156 lines
7.2 KiB
Python
156 lines
7.2 KiB
Python
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from __future__ import absolute_import
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import numpy as np
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import itertools
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import torch
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import torch.nn as nn
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import torch.nn.functional as F
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def grid_sample(input, grid, canvas = None):
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output = F.grid_sample(input, grid)
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if canvas is None:
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return output
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else:
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input_mask = input.data.new(input.size()).fill_(1)
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output_mask = F.grid_sample(input_mask, grid)
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padded_output = output * output_mask + canvas * (1 - output_mask)
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return padded_output
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# phi(x1, x2) = r^2 * log(r), where r = ||x1 - x2||_2
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def compute_partial_repr(input_points, control_points):
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N = input_points.size(0)
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M = control_points.size(0)
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pairwise_diff = input_points.view(N, 1, 2) - control_points.view(1, M, 2)
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# original implementation, very slow
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# pairwise_dist = torch.sum(pairwise_diff ** 2, dim = 2) # square of distance
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pairwise_diff_square = pairwise_diff * pairwise_diff
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pairwise_dist = pairwise_diff_square[:, :, 0] + pairwise_diff_square[:, :, 1]
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repr_matrix = 0.5 * pairwise_dist * torch.log(pairwise_dist)
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# fix numerical error for 0 * log(0), substitute all nan with 0
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mask = repr_matrix != repr_matrix
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repr_matrix.masked_fill_(mask, 0)
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return repr_matrix
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# # output_ctrl_pts are specified, according to our task.
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# def build_output_control_points(num_control_points, margins):
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# margin_x, margin_y = margins
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# margin_x, margin_y = 0,0
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# num_ctrl_pts_per_side = num_control_points // 2
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# ctrl_pts_x = np.linspace(margin_x, 1.0 - margin_x, num_ctrl_pts_per_side)
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# ctrl_pts_y_top = np.ones(num_ctrl_pts_per_side) * margin_y
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# ctrl_pts_y_bottom = np.ones(num_ctrl_pts_per_side) * (1.0 - margin_y)
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# ctrl_pts_top = np.stack([ctrl_pts_x, ctrl_pts_y_top], axis=1)
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# ctrl_pts_bottom = np.stack([ctrl_pts_x, ctrl_pts_y_bottom], axis=1)
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# # ctrl_pts_top = ctrl_pts_top[1:-1,:]
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# # ctrl_pts_bottom = ctrl_pts_bottom[1:-1,:]
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# output_ctrl_pts_arr = np.concatenate([ctrl_pts_top, ctrl_pts_bottom], axis=0)
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# output_ctrl_pts = torch.Tensor(output_ctrl_pts_arr)
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# return output_ctrl_pts
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# output_ctrl_pts are specified, according to our task.
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def build_output_control_points(num_control_points, margins):
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margin_x, margin_y = margins
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# margin_x, margin_y = 0,0
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num_ctrl_pts_per_side = (num_control_points-4) // 4 +2
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ctrl_pts_x = np.linspace(margin_x, 1.0 - margin_x, num_ctrl_pts_per_side)
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ctrl_pts_y_top = np.ones(num_ctrl_pts_per_side) * margin_y
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ctrl_pts_y_bottom = np.ones(num_ctrl_pts_per_side) * (1.0 - margin_y)
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ctrl_pts_top = np.stack([ctrl_pts_x, ctrl_pts_y_top], axis=1)
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ctrl_pts_bottom = np.stack([ctrl_pts_x, ctrl_pts_y_bottom], axis=1)
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ctrl_pts_x_left = np.ones(num_ctrl_pts_per_side) * margin_x
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ctrl_pts_x_right = np.ones(num_ctrl_pts_per_side) * (1.0-margin_x)
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ctrl_pts_left = np.stack([ctrl_pts_x_left[1:-1], ctrl_pts_x[1:-1]], axis=1)
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ctrl_pts_right = np.stack([ctrl_pts_x_right[1:-1], ctrl_pts_x[1:-1]], axis=1)
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output_ctrl_pts_arr = np.concatenate([ctrl_pts_top, ctrl_pts_bottom, ctrl_pts_left, ctrl_pts_right], axis=0)
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output_ctrl_pts = torch.Tensor(output_ctrl_pts_arr)
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return output_ctrl_pts
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# demo: ~/test/models/test_tps_transformation.py
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class TPSSpatialTransformer(nn.Module):
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def __init__(self, output_image_size=None, num_control_points=None, margins=None):
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super(TPSSpatialTransformer, self).__init__()
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self.output_image_size = output_image_size
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self.num_control_points = num_control_points
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self.margins = margins
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self.target_height, self.target_width = output_image_size
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target_control_points = build_output_control_points(num_control_points, margins)
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N = num_control_points
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# N = N - 4
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# create padded kernel matrix
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forward_kernel = torch.zeros(N + 3, N + 3)
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target_control_partial_repr = compute_partial_repr(target_control_points, target_control_points)
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forward_kernel[:N, :N].copy_(target_control_partial_repr)
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forward_kernel[:N, -3].fill_(1)
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forward_kernel[-3, :N].fill_(1)
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forward_kernel[:N, -2:].copy_(target_control_points)
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forward_kernel[-2:, :N].copy_(target_control_points.transpose(0, 1))
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# compute inverse matrix
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# print(forward_kernel.shape)
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inverse_kernel = torch.inverse(forward_kernel)
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# create target cordinate matrix
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HW = self.target_height * self.target_width
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target_coordinate = list(itertools.product(range(self.target_height), range(self.target_width)))
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target_coordinate = torch.Tensor(target_coordinate) # HW x 2
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Y, X = target_coordinate.split(1, dim = 1)
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Y = Y / (self.target_height - 1)
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X = X / (self.target_width - 1)
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target_coordinate = torch.cat([X, Y], dim = 1) # convert from (y, x) to (x, y)
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target_coordinate_partial_repr = compute_partial_repr(target_coordinate, target_control_points)
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target_coordinate_repr = torch.cat([
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target_coordinate_partial_repr, torch.ones(HW, 1), target_coordinate
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], dim = 1)
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# register precomputed matrices
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self.register_buffer('inverse_kernel', inverse_kernel)
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self.register_buffer('padding_matrix', torch.zeros(3, 2))
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self.register_buffer('target_coordinate_repr', target_coordinate_repr)
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self.register_buffer('target_control_points', target_control_points)
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def forward(self, input, source_control_points,direction='dewarp'):
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if direction == 'dewarp':
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assert source_control_points.ndimension() == 3
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assert source_control_points.size(1) == self.num_control_points
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assert source_control_points.size(2) == 2
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batch_size = source_control_points.size(0)
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Y = torch.cat([source_control_points, self.padding_matrix.expand(batch_size, 3, 2)], 1)
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mapping_matrix = torch.matmul(self.inverse_kernel, Y)
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source_coordinate = torch.matmul(self.target_coordinate_repr, mapping_matrix)
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grid = source_coordinate.view(-1, self.target_height, self.target_width, 2)
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grid = torch.clamp(grid, 0, 1) # the source_control_points may be out of [0, 1].
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# the input to grid_sample is normalized [-1, 1], but what we get is [0, 1]
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grid = 2.0 * grid - 1.0
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output_maps = grid_sample(input, grid, canvas=None)
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return output_maps, source_coordinate
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# elif direction == 'warp':
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# target_control_points = source_control_points.clone()
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# source_control_points = (build_output_control_points(self.num_control_points, self.margins)).clone()
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# source_control_points = source_control_points.unsqueeze(0)
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# source_control_points = source_control_points.expand(target_control_points.size(0),self.num_control_points,2)
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# assert source_control_points.ndimension() == 3
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# assert source_control_points.size(1) == self.num_control_points
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# assert source_control_points.size(2) == 2
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# batch_size = source_control_points.size(0)
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# Y = torch.cat([source_control_points.to('cuda'), self.padding_matrix.expand(batch_size, 3, 2)], 1)
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# mapping_matrix = torch.matmul(self.inverse_kernel, Y)
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# source_coordinate = torch.matmul(self.target_coordinate_repr, mapping_matrix)
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# grid = source_coordinate.view(-1, self.target_height, self.target_width, 2)
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# grid = torch.clamp(grid, 0, 1) # the source_control_points may be out of [0, 1].
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# # the input to grid_sample is normalized [-1, 1], but what we get is [0, 1]
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# grid = 2.0 * grid - 1.0
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# output_maps = grid_sample(input, grid, canvas=None)
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# return output_maps, source_coordinate
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