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# 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.
"""
This code is refer from:
https://github.com/ayumiymk/aster.pytorch/blob/master/lib/models/tps_spatial_transformer.py
"""
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 = np.array(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]
padding_matrix = paddle.expand(
self.padding_matrix, shape=[batch_size, 3, 2])
Y = paddle.concat([source_control_points, 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 |