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import torch
import torch.nn.functional as F
from .geometry import coords_grid, generate_window_grid, normalize_coords
def global_correlation_softmax(feature0, feature1,
pred_bidir_flow=False,
):
# global correlation
b, c, h, w = feature0.shape
feature0 = feature0.view(b, c, -1).permute(0, 2, 1) # [B, H*W, C]
feature1 = feature1.view(b, c, -1) # [B, C, H*W]
correlation = torch.matmul(feature0, feature1).view(b, h, w, h, w) / (c ** 0.5) # [B, H, W, H, W]
# flow from softmax
init_grid = coords_grid(b, h, w).to(correlation.device) # [B, 2, H, W]
grid = init_grid.view(b, 2, -1).permute(0, 2, 1) # [B, H*W, 2]
correlation = correlation.view(b, h * w, h * w) # [B, H*W, H*W]
if pred_bidir_flow:
correlation = torch.cat((correlation, correlation.permute(0, 2, 1)), dim=0) # [2*B, H*W, H*W]
init_grid = init_grid.repeat(2, 1, 1, 1) # [2*B, 2, H, W]
grid = grid.repeat(2, 1, 1) # [2*B, H*W, 2]
b = b * 2
prob = F.softmax(correlation, dim=-1) # [B, H*W, H*W]
correspondence = torch.matmul(prob, grid).view(b, h, w, 2).permute(0, 3, 1, 2) # [B, 2, H, W]
# when predicting bidirectional flow, flow is the concatenation of forward flow and backward flow
flow = correspondence - init_grid
return flow, prob
def local_correlation_softmax(feature0, feature1, local_radius,
padding_mode='zeros',
):
b, c, h, w = feature0.size()
coords_init = coords_grid(b, h, w).to(feature0.device) # [B, 2, H, W]
coords = coords_init.view(b, 2, -1).permute(0, 2, 1) # [B, H*W, 2]
local_h = 2 * local_radius + 1
local_w = 2 * local_radius + 1
window_grid = generate_window_grid(-local_radius, local_radius,
-local_radius, local_radius,
local_h, local_w, device=feature0.device) # [2R+1, 2R+1, 2]
window_grid = window_grid.reshape(-1, 2).repeat(b, 1, 1, 1) # [B, 1, (2R+1)^2, 2]
sample_coords = coords.unsqueeze(-2) + window_grid # [B, H*W, (2R+1)^2, 2]
sample_coords_softmax = sample_coords
# exclude coords that are out of image space
valid_x = (sample_coords[:, :, :, 0] >= 0) & (sample_coords[:, :, :, 0] < w) # [B, H*W, (2R+1)^2]
valid_y = (sample_coords[:, :, :, 1] >= 0) & (sample_coords[:, :, :, 1] < h) # [B, H*W, (2R+1)^2]
valid = valid_x & valid_y # [B, H*W, (2R+1)^2], used to mask out invalid values when softmax
# normalize coordinates to [-1, 1]
sample_coords_norm = normalize_coords(sample_coords, h, w) # [-1, 1]
window_feature = F.grid_sample(feature1, sample_coords_norm,
padding_mode=padding_mode, align_corners=True
).permute(0, 2, 1, 3) # [B, H*W, C, (2R+1)^2]
feature0_view = feature0.permute(0, 2, 3, 1).view(b, h * w, 1, c) # [B, H*W, 1, C]
corr = torch.matmul(feature0_view, window_feature).view(b, h * w, -1) / (c ** 0.5) # [B, H*W, (2R+1)^2]
# mask invalid locations
corr[~valid] = -1e9
prob = F.softmax(corr, -1) # [B, H*W, (2R+1)^2]
correspondence = torch.matmul(prob.unsqueeze(-2), sample_coords_softmax).squeeze(-2).view(
b, h, w, 2).permute(0, 3, 1, 2) # [B, 2, H, W]
flow = correspondence - coords_init
match_prob = prob
return flow, match_prob
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