pytorch3d学习之pytorch3d.ops

pytorch3d.ops是pytorch提供的一些关于3d数据，即计算机图形学的一些运算的包。

1.pytorch3d.ops.ball_query（）

pytorch3d.ops.ball_query(p1: torch.Tensor, p2: torch.Tensor, lengths1: Optional[torch.Tensor] = None, lengths2: Optional[torch.Tensor] = None, K: int = 500, radius: float = 0.2, return_nn: bool = True)

Ball Query is an alternative to KNN. It can be used to find all points in p2 that are within a specified radius to the query point in p1 (with an upper limit of K neighbors).

The neighbors returned are not necssarily the nearest to the point in p1, just the first K values in p2 which are within the specified radius.

在p2中找距离p1的在特定半径范围内的点，它不一定是k最邻近点。

2.pytorch3d.ops.cubify()

pytorch3d.ops.cubify(voxels, thresh, device=None, align: str = 'topleft') → pytorch3d.structures.meshes.Meshes[source] 

Converts a voxel to a mesh by replacing each occupied voxel with a cube consisting of 12 faces and 8 vertices. Shared vertices are merged, and internal faces are removed. :param voxels: A FloatTensor of shape (N, D, H, W) containing occupancy probabilities. :param thresh: A scalar threshold. If a voxel occupancy is larger than

将voxel转为mesh

3.pytorch3d.ops.knn_gather

pytorch3d.ops.knn_gather(x: torch.Tensor, idx: torch.Tensor, lengths: Optional[torch.Tensor] = None)[source] 

A helper function for knn that allows indexing a tensor x with the indices idx returned by knn_points.

For example, if dists, idx = knn_points(p, x, lengths_p, lengths, K) where p is a tensor of shape (N, L, D) and x a tensor of shape (N, M, D), then one can compute the K nearest neighbors of p with p_nn = knn_gather(x, idx, lengths). It can also be applied for any tensor x of shape (N, M, U) where U != D.

返回p的k最邻近点以及点的坐标·

4.pytorch3d.ops.knn_points

pytorch3d.ops.knn_points(p1: torch.Tensor, p2: torch.Tensor, lengths1: Optional[torch.Tensor] = None, lengths2: Optional[torch.Tensor] = None, K: int = 1, version: int = -1, return_nn: bool = False, return_sorted: bool = True) → pytorch3d.ops.knn.KNN[source]

Returns:

dists – Tensor of shape (N, P1, K) giving the squared distances to the nearest neighbors. This is padded with zeros both where a cloud in p2 has fewer than K points and where a cloud in p1 has fewer than P1 points. idx: LongTensor of shape (N, P1, K) giving the indices of the K nearest neighbors from points in p1 to points in p2. Concretely, if p1_idx[n, i, k] = j then p2[n, j] is the k-th nearest neighbors to p1[n, i] in p2[n]. This is padded with zeros both where a cloud in p2 has fewer than K points and where a cloud in p1 has fewer than P1 points. nn: Tensor of shape (N, P1, K, D) giving the K nearest neighbors in p2 for each point in p1. Concretely, p2_nn[n, i, k] gives the k-th nearest neighbor for p1[n, i]. Returned if return_nn is True. The nearest neighbors are collected using knn_gather which is a helper function that allows indexing any tensor of shape (N, P2, U) with the indices p1_idx returned by knn_points. The output is a tensor of shape (N, P1, K, U).

5.pytorch3d.ops.corresponding_points_alignment

pytorch3d.ops.corresponding_points_alignment(X: Union[torch.Tensor, Pointclouds], Y: Union[torch.Tensor, Pointclouds], weights: Union[torch.Tensor, List[torch.Tensor], None] = None, estimate_scale: bool = False, allow_reflection: bool = False, eps: float = 1e-09) → pytorch3d.ops.points_alignment.SimilarityTransform[source] 

Finds a similarity transformation (rotation R, translation T and optionally scale s) between two given sets of corresponding d-dimensional points X and Y such that:

s[i] X[i] R[i] + T[i] = Y[i],

for all batch indexes i in the least squares sense.

The algorithm is also known as Umeyama [1].

计算两个向量x，y他们之间的相似变换矩阵，包括旋转矩阵R， 平移矩阵T，缩放矩阵s。

6.拉普拉斯矩阵计算

pytorch3d.ops.cot_laplacian(verts: torch.Tensor, faces: torch.Tensor, eps: float = 1e-12) → Tuple[torch.Tensor, torch.Tensor][source]

Returns the Laplacian matrix with cotangent weights and the inverse of the face areas.

Parameters:	verts – tensor of shape (V, 3) containing the vertices of the graph faces – tensor of shape (F, 3) containing the vertex indices of each face
Returns:	2-element tuple containing - L: Sparse FloatTensor of shape (V,V) for the Laplacian matrix. Here, L[i, j] = cot a_ij + cot b_ij iff (i, j) is an edge in meshes. See the description above for more clarity. inv_areas: FloatTensor of shape (V,) containing the inverse of sum of face areas containing each vertex

 

pytorch3d.ops.laplacian(verts: torch.Tensor, edges: torch.Tensor) → torch.Tensor[source]

Computes the laplacian matrix. The definition of the laplacian is L[i, j] = -1 , if i == j L[i, j] = 1 / deg(i) , if (i, j) is an edge L[i, j] = 0 , otherwise where deg(i) is the degree of the i-th vertex in the graph.

Parameters:	verts – tensor of shape (V, 3) containing the vertices of the graph edges – tensor of shape (E, 2) containing the vertex indices of each edge
Returns:	L – Sparse FloatTensor of shape (V, V)

 

pytorch3d.ops.norm_laplacian(verts: torch.Tensor, edges: torch.Tensor, eps: float = 1e-12) → torch.Tensor[source]

Norm laplacian computes a variant of the laplacian matrix which weights each affinity with the normalized distance of the neighboring nodes. More concretely, L[i, j] = 1. / wij where wij = ||vi - vj|| if (vi, vj) are neighboring nodes

Parameters:	verts – tensor of shape (V, 3) containing the vertices of the graph edges – tensor of shape (E, 2) containing the vertex indices of each edge
Returns:	L – Sparse FloatTensor of shape (V, V)

 

7. ICP算法

pytorch3d.ops.iterative_closest_point(X: Union[torch.Tensor, Pointclouds], Y: Union[torch.Tensor, Pointclouds], init_transform: Optional[pytorch3d.ops.points_alignment.SimilarityTransform] = None, max_iterations: int = 100, relative_rmse_thr: float = 1e-06, estimate_scale: bool = False, allow_reflection: bool = False, verbose: bool = False) → pytorch3d.ops.points_alignment.ICPSolution[source]

Executes the iterative closest point (ICP) algorithm [1, 2] in order to find a similarity transformation (rotation R, translation T, and optionally scale s) between two given differently-sized sets of d-dimensional points X and Y, such that: