mask.shape, dtype=torch.long, device=device)
all_embeddings = embedding_resized[:, mask].t()
size_chunk = 10_000 # Chunking to avoid possible OOM
edm = []
if len(all_embeddings) == 0:
return closest_vertices, mask
for chunk in range((len(all_embeddings) - 1) // size_chunk + 1):
chunk_embeddings = all_embeddings[size_chunk * chunk : size_chunk * (chunk + 1)]
edm.append(
torch.argmin(
squared_euclidean_distance_matrix(chunk_embeddings, mesh_vertex_embeddings), dim=1
)
)
closest_vertices[mask] = torch.cat(edm)
return closest_vertices, mask
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