# %BANNER_BEGIN% # --------------------------------------------------------------------- # %COPYRIGHT_BEGIN% # # Magic Leap, Inc. ("COMPANY") CONFIDENTIAL # # Unpublished Copyright (c) 2020 # Magic Leap, Inc., All Rights Reserved. # # NOTICE: All information contained herein is, and remains the property # of COMPANY. The intellectual and technical concepts contained herein # are proprietary to COMPANY and may be covered by U.S. and Foreign # Patents, patents in process, and are protected by trade secret or # copyright law. Dissemination of this information or reproduction of # this material is strictly forbidden unless prior written permission is # obtained from COMPANY. Access to the source code contained herein is # hereby forbidden to anyone except current COMPANY employees, managers # or contractors who have executed Confidentiality and Non-disclosure # agreements explicitly covering such access. # # The copyright notice above does not evidence any actual or intended # publication or disclosure of this source code, which includes # information that is confidential and/or proprietary, and is a trade # secret, of COMPANY. ANY REPRODUCTION, MODIFICATION, DISTRIBUTION, # PUBLIC PERFORMANCE, OR PUBLIC DISPLAY OF OR THROUGH USE OF THIS # SOURCE CODE WITHOUT THE EXPRESS WRITTEN CONSENT OF COMPANY IS # STRICTLY PROHIBITED, AND IN VIOLATION OF APPLICABLE LAWS AND # INTERNATIONAL TREATIES. THE RECEIPT OR POSSESSION OF THIS SOURCE # CODE AND/OR RELATED INFORMATION DOES NOT CONVEY OR IMPLY ANY RIGHTS # TO REPRODUCE, DISCLOSE OR DISTRIBUTE ITS CONTENTS, OR TO MANUFACTURE, # USE, OR SELL ANYTHING THAT IT MAY DESCRIBE, IN WHOLE OR IN PART. # # %COPYRIGHT_END% # ---------------------------------------------------------------------- # %AUTHORS_BEGIN% # # Originating Authors: Paul-Edouard Sarlin # # %AUTHORS_END% # --------------------------------------------------------------------*/ # %BANNER_END% from copy import deepcopy from typing import List, Tuple import torch from torch import nn def MLP(channels: List[int], do_bn: bool = True) -> nn.Module: """ Multi-layer perceptron """ n = len(channels) layers = [] for i in range(1, n): layers.append( nn.Conv1d(channels[i - 1], channels[i], kernel_size=1, bias=True)) if i < (n-1): if do_bn: layers.append(nn.BatchNorm1d(channels[i])) layers.append(nn.ReLU()) return nn.Sequential(*layers) def normalize_keypoints(kpts, image_shape): """ Normalize keypoints locations based on image image_shape""" height, width = image_shape[:2] one = kpts.new_tensor(1) size = torch.stack([one*width, one*height])[None] center = size / 2 scaling = size.max(1, keepdim=True).values * 0.7 return (kpts - center[:, None, :]) / scaling[:, None, :] class KeypointEncoder(nn.Module): """ Joint encoding of visual appearance and location using MLPs""" def __init__(self, feature_dim: int, layers: List[int]) -> None: super().__init__() self.encoder = MLP([3] + layers + [feature_dim]) nn.init.constant_(self.encoder[-1].bias, 0.0) def forward(self, kpts, scores): inputs = [kpts.transpose(1, 2), scores.unsqueeze(1)] return self.encoder(torch.cat(inputs, dim=1)) def attention(query: torch.Tensor, key: torch.Tensor, value: torch.Tensor) -> Tuple[torch.Tensor,torch.Tensor]: dim = query.shape[1] scores = torch.einsum('bdhn,bdhm->bhnm', query, key) / dim**.5 prob = torch.nn.functional.softmax(scores, dim=-1) return torch.einsum('bhnm,bdhm->bdhn', prob, value), prob class MultiHeadedAttention(nn.Module): """ Multi-head attention to increase model expressivitiy """ def __init__(self, num_heads: int, d_model: int): super().__init__() assert d_model % num_heads == 0 self.dim = d_model // num_heads self.num_heads = num_heads self.merge = nn.Conv1d(d_model, d_model, kernel_size=1) self.proj = nn.ModuleList([deepcopy(self.merge) for _ in range(3)]) def forward(self, query: torch.Tensor, key: torch.Tensor, value: torch.Tensor) -> torch.Tensor: batch_dim = query.size(0) query, key, value = [l(x).view(batch_dim, self.dim, self.num_heads, -1) for l, x in zip(self.proj, (query, key, value))] x, _ = attention(query, key, value) return self.merge(x.contiguous().view(batch_dim, self.dim*self.num_heads, -1)) class AttentionalPropagation(nn.Module): def __init__(self, feature_dim: int, num_heads: int): super().__init__() self.attn = MultiHeadedAttention(num_heads, feature_dim) self.mlp = MLP([feature_dim*2, feature_dim*2, feature_dim]) nn.init.constant_(self.mlp[-1].bias, 0.0) def forward(self, x: torch.Tensor, source: torch.Tensor) -> torch.Tensor: message = self.attn(x, source, source) return self.mlp(torch.cat([x, message], dim=1)) class AttentionalGNN(nn.Module): def __init__(self, feature_dim: int, layer_names: List[str]) -> None: super().__init__() self.layers = nn.ModuleList([ AttentionalPropagation(feature_dim, 4) for _ in range(len(layer_names))]) self.names = layer_names def forward(self, desc0: torch.Tensor, desc1: torch.Tensor) -> Tuple[torch.Tensor,torch.Tensor]: for layer, name in zip(self.layers, self.names): if name == 'cross': src0, src1 = desc1, desc0 else: # if name == 'self': src0, src1 = desc0, desc1 delta0, delta1 = layer(desc0, src0), layer(desc1, src1) desc0, desc1 = (desc0 + delta0), (desc1 + delta1) return desc0, desc1 def log_sinkhorn_iterations(Z: torch.Tensor, log_mu: torch.Tensor, log_nu: torch.Tensor, iters: int) -> torch.Tensor: """ Perform Sinkhorn Normalization in Log-space for stability""" u, v = torch.zeros_like(log_mu), torch.zeros_like(log_nu) for _ in range(iters): u = log_mu - torch.logsumexp(Z + v.unsqueeze(1), dim=2) v = log_nu - torch.logsumexp(Z + u.unsqueeze(2), dim=1) return Z + u.unsqueeze(2) + v.unsqueeze(1) def log_optimal_transport(scores: torch.Tensor, alpha: torch.Tensor, iters: int) -> torch.Tensor: """ Perform Differentiable Optimal Transport in Log-space for stability""" b, m, n = scores.shape one = scores.new_tensor(1) ms, ns = (m*one).to(scores), (n*one).to(scores) bins0 = alpha.expand(b, m, 1) bins1 = alpha.expand(b, 1, n) alpha = alpha.expand(b, 1, 1) couplings = torch.cat([torch.cat([scores, bins0], -1), torch.cat([bins1, alpha], -1)], 1) norm = - (ms + ns).log() log_mu = torch.cat([norm.expand(m), ns.log()[None] + norm]) log_nu = torch.cat([norm.expand(n), ms.log()[None] + norm]) log_mu, log_nu = log_mu[None].expand(b, -1), log_nu[None].expand(b, -1) Z = log_sinkhorn_iterations(couplings, log_mu, log_nu, iters) Z = Z - norm # multiply probabilities by M+N return Z def arange_like(x, dim: int): return x.new_ones(x.shape[dim]).cumsum(0) - 1 # traceable in 1.1 class SuperGlue(nn.Module): """SuperGlue feature matching middle-end Given two sets of keypoints and locations, we determine the correspondences by: 1. Keypoint Encoding (normalization + visual feature and location fusion) 2. Graph Neural Network with multiple self and cross-attention layers 3. Final projection layer 4. Optimal Transport Layer (a differentiable Hungarian matching algorithm) 5. Thresholding matrix based on mutual exclusivity and a match_threshold The correspondence ids use -1 to indicate non-matching points. Paul-Edouard Sarlin, Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. SuperGlue: Learning Feature Matching with Graph Neural Networks. In CVPR, 2020. https://arxiv.org/abs/1911.11763 """ default_config = { 'descriptor_dim': 256, 'weights': 'indoor', 'keypoint_encoder': [32, 64, 128, 256], 'GNN_layers': ['self', 'cross'] * 9, 'sinkhorn_iterations': 100, 'match_threshold': 0.2, } def __init__(self, config): super().__init__() self.config = {**self.default_config, **config} self.kenc = KeypointEncoder( self.config['descriptor_dim'], self.config['keypoint_encoder']) self.gnn = AttentionalGNN( feature_dim=self.config['descriptor_dim'], layer_names=self.config['GNN_layers']) self.final_proj = nn.Conv1d( self.config['descriptor_dim'], self.config['descriptor_dim'], kernel_size=1, bias=True) bin_score = torch.nn.Parameter(torch.tensor(1.)) self.register_parameter('bin_score', bin_score) def forward(self, data): """Run SuperGlue on a pair of keypoints and descriptors""" desc0, desc1 = data['descriptors0'], data['descriptors1'] kpts0, kpts1 = data['keypoints0'], data['keypoints1'] if kpts0.shape[1] == 0 or kpts1.shape[1] == 0: # no keypoints shape0, shape1 = kpts0.shape[:-1], kpts1.shape[:-1] return { 'matches0': kpts0.new_full(shape0, -1, dtype=torch.int), 'matches1': kpts1.new_full(shape1, -1, dtype=torch.int), 'matching_scores0': kpts0.new_zeros(shape0), 'matching_scores1': kpts1.new_zeros(shape1), } # Keypoint normalization. kpts0 = normalize_keypoints(kpts0, data['image0_shape']) kpts1 = normalize_keypoints(kpts1, data['image1_shape']) # Keypoint MLP encoder. desc0 = desc0 + self.kenc(kpts0, data['scores0']) desc1 = desc1 + self.kenc(kpts1, data['scores1']) del data # Multi-layer Transformer network. desc0, desc1 = self.gnn(desc0, desc1) # Final MLP projection. mdesc0, mdesc1 = self.final_proj(desc0), self.final_proj(desc1) # Compute matching descriptor distance. scores = torch.einsum('bdn,bdm->bnm', mdesc0, mdesc1) scores = scores / self.config['descriptor_dim']**.5 # Run the optimal transport. scores = log_optimal_transport( scores, self.bin_score, iters=self.config['sinkhorn_iterations']) # Get the matches with score above "match_threshold". max0, max1 = scores[:, :-1, :-1].max(2), scores[:, :-1, :-1].max(1) indices0, indices1 = max0.indices, max1.indices mutual0 = arange_like(indices0, 1)[None] == indices1.gather(1, indices0) mutual1 = arange_like(indices1, 1)[None] == indices0.gather(1, indices1) zero = scores.new_tensor(0) mscores0 = torch.where(mutual0, max0.values.exp(), zero) mscores1 = torch.where(mutual1, mscores0.gather(1, indices1), zero) valid0 = mutual0 & (mscores0 > self.config['match_threshold']) valid1 = mutual1 & valid0.gather(1, indices1) indices0 = torch.where(valid0, indices0, indices0.new_tensor(-1)) indices1 = torch.where(valid1, indices1, indices1.new_tensor(-1)) return { 'matches0': indices0, # use -1 for invalid match 'matches1': indices1, # use -1 for invalid match 'matching_scores0': mscores0, 'matching_scores1': mscores1, }