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