# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
# NVIDIA CORPORATION & AFFILIATES and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto. Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION & AFFILIATES is strictly prohibited.
import torch
from .tables import *
__all__ = [
'FlexiCubes'
]
class FlexiCubes:
def __init__(self, device="cuda"):
self.device = device
self.dmc_table = torch.tensor(dmc_table, dtype=torch.long, device=device, requires_grad=False)
self.num_vd_table = torch.tensor(num_vd_table,
dtype=torch.long, device=device, requires_grad=False)
self.check_table = torch.tensor(
check_table,
dtype=torch.long, device=device, requires_grad=False)
self.tet_table = torch.tensor(tet_table, dtype=torch.long, device=device, requires_grad=False)
self.quad_split_1 = torch.tensor([0, 1, 2, 0, 2, 3], dtype=torch.long, device=device, requires_grad=False)
self.quad_split_2 = torch.tensor([0, 1, 3, 3, 1, 2], dtype=torch.long, device=device, requires_grad=False)
self.quad_split_train = torch.tensor(
[0, 1, 1, 2, 2, 3, 3, 0], dtype=torch.long, device=device, requires_grad=False)
self.cube_corners = torch.tensor([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [
1, 0, 1], [0, 1, 1], [1, 1, 1]], dtype=torch.float, device=device)
self.cube_corners_idx = torch.pow(2, torch.arange(8, requires_grad=False))
self.cube_edges = torch.tensor([0, 1, 1, 5, 4, 5, 0, 4, 2, 3, 3, 7, 6, 7, 2, 6,
2, 0, 3, 1, 7, 5, 6, 4], dtype=torch.long, device=device, requires_grad=False)
self.edge_dir_table = torch.tensor([0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1],
dtype=torch.long, device=device)
self.dir_faces_table = torch.tensor([
[[5, 4], [3, 2], [4, 5], [2, 3]],
[[5, 4], [1, 0], [4, 5], [0, 1]],
[[3, 2], [1, 0], [2, 3], [0, 1]]
], dtype=torch.long, device=device)
self.adj_pairs = torch.tensor([0, 1, 1, 3, 3, 2, 2, 0], dtype=torch.long, device=device)
def __call__(self, voxelgrid_vertices, scalar_field, cube_idx, resolution, qef_reg_scale=1e-3,
weight_scale=0.99, beta=None, alpha=None, gamma_f=None, voxelgrid_colors=None, training=False):
surf_cubes, occ_fx8 = self._identify_surf_cubes(scalar_field, cube_idx)
if surf_cubes.sum() == 0:
return (
torch.zeros((0, 3), device=self.device),
torch.zeros((0, 3), dtype=torch.long, device=self.device),
torch.zeros((0), device=self.device),
torch.zeros((0, voxelgrid_colors.shape[-1]), device=self.device) if voxelgrid_colors is not None else None
)
beta, alpha, gamma_f = self._normalize_weights(
beta, alpha, gamma_f, surf_cubes, weight_scale)
if voxelgrid_colors is not None:
voxelgrid_colors = torch.sigmoid(voxelgrid_colors)
case_ids = self._get_case_id(occ_fx8, surf_cubes, resolution)
surf_edges, idx_map, edge_counts, surf_edges_mask = self._identify_surf_edges(
scalar_field, cube_idx, surf_cubes
)
vd, L_dev, vd_gamma, vd_idx_map, vd_color = self._compute_vd(
voxelgrid_vertices, cube_idx[surf_cubes], surf_edges, scalar_field,
case_ids, beta, alpha, gamma_f, idx_map, qef_reg_scale, voxelgrid_colors)
vertices, faces, s_edges, edge_indices, vertices_color = self._triangulate(
scalar_field, surf_edges, vd, vd_gamma, edge_counts, idx_map,
vd_idx_map, surf_edges_mask, training, vd_color)
return vertices, faces, L_dev, vertices_color
def _compute_reg_loss(self, vd, ue, edge_group_to_vd, vd_num_edges):
"""
Regularizer L_dev as in Equation 8
"""
dist = torch.norm(ue - torch.index_select(input=vd, index=edge_group_to_vd, dim=0), dim=-1)
mean_l2 = torch.zeros_like(vd[:, 0])
mean_l2 = (mean_l2).index_add_(0, edge_group_to_vd, dist) / vd_num_edges.squeeze(1).float()
mad = (dist - torch.index_select(input=mean_l2, index=edge_group_to_vd, dim=0)).abs()
return mad
def _normalize_weights(self, beta, alpha, gamma_f, surf_cubes, weight_scale):
"""
Normalizes the given weights to be non-negative. If input weights are None, it creates and returns a set of weights of ones.
"""
n_cubes = surf_cubes.shape[0]
if beta is not None:
beta = (torch.tanh(beta) * weight_scale + 1)
else:
beta = torch.ones((n_cubes, 12), dtype=torch.float, device=self.device)
if alpha is not None:
alpha = (torch.tanh(alpha) * weight_scale + 1)
else:
alpha = torch.ones((n_cubes, 8), dtype=torch.float, device=self.device)
if gamma_f is not None:
gamma_f = torch.sigmoid(gamma_f) * weight_scale + (1 - weight_scale) / 2
else:
gamma_f = torch.ones((n_cubes), dtype=torch.float, device=self.device)
return beta[surf_cubes], alpha[surf_cubes], gamma_f[surf_cubes]
@torch.no_grad()
def _get_case_id(self, occ_fx8, surf_cubes, res):
"""
Obtains the ID of topology cases based on cell corner occupancy. This function resolves the
ambiguity in the Dual Marching Cubes (DMC) configurations as described in Section 1.3 of the
supplementary material. It should be noted that this function assumes a regular grid.
"""
case_ids = (occ_fx8[surf_cubes] * self.cube_corners_idx.to(self.device).unsqueeze(0)).sum(-1)
problem_config = self.check_table.to(self.device)[case_ids]
to_check = problem_config[..., 0] == 1
problem_config = problem_config[to_check]
if not isinstance(res, (list, tuple)):
res = [res, res, res]
# The 'problematic_configs' only contain configurations for surface cubes. Next, we construct a 3D array,
# 'problem_config_full', to store configurations for all cubes (with default config for non-surface cubes).
# This allows efficient checking on adjacent cubes.
problem_config_full = torch.zeros(list(res) + [5], device=self.device, dtype=torch.long)
vol_idx = torch.nonzero(problem_config_full[..., 0] == 0) # N, 3
vol_idx_problem = vol_idx[surf_cubes][to_check]
problem_config_full[vol_idx_problem[..., 0], vol_idx_problem[..., 1], vol_idx_problem[..., 2]] = problem_config
vol_idx_problem_adj = vol_idx_problem + problem_config[..., 1:4]
within_range = (
vol_idx_problem_adj[..., 0] >= 0) & (
vol_idx_problem_adj[..., 0] < res[0]) & (
vol_idx_problem_adj[..., 1] >= 0) & (
vol_idx_problem_adj[..., 1] < res[1]) & (
vol_idx_problem_adj[..., 2] >= 0) & (
vol_idx_problem_adj[..., 2] < res[2])
vol_idx_problem = vol_idx_problem[within_range]
vol_idx_problem_adj = vol_idx_problem_adj[within_range]
problem_config = problem_config[within_range]
problem_config_adj = problem_config_full[vol_idx_problem_adj[..., 0],
vol_idx_problem_adj[..., 1], vol_idx_problem_adj[..., 2]]
# If two cubes with cases C16 and C19 share an ambiguous face, both cases are inverted.
to_invert = (problem_config_adj[..., 0] == 1)
idx = torch.arange(case_ids.shape[0], device=self.device)[to_check][within_range][to_invert]
case_ids.index_put_((idx,), problem_config[to_invert][..., -1])
return case_ids
@torch.no_grad()
def _identify_surf_edges(self, scalar_field, cube_idx, surf_cubes):
"""
Identifies grid edges that intersect with the underlying surface by checking for opposite signs. As each edge
can be shared by multiple cubes, this function also assigns a unique index to each surface-intersecting edge
and marks the cube edges with this index.
"""
occ_n = scalar_field < 0
all_edges = cube_idx[surf_cubes][:, self.cube_edges].reshape(-1, 2)
unique_edges, _idx_map, counts = torch.unique(all_edges, dim=0, return_inverse=True, return_counts=True)
unique_edges = unique_edges.long()
mask_edges = occ_n[unique_edges.reshape(-1)].reshape(-1, 2).sum(-1) == 1
surf_edges_mask = mask_edges[_idx_map]
counts = counts[_idx_map]
mapping = torch.ones((unique_edges.shape[0]), dtype=torch.long, device=cube_idx.device) * -1
mapping[mask_edges] = torch.arange(mask_edges.sum(), device=cube_idx.device)
# Shaped as [number of cubes x 12 edges per cube]. This is later used to map a cube edge to the unique index
# for a surface-intersecting edge. Non-surface-intersecting edges are marked with -1.
idx_map = mapping[_idx_map]
surf_edges = unique_edges[mask_edges]
return surf_edges, idx_map, counts, surf_edges_mask
@torch.no_grad()
def _identify_surf_cubes(self, scalar_field, cube_idx):
"""
Identifies grid cubes that intersect with the underlying surface by checking if the signs at
all corners are not identical.
"""
occ_n = scalar_field < 0
occ_fx8 = occ_n[cube_idx.reshape(-1)].reshape(-1, 8)
_occ_sum = torch.sum(occ_fx8, -1)
surf_cubes = (_occ_sum > 0) & (_occ_sum < 8)
return surf_cubes, occ_fx8
def _linear_interp(self, edges_weight, edges_x):
"""
Computes the location of zero-crossings on 'edges_x' using linear interpolation with 'edges_weight'.
"""
edge_dim = edges_weight.dim() - 2
assert edges_weight.shape[edge_dim] == 2
edges_weight = torch.cat([torch.index_select(input=edges_weight, index=torch.tensor(1, device=self.device), dim=edge_dim), -
torch.index_select(input=edges_weight, index=torch.tensor(0, device=self.device), dim=edge_dim)]
, edge_dim)
denominator = edges_weight.sum(edge_dim)
ue = (edges_x * edges_weight).sum(edge_dim) / denominator
return ue
def _solve_vd_QEF(self, p_bxnx3, norm_bxnx3, c_bx3, qef_reg_scale):
p_bxnx3 = p_bxnx3.reshape(-1, 7, 3)
norm_bxnx3 = norm_bxnx3.reshape(-1, 7, 3)
c_bx3 = c_bx3.reshape(-1, 3)
A = norm_bxnx3
B = ((p_bxnx3) * norm_bxnx3).sum(-1, keepdims=True)
A_reg = (torch.eye(3, device=p_bxnx3.device) * qef_reg_scale).unsqueeze(0).repeat(p_bxnx3.shape[0], 1, 1)
B_reg = (qef_reg_scale * c_bx3).unsqueeze(-1)
A = torch.cat([A, A_reg], 1)
B = torch.cat([B, B_reg], 1)
dual_verts = torch.linalg.lstsq(A, B).solution.squeeze(-1)
return dual_verts
def _compute_vd(self, voxelgrid_vertices, surf_cubes_fx8, surf_edges, scalar_field,
case_ids, beta, alpha, gamma_f, idx_map, qef_reg_scale, voxelgrid_colors):
"""
Computes the location of dual vertices as described in Section 4.2
"""
alpha_nx12x2 = torch.index_select(input=alpha, index=self.cube_edges, dim=1).reshape(-1, 12, 2)
surf_edges_x = torch.index_select(input=voxelgrid_vertices, index=surf_edges.reshape(-1), dim=0).reshape(-1, 2, 3)
surf_edges_s = torch.index_select(input=scalar_field, index=surf_edges.reshape(-1), dim=0).reshape(-1, 2, 1)
zero_crossing = self._linear_interp(surf_edges_s, surf_edges_x)
if voxelgrid_colors is not None:
C = voxelgrid_colors.shape[-1]
surf_edges_c = torch.index_select(input=voxelgrid_colors, index=surf_edges.reshape(-1), dim=0).reshape(-1, 2, C)
idx_map = idx_map.reshape(-1, 12)
num_vd = torch.index_select(input=self.num_vd_table, index=case_ids, dim=0)
edge_group, edge_group_to_vd, edge_group_to_cube, vd_num_edges, vd_gamma = [], [], [], [], []
# if color is not None:
# vd_color = []
total_num_vd = 0
vd_idx_map = torch.zeros((case_ids.shape[0], 12), dtype=torch.long, device=self.device, requires_grad=False)
for num in torch.unique(num_vd):
cur_cubes = (num_vd == num) # consider cubes with the same numbers of vd emitted (for batching)
curr_num_vd = cur_cubes.sum() * num
curr_edge_group = self.dmc_table[case_ids[cur_cubes], :num].reshape(-1, num * 7)
curr_edge_group_to_vd = torch.arange(
curr_num_vd, device=self.device).unsqueeze(-1).repeat(1, 7) + total_num_vd
total_num_vd += curr_num_vd
curr_edge_group_to_cube = torch.arange(idx_map.shape[0], device=self.device)[
cur_cubes].unsqueeze(-1).repeat(1, num * 7).reshape_as(curr_edge_group)
curr_mask = (curr_edge_group != -1)
edge_group.append(torch.masked_select(curr_edge_group, curr_mask))
edge_group_to_vd.append(torch.masked_select(curr_edge_group_to_vd.reshape_as(curr_edge_group), curr_mask))
edge_group_to_cube.append(torch.masked_select(curr_edge_group_to_cube, curr_mask))
vd_num_edges.append(curr_mask.reshape(-1, 7).sum(-1, keepdims=True))
vd_gamma.append(torch.masked_select(gamma_f, cur_cubes).unsqueeze(-1).repeat(1, num).reshape(-1))
# if color is not None:
# vd_color.append(color[cur_cubes].unsqueeze(1).repeat(1, num, 1).reshape(-1, 3))
edge_group = torch.cat(edge_group)
edge_group_to_vd = torch.cat(edge_group_to_vd)
edge_group_to_cube = torch.cat(edge_group_to_cube)
vd_num_edges = torch.cat(vd_num_edges)
vd_gamma = torch.cat(vd_gamma)
# if color is not None:
# vd_color = torch.cat(vd_color)
# else:
# vd_color = None
vd = torch.zeros((total_num_vd, 3), device=self.device)
beta_sum = torch.zeros((total_num_vd, 1), device=self.device)
idx_group = torch.gather(input=idx_map.reshape(-1), dim=0, index=edge_group_to_cube * 12 + edge_group)
x_group = torch.index_select(input=surf_edges_x, index=idx_group.reshape(-1), dim=0).reshape(-1, 2, 3)
s_group = torch.index_select(input=surf_edges_s, index=idx_group.reshape(-1), dim=0).reshape(-1, 2, 1)
zero_crossing_group = torch.index_select(
input=zero_crossing, index=idx_group.reshape(-1), dim=0).reshape(-1, 3)
alpha_group = torch.index_select(input=alpha_nx12x2.reshape(-1, 2), dim=0,
index=edge_group_to_cube * 12 + edge_group).reshape(-1, 2, 1)
ue_group = self._linear_interp(s_group * alpha_group, x_group)
beta_group = torch.gather(input=beta.reshape(-1), dim=0,
index=edge_group_to_cube * 12 + edge_group).reshape(-1, 1)
beta_sum = beta_sum.index_add_(0, index=edge_group_to_vd, source=beta_group)
vd = vd.index_add_(0, index=edge_group_to_vd, source=ue_group * beta_group) / beta_sum
'''
interpolate colors use the same method as dual vertices
'''
if voxelgrid_colors is not None:
vd_color = torch.zeros((total_num_vd, C), device=self.device)
c_group = torch.index_select(input=surf_edges_c, index=idx_group.reshape(-1), dim=0).reshape(-1, 2, C)
uc_group = self._linear_interp(s_group * alpha_group, c_group)
vd_color = vd_color.index_add_(0, index=edge_group_to_vd, source=uc_group * beta_group) / beta_sum
else:
vd_color = None
L_dev = self._compute_reg_loss(vd, zero_crossing_group, edge_group_to_vd, vd_num_edges)
v_idx = torch.arange(vd.shape[0], device=self.device) # + total_num_vd
vd_idx_map = (vd_idx_map.reshape(-1)).scatter(dim=0, index=edge_group_to_cube *
12 + edge_group, src=v_idx[edge_group_to_vd])
return vd, L_dev, vd_gamma, vd_idx_map, vd_color
def _triangulate(self, scalar_field, surf_edges, vd, vd_gamma, edge_counts, idx_map, vd_idx_map, surf_edges_mask, training, vd_color):
"""
Connects four neighboring dual vertices to form a quadrilateral. The quadrilaterals are then split into
triangles based on the gamma parameter, as described in Section 4.3.
"""
with torch.no_grad():
group_mask = (edge_counts == 4) & surf_edges_mask # surface edges shared by 4 cubes.
group = idx_map.reshape(-1)[group_mask]
vd_idx = vd_idx_map[group_mask]
edge_indices, indices = torch.sort(group, stable=True)
quad_vd_idx = vd_idx[indices].reshape(-1, 4)
# Ensure all face directions point towards the positive SDF to maintain consistent winding.
s_edges = scalar_field[surf_edges[edge_indices.reshape(-1, 4)[:, 0]].reshape(-1)].reshape(-1, 2)
flip_mask = s_edges[:, 0] > 0
quad_vd_idx = torch.cat((quad_vd_idx[flip_mask][:, [0, 1, 3, 2]],
quad_vd_idx[~flip_mask][:, [2, 3, 1, 0]]))
quad_gamma = torch.index_select(input=vd_gamma, index=quad_vd_idx.reshape(-1), dim=0).reshape(-1, 4)
gamma_02 = quad_gamma[:, 0] * quad_gamma[:, 2]
gamma_13 = quad_gamma[:, 1] * quad_gamma[:, 3]
if not training:
mask = (gamma_02 > gamma_13)
faces = torch.zeros((quad_gamma.shape[0], 6), dtype=torch.long, device=quad_vd_idx.device)
faces[mask] = quad_vd_idx[mask][:, self.quad_split_1]
faces[~mask] = quad_vd_idx[~mask][:, self.quad_split_2]
faces = faces.reshape(-1, 3)
else:
vd_quad = torch.index_select(input=vd, index=quad_vd_idx.reshape(-1), dim=0).reshape(-1, 4, 3)
vd_02 = (vd_quad[:, 0] + vd_quad[:, 2]) / 2
vd_13 = (vd_quad[:, 1] + vd_quad[:, 3]) / 2
weight_sum = (gamma_02 + gamma_13) + 1e-8
vd_center = (vd_02 * gamma_02.unsqueeze(-1) + vd_13 * gamma_13.unsqueeze(-1)) / weight_sum.unsqueeze(-1)
if vd_color is not None:
color_quad = torch.index_select(input=vd_color, index=quad_vd_idx.reshape(-1), dim=0).reshape(-1, 4, vd_color.shape[-1])
color_02 = (color_quad[:, 0] + color_quad[:, 2]) / 2
color_13 = (color_quad[:, 1] + color_quad[:, 3]) / 2
color_center = (color_02 * gamma_02.unsqueeze(-1) + color_13 * gamma_13.unsqueeze(-1)) / weight_sum.unsqueeze(-1)
vd_color = torch.cat([vd_color, color_center])
vd_center_idx = torch.arange(vd_center.shape[0], device=self.device) + vd.shape[0]
vd = torch.cat([vd, vd_center])
faces = quad_vd_idx[:, self.quad_split_train].reshape(-1, 4, 2)
faces = torch.cat([faces, vd_center_idx.reshape(-1, 1, 1).repeat(1, 4, 1)], -1).reshape(-1, 3)
return vd, faces, s_edges, edge_indices, vd_color