init

backend/ppocr/modeling/transforms/__init__.py

@@ -0,0 +1,28 @@
+# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+#
+# 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.
+
+__all__ = ['build_transform']
+
+
+def build_transform(config):
+    from .tps import TPS
+    from .stn import STN_ON
+
+    support_dict = ['TPS', 'STN_ON']
+
+    module_name = config.pop('name')
+    assert module_name in support_dict, Exception(
+        'transform only support {}'.format(support_dict))
+    module_class = eval(module_name)(**config)
+    return module_class

backend/ppocr/modeling/transforms/stn.py

@@ -0,0 +1,135 @@
+# 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/stn_head.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
+
+from .tps_spatial_transformer import TPSSpatialTransformer
+
+
+def conv3x3_block(in_channels, out_channels, stride=1):
+    n = 3 * 3 * out_channels
+    w = math.sqrt(2. / n)
+    conv_layer = nn.Conv2D(
+        in_channels,
+        out_channels,
+        kernel_size=3,
+        stride=stride,
+        padding=1,
+        weight_attr=nn.initializer.Normal(
+            mean=0.0, std=w),
+        bias_attr=nn.initializer.Constant(0))
+    block = nn.Sequential(conv_layer, nn.BatchNorm2D(out_channels), nn.ReLU())
+    return block
+
+
+class STN(nn.Layer):
+    def __init__(self, in_channels, num_ctrlpoints, activation='none'):
+        super(STN, self).__init__()
+        self.in_channels = in_channels
+        self.num_ctrlpoints = num_ctrlpoints
+        self.activation = activation
+        self.stn_convnet = nn.Sequential(
+            conv3x3_block(in_channels, 32),  #32x64
+            nn.MaxPool2D(
+                kernel_size=2, stride=2),
+            conv3x3_block(32, 64),  #16x32
+            nn.MaxPool2D(
+                kernel_size=2, stride=2),
+            conv3x3_block(64, 128),  # 8*16
+            nn.MaxPool2D(
+                kernel_size=2, stride=2),
+            conv3x3_block(128, 256),  # 4*8
+            nn.MaxPool2D(
+                kernel_size=2, stride=2),
+            conv3x3_block(256, 256),  # 2*4,
+            nn.MaxPool2D(
+                kernel_size=2, stride=2),
+            conv3x3_block(256, 256))  # 1*2
+        self.stn_fc1 = nn.Sequential(
+            nn.Linear(
+                2 * 256,
+                512,
+                weight_attr=nn.initializer.Normal(0, 0.001),
+                bias_attr=nn.initializer.Constant(0)),
+            nn.BatchNorm1D(512),
+            nn.ReLU())
+        fc2_bias = self.init_stn()
+        self.stn_fc2 = nn.Linear(
+            512,
+            num_ctrlpoints * 2,
+            weight_attr=nn.initializer.Constant(0.0),
+            bias_attr=nn.initializer.Assign(fc2_bias))
+
+    def init_stn(self):
+        margin = 0.01
+        sampling_num_per_side = int(self.num_ctrlpoints / 2)
+        ctrl_pts_x = np.linspace(margin, 1. - margin, sampling_num_per_side)
+        ctrl_pts_y_top = np.ones(sampling_num_per_side) * margin
+        ctrl_pts_y_bottom = np.ones(sampling_num_per_side) * (1 - margin)
+        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_points = np.concatenate(
+            [ctrl_pts_top, ctrl_pts_bottom], axis=0).astype(np.float32)
+        if self.activation == 'none':
+            pass
+        elif self.activation == 'sigmoid':
+            ctrl_points = -np.log(1. / ctrl_points - 1.)
+        ctrl_points = paddle.to_tensor(ctrl_points)
+        fc2_bias = paddle.reshape(
+            ctrl_points, shape=[ctrl_points.shape[0] * ctrl_points.shape[1]])
+        return fc2_bias
+
+    def forward(self, x):
+        x = self.stn_convnet(x)
+        batch_size, _, h, w = x.shape
+        x = paddle.reshape(x, shape=(batch_size, -1))
+        img_feat = self.stn_fc1(x)
+        x = self.stn_fc2(0.1 * img_feat)
+        if self.activation == 'sigmoid':
+            x = F.sigmoid(x)
+        x = paddle.reshape(x, shape=[-1, self.num_ctrlpoints, 2])
+        return img_feat, x
+
+
+class STN_ON(nn.Layer):
+    def __init__(self, in_channels, tps_inputsize, tps_outputsize,
+                 num_control_points, tps_margins, stn_activation):
+        super(STN_ON, self).__init__()
+        self.tps = TPSSpatialTransformer(
+            output_image_size=tuple(tps_outputsize),
+            num_control_points=num_control_points,
+            margins=tuple(tps_margins))
+        self.stn_head = STN(in_channels=in_channels,
+                            num_ctrlpoints=num_control_points,
+                            activation=stn_activation)
+        self.tps_inputsize = tps_inputsize
+        self.out_channels = in_channels
+
+    def forward(self, image):
+        stn_input = paddle.nn.functional.interpolate(
+            image, self.tps_inputsize, mode="bilinear", align_corners=True)
+        stn_img_feat, ctrl_points = self.stn_head(stn_input)
+        x, _ = self.tps(image, ctrl_points)
+        return x

backend/ppocr/modeling/transforms/tps.py

@@ -0,0 +1,308 @@
+# 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/clovaai/deep-text-recognition-benchmark/blob/master/modules/transformation.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
+
+
+class ConvBNLayer(nn.Layer):
+    def __init__(self,
+                 in_channels,
+                 out_channels,
+                 kernel_size,
+                 stride=1,
+                 groups=1,
+                 act=None,
+                 name=None):
+        super(ConvBNLayer, self).__init__()
+        self.conv = nn.Conv2D(
+            in_channels=in_channels,
+            out_channels=out_channels,
+            kernel_size=kernel_size,
+            stride=stride,
+            padding=(kernel_size - 1) // 2,
+            groups=groups,
+            weight_attr=ParamAttr(name=name + "_weights"),
+            bias_attr=False)
+        bn_name = "bn_" + name
+        self.bn = nn.BatchNorm(
+            out_channels,
+            act=act,
+            param_attr=ParamAttr(name=bn_name + '_scale'),
+            bias_attr=ParamAttr(bn_name + '_offset'),
+            moving_mean_name=bn_name + '_mean',
+            moving_variance_name=bn_name + '_variance')
+
+    def forward(self, x):
+        x = self.conv(x)
+        x = self.bn(x)
+        return x
+
+
+class LocalizationNetwork(nn.Layer):
+    def __init__(self, in_channels, num_fiducial, loc_lr, model_name):
+        super(LocalizationNetwork, self).__init__()
+        self.F = num_fiducial
+        F = num_fiducial
+        if model_name == "large":
+            num_filters_list = [64, 128, 256, 512]
+            fc_dim = 256
+        else:
+            num_filters_list = [16, 32, 64, 128]
+            fc_dim = 64
+
+        self.block_list = []
+        for fno in range(0, len(num_filters_list)):
+            num_filters = num_filters_list[fno]
+            name = "loc_conv%d" % fno
+            conv = self.add_sublayer(
+                name,
+                ConvBNLayer(
+                    in_channels=in_channels,
+                    out_channels=num_filters,
+                    kernel_size=3,
+                    act='relu',
+                    name=name))
+            self.block_list.append(conv)
+            if fno == len(num_filters_list) - 1:
+                pool = nn.AdaptiveAvgPool2D(1)
+            else:
+                pool = nn.MaxPool2D(kernel_size=2, stride=2, padding=0)
+            in_channels = num_filters
+            self.block_list.append(pool)
+        name = "loc_fc1"
+        stdv = 1.0 / math.sqrt(num_filters_list[-1] * 1.0)
+        self.fc1 = nn.Linear(
+            in_channels,
+            fc_dim,
+            weight_attr=ParamAttr(
+                learning_rate=loc_lr,
+                name=name + "_w",
+                initializer=nn.initializer.Uniform(-stdv, stdv)),
+            bias_attr=ParamAttr(name=name + '.b_0'),
+            name=name)
+
+        # Init fc2 in LocalizationNetwork
+        initial_bias = self.get_initial_fiducials()
+        initial_bias = initial_bias.reshape(-1)
+        name = "loc_fc2"
+        param_attr = ParamAttr(
+            learning_rate=loc_lr,
+            initializer=nn.initializer.Assign(np.zeros([fc_dim, F * 2])),
+            name=name + "_w")
+        bias_attr = ParamAttr(
+            learning_rate=loc_lr,
+            initializer=nn.initializer.Assign(initial_bias),
+            name=name + "_b")
+        self.fc2 = nn.Linear(
+            fc_dim,
+            F * 2,
+            weight_attr=param_attr,
+            bias_attr=bias_attr,
+            name=name)
+        self.out_channels = F * 2
+
+    def forward(self, x):
+        """
+           Estimating parameters of geometric transformation
+           Args:
+               image: input
+           Return:
+               batch_C_prime: the matrix of the geometric transformation
+        """
+        B = x.shape[0]
+        i = 0
+        for block in self.block_list:
+            x = block(x)
+        x = x.squeeze(axis=2).squeeze(axis=2)
+        x = self.fc1(x)
+
+        x = F.relu(x)
+        x = self.fc2(x)
+        x = x.reshape(shape=[-1, self.F, 2])
+        return x
+
+    def get_initial_fiducials(self):
+        """ see RARE paper Fig. 6 (a) """
+        F = self.F
+        ctrl_pts_x = np.linspace(-1.0, 1.0, int(F / 2))
+        ctrl_pts_y_top = np.linspace(0.0, -1.0, num=int(F / 2))
+        ctrl_pts_y_bottom = np.linspace(1.0, 0.0, num=int(F / 2))
+        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)
+        initial_bias = np.concatenate([ctrl_pts_top, ctrl_pts_bottom], axis=0)
+        return initial_bias
+
+
+class GridGenerator(nn.Layer):
+    def __init__(self, in_channels, num_fiducial):
+        super(GridGenerator, self).__init__()
+        self.eps = 1e-6
+        self.F = num_fiducial
+
+        name = "ex_fc"
+        initializer = nn.initializer.Constant(value=0.0)
+        param_attr = ParamAttr(
+            learning_rate=0.0, initializer=initializer, name=name + "_w")
+        bias_attr = ParamAttr(
+            learning_rate=0.0, initializer=initializer, name=name + "_b")
+        self.fc = nn.Linear(
+            in_channels,
+            6,
+            weight_attr=param_attr,
+            bias_attr=bias_attr,
+            name=name)
+
+    def forward(self, batch_C_prime, I_r_size):
+        """
+        Generate the grid for the grid_sampler.
+        Args:
+            batch_C_prime: the matrix of the geometric transformation
+            I_r_size: the shape of the input image
+        Return:
+            batch_P_prime: the grid for the grid_sampler
+        """
+        C = self.build_C_paddle()
+        P = self.build_P_paddle(I_r_size)
+
+        inv_delta_C_tensor = self.build_inv_delta_C_paddle(C).astype('float32')
+        P_hat_tensor = self.build_P_hat_paddle(
+            C, paddle.to_tensor(P)).astype('float32')
+
+        inv_delta_C_tensor.stop_gradient = True
+        P_hat_tensor.stop_gradient = True
+
+        batch_C_ex_part_tensor = self.get_expand_tensor(batch_C_prime)
+
+        batch_C_ex_part_tensor.stop_gradient = True
+
+        batch_C_prime_with_zeros = paddle.concat(
+            [batch_C_prime, batch_C_ex_part_tensor], axis=1)
+        batch_T = paddle.matmul(inv_delta_C_tensor, batch_C_prime_with_zeros)
+        batch_P_prime = paddle.matmul(P_hat_tensor, batch_T)
+        return batch_P_prime
+
+    def build_C_paddle(self):
+        """ Return coordinates of fiducial points in I_r; C """
+        F = self.F
+        ctrl_pts_x = paddle.linspace(-1.0, 1.0, int(F / 2), dtype='float64')
+        ctrl_pts_y_top = -1 * paddle.ones([int(F / 2)], dtype='float64')
+        ctrl_pts_y_bottom = paddle.ones([int(F / 2)], dtype='float64')
+        ctrl_pts_top = paddle.stack([ctrl_pts_x, ctrl_pts_y_top], axis=1)
+        ctrl_pts_bottom = paddle.stack([ctrl_pts_x, ctrl_pts_y_bottom], axis=1)
+        C = paddle.concat([ctrl_pts_top, ctrl_pts_bottom], axis=0)
+        return C  # F x 2
+
+    def build_P_paddle(self, I_r_size):
+        I_r_height, I_r_width = I_r_size
+        I_r_grid_x = (paddle.arange(
+            -I_r_width, I_r_width, 2, dtype='float64') + 1.0
+                      ) / paddle.to_tensor(np.array([I_r_width]))
+
+        I_r_grid_y = (paddle.arange(
+            -I_r_height, I_r_height, 2, dtype='float64') + 1.0
+                      ) / paddle.to_tensor(np.array([I_r_height]))
+
+        # P: self.I_r_width x self.I_r_height x 2
+        P = paddle.stack(paddle.meshgrid(I_r_grid_x, I_r_grid_y), axis=2)
+        P = paddle.transpose(P, perm=[1, 0, 2])
+        # n (= self.I_r_width x self.I_r_height) x 2
+        return P.reshape([-1, 2])
+
+    def build_inv_delta_C_paddle(self, C):
+        """ Return inv_delta_C which is needed to calculate T """
+        F = self.F
+        hat_eye = paddle.eye(F, dtype='float64')  # F x F
+        hat_C = paddle.norm(
+            C.reshape([1, F, 2]) - C.reshape([F, 1, 2]), axis=2) + hat_eye
+        hat_C = (hat_C**2) * paddle.log(hat_C)
+        delta_C = paddle.concat(  # F+3 x F+3
+            [
+                paddle.concat(
+                    [paddle.ones(
+                        (F, 1), dtype='float64'), C, hat_C], axis=1),  # F x F+3
+                paddle.concat(
+                    [
+                        paddle.zeros(
+                            (2, 3), dtype='float64'), paddle.transpose(
+                                C, perm=[1, 0])
+                    ],
+                    axis=1),  # 2 x F+3
+                paddle.concat(
+                    [
+                        paddle.zeros(
+                            (1, 3), dtype='float64'), paddle.ones(
+                                (1, F), dtype='float64')
+                    ],
+                    axis=1)  # 1 x F+3
+            ],
+            axis=0)
+        inv_delta_C = paddle.inverse(delta_C)
+        return inv_delta_C  # F+3 x F+3
+
+    def build_P_hat_paddle(self, C, P):
+        F = self.F
+        eps = self.eps
+        n = P.shape[0]  # n (= self.I_r_width x self.I_r_height)
+        # P_tile: n x 2 -> n x 1 x 2 -> n x F x 2
+        P_tile = paddle.tile(paddle.unsqueeze(P, axis=1), (1, F, 1))
+        C_tile = paddle.unsqueeze(C, axis=0)  # 1 x F x 2
+        P_diff = P_tile - C_tile  # n x F x 2
+        # rbf_norm: n x F
+        rbf_norm = paddle.norm(P_diff, p=2, axis=2, keepdim=False)
+
+        # rbf: n x F
+        rbf = paddle.multiply(
+            paddle.square(rbf_norm), paddle.log(rbf_norm + eps))
+        P_hat = paddle.concat(
+            [paddle.ones(
+                (n, 1), dtype='float64'), P, rbf], axis=1)
+        return P_hat  # n x F+3
+
+    def get_expand_tensor(self, batch_C_prime):
+        B, H, C = batch_C_prime.shape
+        batch_C_prime = batch_C_prime.reshape([B, H * C])
+        batch_C_ex_part_tensor = self.fc(batch_C_prime)
+        batch_C_ex_part_tensor = batch_C_ex_part_tensor.reshape([-1, 3, 2])
+        return batch_C_ex_part_tensor
+
+
+class TPS(nn.Layer):
+    def __init__(self, in_channels, num_fiducial, loc_lr, model_name):
+        super(TPS, self).__init__()
+        self.loc_net = LocalizationNetwork(in_channels, num_fiducial, loc_lr,
+                                           model_name)
+        self.grid_generator = GridGenerator(self.loc_net.out_channels,
+                                            num_fiducial)
+        self.out_channels = in_channels
+
+    def forward(self, image):
+        image.stop_gradient = False
+        batch_C_prime = self.loc_net(image)
+        batch_P_prime = self.grid_generator(batch_C_prime, image.shape[2:])
+        batch_P_prime = batch_P_prime.reshape(
+            [-1, image.shape[2], image.shape[3], 2])
+        batch_I_r = F.grid_sample(x=image, grid=batch_P_prime)
+        return batch_I_r

backend/ppocr/modeling/transforms/tps_spatial_transformer.py

@@ -0,0 +1,156 @@
+# 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