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# Originating Authors: Paul-Edouard Sarlin
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from copy import deepcopy
from pathlib import Path
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
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)
assert self.config['weights'] in ['indoor', 'outdoor']
path = Path(__file__).parent
path = path / 'weights/superglue_{}.pth'.format(self.config['weights'])
self.load_state_dict(torch.load(str(path)))
print('Loaded SuperGlue model (\"{}\" weights)'.format(
self.config['weights']))
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'])
# 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,
}