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feature_extraction

import torch.nn as nn
import torch.nn.functional as F


class VGG_FeatureExtractor(nn.Module):
    """ FeatureExtractor of CRNN (https://arxiv.org/pdf/1507.05717.pdf) """

    def __init__(self, input_channel, output_channel=512):
        super(VGG_FeatureExtractor, self).__init__()
        self.output_channel = [int(output_channel / 8), int(output_channel / 4),
                               int(output_channel / 2), output_channel]  # [64, 128, 256, 512]
        self.ConvNet = nn.Sequential(
            nn.Conv2d(input_channel, self.output_channel[0], 3, 1, 1), nn.ReLU(True),
            nn.MaxPool2d(2, 2),  # 64x16x50
            nn.Conv2d(self.output_channel[0], self.output_channel[1], 3, 1, 1), nn.ReLU(True),
            nn.MaxPool2d(2, 2),  # 128x8x25
            nn.Conv2d(self.output_channel[1], self.output_channel[2], 3, 1, 1), nn.ReLU(True),  # 256x8x25
            nn.Conv2d(self.output_channel[2], self.output_channel[2], 3, 1, 1), nn.ReLU(True),
            nn.MaxPool2d((2, 1), (2, 1)),  # 256x4x25
            nn.Conv2d(self.output_channel[2], self.output_channel[3], 3, 1, 1, bias=False),
            nn.BatchNorm2d(self.output_channel[3]), nn.ReLU(True),  # 512x4x25
            nn.Conv2d(self.output_channel[3], self.output_channel[3], 3, 1, 1, bias=False),
            nn.BatchNorm2d(self.output_channel[3]), nn.ReLU(True),
            nn.MaxPool2d((2, 1), (2, 1)),  # 512x2x25
            nn.Conv2d(self.output_channel[3], self.output_channel[3], 2, 1, 0), nn.ReLU(True))  # 512x1x24

    def forward(self, input):
        return self.ConvNet(input)


class RCNN_FeatureExtractor(nn.Module):
    """ FeatureExtractor of GRCNN (https://papers.nips.cc/paper/6637-gated-recurrent-convolution-neural-network-for-ocr.pdf) """

    def __init__(self, input_channel, output_channel=512):
        super(RCNN_FeatureExtractor, self).__init__()
        self.output_channel = [int(output_channel / 8), int(output_channel / 4),
                               int(output_channel / 2), output_channel]  # [64, 128, 256, 512]
        self.ConvNet = nn.Sequential(
            nn.Conv2d(input_channel, self.output_channel[0], 3, 1, 1), nn.ReLU(True),
            nn.MaxPool2d(2, 2),  # 64 x 16 x 50
            GRCL(self.output_channel[0], self.output_channel[0], num_iteration=5, kernel_size=3, pad=1),
            nn.MaxPool2d(2, 2),  # 64 x 8 x 25
            GRCL(self.output_channel[0], self.output_channel[1], num_iteration=5, kernel_size=3, pad=1),
            nn.MaxPool2d(2, (2, 1), (0, 1)),  # 128 x 4 x 26
            GRCL(self.output_channel[1], self.output_channel[2], num_iteration=5, kernel_size=3, pad=1),
            nn.MaxPool2d(2, (2, 1), (0, 1)),  # 256 x 2 x 27
            nn.Conv2d(self.output_channel[2], self.output_channel[3], 2, 1, 0, bias=False),
            nn.BatchNorm2d(self.output_channel[3]), nn.ReLU(True))  # 512 x 1 x 26

    def forward(self, input):
        return self.ConvNet(input)


class ResNet_FeatureExtractor(nn.Module):
    """ FeatureExtractor of FAN (http://openaccess.thecvf.com/content_ICCV_2017/papers/Cheng_Focusing_Attention_Towards_ICCV_2017_paper.pdf) """

    def __init__(self, input_channel, output_channel=512):
        super(ResNet_FeatureExtractor, self).__init__()
        self.ConvNet = ResNet(input_channel, output_channel, BasicBlock, [1, 2, 5, 3])

    def forward(self, input):
        return self.ConvNet(input)


# For Gated RCNN
class GRCL(nn.Module):

    def __init__(self, input_channel, output_channel, num_iteration, kernel_size, pad):
        super(GRCL, self).__init__()
        self.wgf_u = nn.Conv2d(input_channel, output_channel, 1, 1, 0, bias=False)
        self.wgr_x = nn.Conv2d(output_channel, output_channel, 1, 1, 0, bias=False)
        self.wf_u = nn.Conv2d(input_channel, output_channel, kernel_size, 1, pad, bias=False)
        self.wr_x = nn.Conv2d(output_channel, output_channel, kernel_size, 1, pad, bias=False)

        self.BN_x_init = nn.BatchNorm2d(output_channel)

        self.num_iteration = num_iteration
        self.GRCL = [GRCL_unit(output_channel) for _ in range(num_iteration)]
        self.GRCL = nn.Sequential(*self.GRCL)

    def forward(self, input):
        """ The input of GRCL is consistant over time t, which is denoted by u(0)
        thus wgf_u / wf_u is also consistant over time t.
        """
        wgf_u = self.wgf_u(input)
        wf_u = self.wf_u(input)
        x = F.relu(self.BN_x_init(wf_u))

        for i in range(self.num_iteration):
            x = self.GRCL[i](wgf_u, self.wgr_x(x), wf_u, self.wr_x(x))

        return x


class GRCL_unit(nn.Module):

    def __init__(self, output_channel):
        super(GRCL_unit, self).__init__()
        self.BN_gfu = nn.BatchNorm2d(output_channel)
        self.BN_grx = nn.BatchNorm2d(output_channel)
        self.BN_fu = nn.BatchNorm2d(output_channel)
        self.BN_rx = nn.BatchNorm2d(output_channel)
        self.BN_Gx = nn.BatchNorm2d(output_channel)

    def forward(self, wgf_u, wgr_x, wf_u, wr_x):
        G_first_term = self.BN_gfu(wgf_u)
        G_second_term = self.BN_grx(wgr_x)
        G = F.sigmoid(G_first_term + G_second_term)

        x_first_term = self.BN_fu(wf_u)
        x_second_term = self.BN_Gx(self.BN_rx(wr_x) * G)
        x = F.relu(x_first_term + x_second_term)

        return x


class BasicBlock(nn.Module):
    expansion = 1

    def __init__(self, inplanes, planes, stride=1, downsample=None):
        super(BasicBlock, self).__init__()
        self.conv1 = self._conv3x3(inplanes, planes)
        self.bn1 = nn.BatchNorm2d(planes)
        self.conv2 = self._conv3x3(planes, planes)
        self.bn2 = nn.BatchNorm2d(planes)
        self.relu = nn.ReLU(inplace=True)
        self.downsample = downsample
        self.stride = stride

    def _conv3x3(self, in_planes, out_planes, stride=1):
        "3x3 convolution with padding"
        return nn.Conv2d(in_planes, out_planes, kernel_size=3, stride=stride,
                         padding=1, bias=False)

    def forward(self, x):
        residual = x

        out = self.conv1(x)
        out = self.bn1(out)
        out = self.relu(out)

        out = self.conv2(out)
        out = self.bn2(out)

        if self.downsample is not None:
            residual = self.downsample(x)
        out += residual
        out = self.relu(out)

        return out


class ResNet(nn.Module):

    def __init__(self, input_channel, output_channel, block, layers):
        super(ResNet, self).__init__()

        self.output_channel_block = [int(output_channel / 4), int(output_channel / 2), output_channel, output_channel]

        self.inplanes = int(output_channel / 8)
        self.conv0_1 = nn.Conv2d(input_channel, int(output_channel / 16),
                                 kernel_size=3, stride=1, padding=1, bias=False)
        self.bn0_1 = nn.BatchNorm2d(int(output_channel / 16))
        self.conv0_2 = nn.Conv2d(int(output_channel / 16), self.inplanes,
                                 kernel_size=3, stride=1, padding=1, bias=False)
        self.bn0_2 = nn.BatchNorm2d(self.inplanes)
        self.relu = nn.ReLU(inplace=True)

        self.maxpool1 = nn.MaxPool2d(kernel_size=2, stride=2, padding=0)
        self.layer1 = self._make_layer(block, self.output_channel_block[0], layers[0])
        self.conv1 = nn.Conv2d(self.output_channel_block[0], self.output_channel_block[
                               0], kernel_size=3, stride=1, padding=1, bias=False)
        self.bn1 = nn.BatchNorm2d(self.output_channel_block[0])

        self.maxpool2 = nn.MaxPool2d(kernel_size=2, stride=2, padding=0)
        self.layer2 = self._make_layer(block, self.output_channel_block[1], layers[1], stride=1)
        self.conv2 = nn.Conv2d(self.output_channel_block[1], self.output_channel_block[
                               1], kernel_size=3, stride=1, padding=1, bias=False)
        self.bn2 = nn.BatchNorm2d(self.output_channel_block[1])

        self.maxpool3 = nn.MaxPool2d(kernel_size=2, stride=(2, 1), padding=(0, 1))
        self.layer3 = self._make_layer(block, self.output_channel_block[2], layers[2], stride=1)
        self.conv3 = nn.Conv2d(self.output_channel_block[2], self.output_channel_block[
                               2], kernel_size=3, stride=1, padding=1, bias=False)
        self.bn3 = nn.BatchNorm2d(self.output_channel_block[2])

        self.layer4 = self._make_layer(block, self.output_channel_block[3], layers[3], stride=1)
        self.conv4_1 = nn.Conv2d(self.output_channel_block[3], self.output_channel_block[
                                 3], kernel_size=2, stride=(2, 1), padding=(0, 1), bias=False)
        self.bn4_1 = nn.BatchNorm2d(self.output_channel_block[3])
        self.conv4_2 = nn.Conv2d(self.output_channel_block[3], self.output_channel_block[
                                 3], kernel_size=2, stride=1, padding=0, bias=False)
        self.bn4_2 = nn.BatchNorm2d(self.output_channel_block[3])

    def _make_layer(self, block, planes, blocks, stride=1):
        downsample = None
        if stride != 1 or self.inplanes != planes * block.expansion:
            downsample = nn.Sequential(
                nn.Conv2d(self.inplanes, planes * block.expansion,
                          kernel_size=1, stride=stride, bias=False),
                nn.BatchNorm2d(planes * block.expansion),
            )

        layers = []
        layers.append(block(self.inplanes, planes, stride, downsample))
        self.inplanes = planes * block.expansion
        for i in range(1, blocks):
            layers.append(block(self.inplanes, planes))

        return nn.Sequential(*layers)

    def forward(self, x):
        x = self.conv0_1(x)
        x = self.bn0_1(x)
        x = self.relu(x)
        x = self.conv0_2(x)
        x = self.bn0_2(x)
        x = self.relu(x)

        x = self.maxpool1(x)
        x = self.layer1(x)
        x = self.conv1(x)
        x = self.bn1(x)
        x = self.relu(x)

        x = self.maxpool2(x)
        x = self.layer2(x)
        x = self.conv2(x)
        x = self.bn2(x)
        x = self.relu(x)

        x = self.maxpool3(x)
        x = self.layer3(x)
        x = self.conv3(x)
        x = self.bn3(x)
        x = self.relu(x)

        x = self.layer4(x)
        x = self.conv4_1(x)
        x = self.bn4_1(x)
        x = self.relu(x)
        x = self.conv4_2(x)
        x = self.bn4_2(x)
        x = self.relu(x)

        return x
        
        
prediction

import torch
import torch.nn as nn
import torch.nn.functional as F
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')


class Attention(nn.Module):

    def __init__(self, input_size, hidden_size, num_classes):
        super(Attention, self).__init__()
        self.attention_cell = AttentionCell(input_size, hidden_size, num_classes)
        self.hidden_size = hidden_size
        self.num_classes = num_classes
        self.generator = nn.Linear(hidden_size, num_classes)

    def _char_to_onehot(self, input_char, onehot_dim=38):
        input_char = input_char.unsqueeze(1)
        batch_size = input_char.size(0)
        one_hot = torch.FloatTensor(batch_size, onehot_dim).zero_().to(device)
        one_hot = one_hot.scatter_(1, input_char, 1)
        return one_hot

    def forward(self, batch_H, text, is_train=True, batch_max_length=25):
        """
        input:
            batch_H : contextual_feature H = hidden state of encoder. [batch_size x num_steps x num_classes]
            text : the text-index of each image. [batch_size x (max_length+1)]. +1 for [GO] token. text[:, 0] = [GO].
        output: probability distribution at each step [batch_size x num_steps x num_classes]
        """
        batch_size = batch_H.size(0)
        num_steps = batch_max_length + 1  # +1 for [s] at end of sentence.

        output_hiddens = torch.FloatTensor(batch_size, num_steps, self.hidden_size).fill_(0).to(device)
        hidden = (torch.FloatTensor(batch_size, self.hidden_size).fill_(0).to(device),
                  torch.FloatTensor(batch_size, self.hidden_size).fill_(0).to(device))

        if is_train:
            for i in range(num_steps):
                # one-hot vectors for a i-th char. in a batch
                char_onehots = self._char_to_onehot(text[:, i], onehot_dim=self.num_classes)
                # hidden : decoder's hidden s_{t-1}, batch_H : encoder's hidden H, char_onehots : one-hot(y_{t-1})
                hidden, alpha = self.attention_cell(hidden, batch_H, char_onehots)
                output_hiddens[:, i, :] = hidden[0]  # LSTM hidden index (0: hidden, 1: Cell)
            probs = self.generator(output_hiddens)

        else:
            targets = torch.LongTensor(batch_size).fill_(0).to(device)  # [GO] token
            probs = torch.FloatTensor(batch_size, num_steps, self.num_classes).fill_(0).to(device)

            for i in range(num_steps):
                char_onehots = self._char_to_onehot(targets, onehot_dim=self.num_classes)
                hidden, alpha = self.attention_cell(hidden, batch_H, char_onehots)
                probs_step = self.generator(hidden[0])
                probs[:, i, :] = probs_step
                _, next_input = probs_step.max(1)
                targets = next_input

        return probs  # batch_size x num_steps x num_classes


class AttentionCell(nn.Module):

    def __init__(self, input_size, hidden_size, num_embeddings):
        super(AttentionCell, self).__init__()
        self.i2h = nn.Linear(input_size, hidden_size, bias=False)
        self.h2h = nn.Linear(hidden_size, hidden_size)  # either i2i or h2h should have bias
        self.score = nn.Linear(hidden_size, 1, bias=False)
        self.rnn = nn.LSTMCell(input_size + num_embeddings, hidden_size)
        self.hidden_size = hidden_size

    def forward(self, prev_hidden, batch_H, char_onehots):
        # [batch_size x num_encoder_step x num_channel] -> [batch_size x num_encoder_step x hidden_size]
        batch_H_proj = self.i2h(batch_H)
        prev_hidden_proj = self.h2h(prev_hidden[0]).unsqueeze(1)
        e = self.score(torch.tanh(batch_H_proj + prev_hidden_proj))  # batch_size x num_encoder_step * 1

        alpha = F.softmax(e, dim=1)
        context = torch.bmm(alpha.permute(0, 2, 1), batch_H).squeeze(1)  # batch_size x num_channel
        concat_context = torch.cat([context, char_onehots], 1)  # batch_size x (num_channel + num_embedding)
        cur_hidden = self.rnn(concat_context, prev_hidden)
        return cur_hidden, alpha



sequence_modeling

import torch.nn as nn


class BidirectionalLSTM(nn.Module):

    def __init__(self, input_size, hidden_size, output_size):
        super(BidirectionalLSTM, self).__init__()
        self.rnn = nn.LSTM(input_size, hidden_size, bidirectional=True, batch_first=True)
        self.linear = nn.Linear(hidden_size * 2, output_size)

    def forward(self, input):
        """
        input : visual feature [batch_size x T x input_size]
        output : contextual feature [batch_size x T x output_size]
        """
        try:
            self.rnn.flatten_parameters()
        except:
            pass
        recurrent, _ = self.rnn(input)  # batch_size x T x input_size -> batch_size x T x (2*hidden_size)
        output = self.linear(recurrent)  # batch_size x T x output_size
        return output


transformation

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')


class TPS_SpatialTransformerNetwork(nn.Module):
    """ Rectification Network of RARE, namely TPS based STN """

    def __init__(self, F, I_size, I_r_size, I_channel_num=1):
        """ Based on RARE TPS
        input:
            batch_I: Batch Input Image [batch_size x I_channel_num x I_height x I_width]
            I_size : (height, width) of the input image I
            I_r_size : (height, width) of the rectified image I_r
            I_channel_num : the number of channels of the input image I
        output:
            batch_I_r: rectified image [batch_size x I_channel_num x I_r_height x I_r_width]
        """
        super(TPS_SpatialTransformerNetwork, self).__init__()
        self.F = F
        self.I_size = I_size
        self.I_r_size = I_r_size  # = (I_r_height, I_r_width)
        self.I_channel_num = I_channel_num
        self.LocalizationNetwork = LocalizationNetwork(self.F, self.I_channel_num)
        self.GridGenerator = GridGenerator(self.F, self.I_r_size)

    def forward(self, batch_I):
        batch_C_prime = self.LocalizationNetwork(batch_I)  # batch_size x K x 2
        build_P_prime = self.GridGenerator.build_P_prime(batch_C_prime)  # batch_size x n (= I_r_width x I_r_height) x 2
        build_P_prime_reshape = build_P_prime.reshape([build_P_prime.size(0), self.I_r_size[0], self.I_r_size[1], 2])
        batch_I_r = F.grid_sample(batch_I, build_P_prime_reshape, padding_mode='border')

        return batch_I_r


class LocalizationNetwork(nn.Module):
    """ Localization Network of RARE, which predicts C' (K x 2) from I (I_width x I_height) """

    def __init__(self, F, I_channel_num):
        super(LocalizationNetwork, self).__init__()
        self.F = F
        self.I_channel_num = I_channel_num
        self.conv = nn.Sequential(
            nn.Conv2d(in_channels=self.I_channel_num, out_channels=64, kernel_size=3, stride=1, padding=1,
                      bias=False), nn.BatchNorm2d(64), nn.ReLU(True),
            nn.MaxPool2d(2, 2),  # batch_size x 64 x I_height/2 x I_width/2
            nn.Conv2d(64, 128, 3, 1, 1, bias=False), nn.BatchNorm2d(128), nn.ReLU(True),
            nn.MaxPool2d(2, 2),  # batch_size x 128 x I_height/4 x I_width/4
            nn.Conv2d(128, 256, 3, 1, 1, bias=False), nn.BatchNorm2d(256), nn.ReLU(True),
            nn.MaxPool2d(2, 2),  # batch_size x 256 x I_height/8 x I_width/8
            nn.Conv2d(256, 512, 3, 1, 1, bias=False), nn.BatchNorm2d(512), nn.ReLU(True),
            nn.AdaptiveAvgPool2d(1)  # batch_size x 512
        )

        self.localization_fc1 = nn.Sequential(nn.Linear(512, 256), nn.ReLU(True))
        self.localization_fc2 = nn.Linear(256, self.F * 2)

        # Init fc2 in LocalizationNetwork
        self.localization_fc2.weight.data.fill_(0)
        """ see RARE paper Fig. 6 (a) """
        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)
        self.localization_fc2.bias.data = torch.from_numpy(initial_bias).float().view(-1)

    def forward(self, batch_I):
        """
        input:     batch_I : Batch Input Image [batch_size x I_channel_num x I_height x I_width]
        output:    batch_C_prime : Predicted coordinates of fiducial points for input batch [batch_size x F x 2]
        """
        batch_size = batch_I.size(0)
        features = self.conv(batch_I).view(batch_size, -1)
        batch_C_prime = self.localization_fc2(self.localization_fc1(features)).view(batch_size, self.F, 2)
        return batch_C_prime


class GridGenerator(nn.Module):
    """ Grid Generator of RARE, which produces P_prime by multiplying T with P """

    def __init__(self, F, I_r_size):
        """ Generate P_hat and inv_delta_C for later """
        super(GridGenerator, self).__init__()
        self.eps = 1e-6
        self.I_r_height, self.I_r_width = I_r_size
        self.F = F
        self.C = self._build_C(self.F)  # F x 2
        self.P = self._build_P(self.I_r_width, self.I_r_height)
        ## for multi-gpu, you need register buffer
        self.register_buffer("inv_delta_C", torch.tensor(self._build_inv_delta_C(self.F, self.C)).float())  # F+3 x F+3
        self.register_buffer("P_hat", torch.tensor(self._build_P_hat(self.F, self.C, self.P)).float())  # n x F+3
        ## for fine-tuning with different image width, you may use below instead of self.register_buffer
        #self.inv_delta_C = torch.tensor(self._build_inv_delta_C(self.F, self.C)).float().cuda()  # F+3 x F+3
        #self.P_hat = torch.tensor(self._build_P_hat(self.F, self.C, self.P)).float().cuda()  # n x F+3

    def _build_C(self, F):
        """ Return coordinates of fiducial points in I_r; C """
        ctrl_pts_x = np.linspace(-1.0, 1.0, int(F / 2))
        ctrl_pts_y_top = -1 * np.ones(int(F / 2))
        ctrl_pts_y_bottom = np.ones(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)
        C = np.concatenate([ctrl_pts_top, ctrl_pts_bottom], axis=0)
        return C  # F x 2

    def _build_inv_delta_C(self, F, C):
        """ Return inv_delta_C which is needed to calculate T """
        hat_C = np.zeros((F, F), dtype=float)  # F x F
        for i in range(0, F):
            for j in range(i, F):
                r = np.linalg.norm(C[i] - C[j])
                hat_C[i, j] = r
                hat_C[j, i] = r
        np.fill_diagonal(hat_C, 1)
        hat_C = (hat_C ** 2) * np.log(hat_C)
        # print(C.shape, hat_C.shape)
        delta_C = np.concatenate(  # F+3 x F+3
            [
                np.concatenate([np.ones((F, 1)), C, hat_C], axis=1),  # F x F+3
                np.concatenate([np.zeros((2, 3)), np.transpose(C)], axis=1),  # 2 x F+3
                np.concatenate([np.zeros((1, 3)), np.ones((1, F))], axis=1)  # 1 x F+3
            ],
            axis=0
        )
        inv_delta_C = np.linalg.inv(delta_C)
        return inv_delta_C  # F+3 x F+3

    def _build_P(self, I_r_width, I_r_height):
        I_r_grid_x = (np.arange(-I_r_width, I_r_width, 2) + 1.0) / I_r_width  # self.I_r_width
        I_r_grid_y = (np.arange(-I_r_height, I_r_height, 2) + 1.0) / I_r_height  # self.I_r_height
        P = np.stack(  # self.I_r_width x self.I_r_height x 2
            np.meshgrid(I_r_grid_x, I_r_grid_y),
            axis=2
        )
        return P.reshape([-1, 2])  # n (= self.I_r_width x self.I_r_height) x 2

    def _build_P_hat(self, F, C, P):
        n = P.shape[0]  # n (= self.I_r_width x self.I_r_height)
        P_tile = np.tile(np.expand_dims(P, axis=1), (1, F, 1))  # n x 2 -> n x 1 x 2 -> n x F x 2
        C_tile = np.expand_dims(C, axis=0)  # 1 x F x 2
        P_diff = P_tile - C_tile  # n x F x 2
        rbf_norm = np.linalg.norm(P_diff, ord=2, axis=2, keepdims=False)  # n x F
        rbf = np.multiply(np.square(rbf_norm), np.log(rbf_norm + self.eps))  # n x F
        P_hat = np.concatenate([np.ones((n, 1)), P, rbf], axis=1)
        return P_hat  # n x F+3

    def build_P_prime(self, batch_C_prime):
        """ Generate Grid from batch_C_prime [batch_size x F x 2] """
        batch_size = batch_C_prime.size(0)
        batch_inv_delta_C = self.inv_delta_C.repeat(batch_size, 1, 1)
        batch_P_hat = self.P_hat.repeat(batch_size, 1, 1)
        batch_C_prime_with_zeros = torch.cat((batch_C_prime, torch.zeros(
            batch_size, 3, 2).float().to(device)), dim=1)  # batch_size x F+3 x 2
        batch_T = torch.bmm(batch_inv_delta_C, batch_C_prime_with_zeros)  # batch_size x F+3 x 2
        batch_P_prime = torch.bmm(batch_P_hat, batch_T)  # batch_size x n x 2
        return batch_P_prime  # batch_size x n x 2

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