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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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