text: from torch import nn
  import torch.nn.functional as F
  import torch
  from modules.util import Hourglass, AntiAliasInterpolation2d, make_coordinate_grid, kp2gaussian
  
  
  class DenseMotionNetwork(nn.Module):
      """
      Module that predicting a dense motion from sparse motion representation given by kp_source and kp_driving
      """
  
      def __init__(self, block_expansion, num_blocks, max_features, num_kp, num_channels, estimate_occlusion_map=False,
                   scale_factor=1, kp_variance=0.01):
          super(DenseMotionNetwork, self).__init__()
          self.hourglass = Hourglass(block_expansion=block_expansion, in_features=(num_kp + 1) * (num_channels + 1),
                                     max_features=max_features, num_blocks=num_blocks)
  
          self.mask = nn.Conv2d(self.hourglass.out_filters, num_kp + 1, kernel_size=(7, 7), padding=(3, 3))
  
          if estimate_occlusion_map:
              self.occlusion = nn.Conv2d(self.hourglass.out_filters, 1, kernel_size=(7, 7), padding=(3, 3))
          else:
              self.occlusion = None
  
          self.num_kp = num_kp
          self.scale_factor = scale_factor
          self.kp_variance = kp_variance
  
          if self.scale_factor != 1:
              self.down = AntiAliasInterpolation2d(num_channels, self.scale_factor)
  
      def create_heatmap_representations(self, source_image, kp_driving, kp_source):
          """
          Eq 6. in the paper H_k(z)
          """
          spatial_size = source_image.shape[2:]
          gaussian_driving = kp2gaussian(kp_driving, spatial_size=spatial_size, kp_variance=self.kp_variance)
          gaussian_source = kp2gaussian(kp_source, spatial_size=spatial_size, kp_variance=self.kp_variance)
          heatmap = gaussian_driving - gaussian_source
  
          #adding background feature
          zeros = torch.zeros(heatmap.shape[0], 1, spatial_size[0], spatial_size[1]).type(heatmap.type())
          heatmap = torch.cat([zeros, heatmap], dim=1)
          heatmap = heatmap.unsqueeze(2)
          return heatmap
  
      def create_sparse_motions(self, source_image, kp_driving, kp_source):
          """
          Eq 4. in the paper T_{s<-d}(z)
          """
          bs, _, h, w = source_image.shape
          identity_grid = make_coordinate_grid((h, w), type=kp_source['value'].type())
          identity_grid = identity_grid.view(1, 1, h, w, 2)
          coordinate_grid = identity_grid - kp_driving['value'].view(bs, self.num_kp, 1, 1, 2)
          if 'jacobian' in kp_driving:
              jacobian = torch.matmul(kp_source['jacobian'], torch.inverse(kp_driving['jacobian']))
              jacobian = jacobian.unsqueeze(-3).unsqueeze(-3)
              jacobian = jacobian.repeat(1, 1, h, w, 1, 1)
              coordinate_grid = torch.matmul(jacobian, coordinate_grid.unsqueeze(-1))
              coordinate_grid = coordinate_grid.squeeze(-1)
  
          driving_to_source = coordinate_grid + kp_source['value'].view(bs, self.num_kp, 1, 1, 2)
  
          #adding background feature
          identity_grid = identity_grid.repeat(bs, 1, 1, 1, 1)
          sparse_motions = torch.cat([identity_grid, driving_to_source], dim=1)
          return sparse_motions
  
      def create_deformed_source_image(self, source_image, sparse_motions):
          """
          Eq 7. in the paper \hat{T}_{s<-d}(z)
          """
          bs, _, h, w = source_image.shape
          source_repeat = source_image.unsqueeze(1).unsqueeze(1).repeat(1, self.num_kp + 1, 1, 1, 1, 1)
          source_repeat = source_repeat.view(bs * (self.num_kp + 1), -1, h, w)
          sparse_motions = sparse_motions.view((bs * (self.num_kp + 1), h, w, -1))
          sparse_deformed = F.grid_sample(source_repeat, sparse_motions)
          sparse_deformed = sparse_deformed.view((bs, self.num_kp + 1, -1, h, w))
          return sparse_deformed
  
      def forward(self, source_image, kp_driving, kp_source):
          if self.scale_factor != 1:
              source_image = self.down(source_image)
  
          bs, _, h, w = source_image.shape
  
          out_dict = dict()
          heatmap_representation = self.create_heatmap_representations(source_image, kp_driving, kp_source)
          sparse_motion = self.create_sparse_motions(source_image, kp_driving, kp_source)
          deformed_source = self.create_deformed_source_image(source_image, sparse_motion)
          out_dict['sparse_deformed'] = deformed_source
  
          input = torch.cat([heatmap_representation, deformed_source], dim=2)
          input = input.view(bs, -1, h, w)
  
          prediction = self.hourglass(input)
  
          mask = self.mask(prediction)
          mask = F.softmax(mask, dim=1)
          out_dict['mask'] = mask
          mask = mask.unsqueeze(2)
          sparse_motion = sparse_motion.permute(0, 1, 4, 2, 3)
          deformation = (sparse_motion * mask).sum(dim=1)
          deformation = deformation.permute(0, 2, 3, 1)
  
          out_dict['deformation'] = deformation
  
          # Sec. 3.2 in the paper
          if self.occlusion:
              occlusion_map = torch.sigmoid(self.occlusion(prediction))
              out_dict['occlusion_map'] = occlusion_map
  
          return out_dict
  