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