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 def build_output_control_points(num_control_points, margins): points = [0.25,0.5,0.75] pts2 = [[0, 0],[1, 0], [0, 1],[1, 1]] # pts22 = [] for ratio in points: pts2.append([1*ratio,0]) for ratio in points: pts2.append([1*ratio,1]) for ratio in points: pts2.append([0,1*ratio]) for ratio in points: pts2.append([1,1*ratio]) pts2 = np.float32(pts2) 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_arr = np.asarray([[0,0],[1,0],[1,1],[0,1], # [],[],[],[], # [],[],[],[], # [],[],[],[]]) output_ctrl_pts_arr = pts2 # print(output_ctrl_pts_arr.shape,'=================') output_ctrl_pts = torch.FloatTensor(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 = grid_sample(input, grid, canvas=None) return output, grid # 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