Module: Gsplat::Backend::RubyTileCompositorBackward

Defined in:
lib/gsplat/backend/ruby/tile_compositor_backward.rb

Overview

Reverse per-tile compositor with scatter-add into Gaussian gradients.

Class Method Summary collapse

Class Method Details

.backward!(grad_means, grad_conics, grad_colors, grad_opacities, means2d, conics, colors, opacities, flatten_ids, range_start, range_end, pixels_x, pixels_y, render_alphas, last_ids, grad_render_colors, grad_render_alphas, background, grad_means_abs: nil) ⇒ Object

rubocop:disable Metrics/AbcSize, Metrics/BlockLength, Metrics/MethodLength, Metrics/ParameterLists



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# File 'lib/gsplat/backend/ruby/tile_compositor_backward.rb', line 10

def backward!(grad_means, grad_conics, grad_colors, grad_opacities, means2d, conics,
              colors, opacities, flatten_ids, range_start, range_end, pixels_x, pixels_y,
              render_alphas, last_ids, grad_render_colors, grad_render_alphas, background,
              grad_means_abs: nil)
  # rubocop:enable Metrics/ParameterLists
  pixel_count = pixels_x.size
  current_transmittance = 1 - render_alphas
  after_transmittance = means2d.class.ones(pixel_count)
  remaining_color = means2d.class.zeros(pixel_count, colors.shape[-1])
  remaining_color[true, true] = background if background
  (range_start...range_end).reverse_each do |intersection_index|
    gaussian_index = flatten_ids[intersection_index]
    delta_x = means2d[gaussian_index, 0] - pixels_x
    delta_y = means2d[gaussian_index, 1] - pixels_y
    sigma = (0.5 * (
      (conics[gaussian_index, 0] * (delta_x**2)) +
      (conics[gaussian_index, 2] * (delta_y**2))
    )) + (conics[gaussian_index, 1] * delta_x * delta_y)
    gaussian_response = Numo::NMath.exp(-sigma)
    raw_alpha = opacities[gaussian_index] * gaussian_response
    alpha = raw_alpha.dup
    clamped = alpha.gt(RubyAccumulate::ALPHA_CLAMP)
    alpha[clamped] = RubyAccumulate::ALPHA_CLAMP if clamped.any?
    valid = render_alphas.gt(0) & sigma.ge(0) & alpha.ge(RubyAccumulate::ALPHA_SKIP)
    valid &= last_ids.ge(intersection_index)
    valid &= current_transmittance.lt(1)
    valid &= alpha.lt(1)
    next unless valid.any?

    transmittance_before = current_transmittance.dup
    transmittance_before[valid] = current_transmittance[valid] / (1 - alpha[valid])
    visibility = means2d.class.zeros(pixel_count)
    visibility[valid] = (transmittance_before * alpha)[valid]
    color = colors[gaussian_index, true]
    grad_colors[gaussian_index, true] += (
      grad_render_colors * visibility.reshape(pixel_count, 1)
    ).sum(axis: 0)
    color_difference = color.reshape(1, colors.shape[-1]) - remaining_color
    grad_alpha = transmittance_before * (
      (grad_render_colors * color_difference).sum(axis: 1) +
      (grad_render_alphas * after_transmittance)
    )
    unclamped = valid & raw_alpha.lt(RubyAccumulate::ALPHA_CLAMP)
    grad_raw_alpha = means2d.class.zeros(pixel_count)
    grad_raw_alpha[unclamped] = grad_alpha[unclamped] if unclamped.any?
    grad_opacities[gaussian_index] += (grad_raw_alpha * gaussian_response).sum
    grad_sigma = -grad_raw_alpha * raw_alpha
    mean_x = grad_sigma * (
      (conics[gaussian_index, 0] * delta_x) +
      (conics[gaussian_index, 1] * delta_y)
    )
    mean_y = grad_sigma * (
      (conics[gaussian_index, 2] * delta_y) +
      (conics[gaussian_index, 1] * delta_x)
    )
    grad_means[gaussian_index, 0] += mean_x.sum
    grad_means[gaussian_index, 1] += mean_y.sum
    if grad_means_abs
      grad_means_abs[gaussian_index, 0] += mean_x.abs.sum
      grad_means_abs[gaussian_index, 1] += mean_y.abs.sum
    end
    grad_conics[gaussian_index, 0] += (grad_sigma * 0.5 * (delta_x**2)).sum
    grad_conics[gaussian_index, 1] += (grad_sigma * delta_x * delta_y).sum
    grad_conics[gaussian_index, 2] += (grad_sigma * 0.5 * (delta_y**2)).sum
    updated_color = (alpha.reshape(pixel_count, 1) * color.reshape(1, colors.shape[-1])) +
                    ((1 - alpha).reshape(pixel_count, 1) * remaining_color)
    remaining_color[valid, true] = updated_color[valid, true]
    after_transmittance[valid] *= 1 - alpha[valid]
    current_transmittance[valid] = transmittance_before[valid]
  end
end