# copyright (c) 2020 PaddlePaddle Authors. All Rights Reserve. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from __future__ import absolute_import from __future__ import division from __future__ import print_function import math import paddle from paddle import nn, ParamAttr from paddle.nn import functional as F import numpy as np import itertools def grid_sample(input, grid, canvas=None): input.stop_gradient = False output = F.grid_sample(input, grid) if canvas is None: return output else: input_mask = paddle.ones(shape=input.shape) 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.shape[0] M = control_points.shape[0] pairwise_diff = paddle.reshape( input_points, shape=[N, 1, 2]) - paddle.reshape( control_points, shape=[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 * paddle.log(pairwise_dist) # fix numerical error for 0 * log(0), substitute all nan with 0 mask = repr_matrix != repr_matrix repr_matrix[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 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) output_ctrl_pts_arr = np.concatenate( [ctrl_pts_top, ctrl_pts_bottom], axis=0) output_ctrl_pts = paddle.to_tensor(output_ctrl_pts_arr) return output_ctrl_pts class TPSSpatialTransformer(nn.Layer): 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 # create padded kernel matrix forward_kernel = paddle.zeros(shape=[N + 3, N + 3]) target_control_partial_repr = compute_partial_repr( target_control_points, target_control_points) target_control_partial_repr = paddle.cast(target_control_partial_repr, forward_kernel.dtype) forward_kernel[:N, :N] = target_control_partial_repr forward_kernel[:N, -3] = 1 forward_kernel[-3, :N] = 1 target_control_points = paddle.cast(target_control_points, forward_kernel.dtype) forward_kernel[:N, -2:] = target_control_points forward_kernel[-2:, :N] = paddle.transpose( target_control_points, perm=[1, 0]) # compute inverse matrix inverse_kernel = paddle.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 = paddle.to_tensor(target_coordinate) # HW x 2 Y, X = paddle.split( target_coordinate, target_coordinate.shape[1], axis=1) Y = Y / (self.target_height - 1) X = X / (self.target_width - 1) target_coordinate = paddle.concat( [X, Y], axis=1) # convert from (y, x) to (x, y) target_coordinate_partial_repr = compute_partial_repr( target_coordinate, target_control_points) target_coordinate_repr = paddle.concat( [ target_coordinate_partial_repr, paddle.ones(shape=[HW, 1]), target_coordinate ], axis=1) # register precomputed matrices self.inverse_kernel = inverse_kernel self.padding_matrix = paddle.zeros(shape=[3, 2]) self.target_coordinate_repr = target_coordinate_repr self.target_control_points = target_control_points def forward(self, input, source_control_points): assert source_control_points.ndimension() == 3 assert source_control_points.shape[1] == self.num_control_points assert source_control_points.shape[2] == 2 batch_size = paddle.shape(source_control_points)[0] self.padding_matrix = paddle.expand( self.padding_matrix, shape=[batch_size, 3, 2]) Y = paddle.concat([source_control_points, self.padding_matrix], 1) mapping_matrix = paddle.matmul(self.inverse_kernel, Y) source_coordinate = paddle.matmul(self.target_coordinate_repr, mapping_matrix) grid = paddle.reshape( source_coordinate, shape=[-1, self.target_height, self.target_width, 2]) grid = paddle.clip(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