code: def optimize_for_mask(
      geometry_network,
      mask,
      focal,
      principal_point,
      rotation_matrix,
      translation_vector,
      w2v_alpha,
      w2v_beta,
      density=20,
      mirror_weight=1.0,
      near=1.25,
      far=3.5,
      n_samples=128,
      learning_rate_network=0.0001,
      learning_rate_code=0.1,
      n_rays=1024,
      n_iter=100,
      opt_mode="code",
      nearest_train_shape=None,
      ray_sampling_strategy="stratified",
      verbose_steps=10,
  ):
      """Optimize geometry network and/or its latent codes to fit a mask.
  
      Args:
        geometry_network: A keras model for the geometry network.
        mask: A tensor with shape `[1, H, W, 1]`
          where H and W are the height and width of the target mask.
        focal: A tensor with shape `[1, 2]`
        principal_point:  A tensor with shape `[1, 2]`.
        rotation_matrix:  A tensor with shape `[1, 3, 3]`.
        translation_vector: A tensor with shape `[1, 3, 1]`.
        w2v_alpha: A tensor with shape `[1, 3, 1]` containing the
          scaling transformation between world and voxel coordinates.
        w2v_beta: A tensor with shape `[1, 3, 1]` containing the
          translation transformation between world and voxel coordinates.
        density: A scalar weight for rendering the voxel grid.
        mirror_weight: A scalar for the weight for the mirror (symmetry) loss.
        near: A scalar for the lower bound for sampling along a ray.
        far: A scalar for the uper bound for sampling along a ray.
        n_samples: The number of samples along a ray.
        learning_rate_network: The fine-tuning learning rate of the nework.
        learning_rate_code: The fine-tuning learning rate of the latent codes.
        n_rays: The number of random rays to sample per iteration.
        n_iter: The number of iterations for the optimization.
        opt_mode: A string indicating the optimization strategy ('network', 'code').
        nearest_train_shape: Index of the nearest training shape if available.
        ray_sampling_strategy: A string indicating the ray sampling strategy.
        verbose_steps: After how many steps to print the losses.
  
      Returns:
        The optimized latent code for the input mask ().
      """
      height, width = mask.shape[-3], mask.shape[-2]
      # Retrieve the latent code of the nearest shape if available.
      if nearest_train_shape:
          voxel_code_var = tf.gather(
              geometry_network.latent_code_vars, [nearest_train_shape]
          )
      else:
          voxel_code_var = tf.reduce_mean(
              geometry_network.latent_code_vars, axis=0, keepdims=True
          )
      voxel_code_var = tf.Variable(voxel_code_var)
      # Set up the optimizers and variables to be optimized
      optimizer_network = tf.keras.optimizers.Adam(
          learning_rate=learning_rate_network
      )
      optimizer_latent = tf.keras.optimizers.Adam(
          learning_rate=learning_rate_code
      )
      if opt_mode == "all":
          network_vars = geometry_network.model.trainable_variables
      else:
          network_vars = []
  
      # The main optimization function
      @tf.function
      def opt_step(r_org, r_dir, gt_a):
          with tf.GradientTape() as tape:
              # Run the network
              pred_logits_voxels = geometry_network.model(
                  voxel_code_var
              )
              voxels = (
                  tf.sigmoid(pred_logits_voxels)
                  * geometry_network.mask_voxels
              )
              # Sample points along the rays and estimate the voxel values
              ray_points_coarse, _ = ray.sample_1d(
                  r_org,
                  r_dir,
                  near=near,
                  far=far,
                  n_samples=n_samples,
                  strategy=ray_sampling_strategy,
              )
              voxel_values = voxel_functions.ray_sample_voxel_grid(
                  ray_points_coarse, voxels, w2v_alpha, w2v_beta
              )
              # Render the silhouette
              silhouettes, *_ = ray_density.compute_density(
                  voxel_values,
                  density * tf.ones_like(voxel_values[..., 0]),
              )
              silhouette_loss = utils.l2_loss(silhouettes, gt_a)
              mirror_voxel_loss = utils.l2_loss(
                  voxels, tf.reverse(voxels, [1])
              )
              total_loss = (
                  silhouette_loss + mirror_weight * mirror_voxel_loss
              )
          gradients = tape.gradient(
              total_loss, network_vars + [voxel_code_var]
          )
          optimizer_network.apply_gradients(
              zip(gradients[: len(network_vars)], network_vars)
          )
          optimizer_latent.apply_gradients(
              zip(gradients[len(network_vars) :], [voxel_code_var])
          )
          return total_loss, silhouettes
  
      for it in range(n_iter):
          # Sample random rays.
          random_rays, random_pixels_xy = perspective.random_rays(
              focal, principal_point, height, width, n_rays
          )
          # Change the coordinate system from TFG to blender SRN
          random_rays = utils.change_coordinate_system(
              random_rays, (0.0, math.pi, math.pi), (-1.0, 1.0, 1.0)
          )
          rays_org, rays_dir = utils.camera_rays_from_extrinsics(
              random_rays, rotation_matrix, translation_vector
          )
          random_pixels_yx = tf.reverse(random_pixels_xy, axis=[-1])
          random_pixels_yx = tf.cast(random_pixels_yx, tf.int32)
          pixels = tf.gather_nd(mask, random_pixels_yx, batch_dims=1)
  
          loss, _ = opt_step(rays_org, rays_dir, pixels)
          if it % verbose_steps == 0:
              logging.info("Iter %d. loss: %.5f", it, loss)
      return voxel_code_var
  
file_path: graphics/tensorflow_graphics/projects/radiance_fields/sharf/geometry_net/optimization.py
imports: import math
  from absl import logging
  import tensorflow
  import tensorflow_graphics.geometry.representation.ray
  import tensorflow_graphics.projects.radiance_fields.sharf.voxel_functions
  import tensorflow_graphics.projects.radiance_fields.utils
  import tensorflow_graphics.rendering.camera.perspective
  import tensorflow_graphics.rendering.volumetric.ray_density
label_desc: Use image node_id 1 for calling a global function with example usage: optimize_for_mask(geometry_network, mask, focal, principal_point, rotation_matrix, translation_vector, w2v_alpha, w2v_beta, density, mirror_weight, near, far, n_samples, learning_rate_network, learning_rate_code, n_rays, n_iter, opt_mode, nearest_train_shape, ray_sampling_strategy, verbose_steps) and returns: voxel_code_var, total_loss,  silhouettes