# python3.8 """Contains the function of ray marching. Ray marching focuses on a single marching ray, which goes through a collection of particles (points). Each point in the 3D space is represented by emitted color and volume density. The final color to appear for each ray can be obtained by accumulating the per-point color regarding the per-point density. Ray marching is an important step for Neural Radiance Field (NeRF). Paper: https://arxiv.org/pdf/2003.08934.pdf """ import torch import torch.nn.functional as F __all__ = ['PointIntegrator'] _DENSITY_CLAMP_MODES = ['relu', 'softplus', 'mipnerf'] _COLOR_CLAMP_MODES = ['none', 'widen_sigmoid'] EPS = 1e-3 class PointIntegrator(torch.nn.Module): """Defines the class to accumulate points along each ray. This class implements the `forward()` function for ray marching, which includes the following steps: 1. Get the color and density of the points for each ray. 2. Get alpha values for alpha compositing. 3. Get accumulated transmittances. 4. Get composite color and density with weighted sum (i.e., integration). More details can be found in Section 4 of paper https://arxiv.org/pdf/2003.08934.pdf """ def __init__(self, use_mid_point=True, use_dist=True, max_radial_dist=1e10, density_noise_std=0.0, density_clamp_mode='relu', color_clamp_mode='none', normalize_color=False, delta_modulate_scalar=1.0, use_white_background=False, scale_color=True, normalize_radial_dist=False, clip_radial_dist=False): """Initializes hyper-parameters for ray marching. Args: use_mid_point: Whether to use the middle point between two adjacent points on each ray for accumulation. Defaults to `True`. use_dist: Whether to consider the distance between two adjacent points on each ray for accumulation. If set as `False`, the distance between two adjacent points is constantly set as `1`. Defaults to `True`. max_radial_dist: The maximum radial distance between a particular point to the camera. This argument is used to prevent the ray from going too far away. Defaults to `1e10`. density_noise_std: Standard deviation of the gaussian noise added to densities. density_clamp_mode: Mode of clamping densities. Defaults to `relu`. color_clamp_mode: Mode of clamping colors. Defaults to `none`. normalize_color: Whether to normalize the output composite color per ray. Defaults to `False`. delta_modulate_scalar: Scalar value to modulate delta of radial distance. use_white_background: Whether to use white background. Defaults to `False`. scale_color: Whether to scale the output composite color to range (-1, 1). Defaults to `True`. normalize_radial_dist: Whether to normalize the output composite radial distance per ray. Defaults to `True`. clip_radial_dist: Whether to clip the output composite radial distance. Defaults to `True`. """ super().__init__() self.use_mid_point = use_mid_point self.use_dist = use_dist self.max_radial_dist = max_radial_dist self.density_noise_std = density_noise_std self.density_clamp_mode = density_clamp_mode self.color_clamp_mode = color_clamp_mode self.normalize_color = normalize_color self.delta_modulate_scalar = delta_modulate_scalar self.use_white_background = use_white_background self.scale_color = scale_color self.normalize_radial_dist = normalize_radial_dist self.clip_radial_dist = clip_radial_dist def forward(self, colors, densities, radii, **kwargs): """Integrates points along each ray. For simplicity, we define the following notations: `N` denotes batch size. `R` denotes the number of rays, which usually equals `H * W`. `K` denotes the number of points on each ray. Args: colors: Per-point emitted color, with shape [N, R, K, C]. Here `C` denotes the number of color channels. Note that, the color can be represented by gray value (`C = 1`), RGB values (`C = 3`), or a feature vector (such as `C = 64`). densities: Per-point volume density, with shape [N, R, K, 1]. Here, the density can be roughly interpreted as how likely a ray will be blocked by this point. radii: Per-point radial distance, with shape [N, R, K, 1]. Here, the distance is measured by treating the camera as the origin. **kwargs: Additional keyword arguments to override the variables initialized in `__init__()`. Returns: A dictionary, containing - `composite_color`: The final per-ray composite color (or color feature), with shape [N, R, C]. - `composite_radial_dist`: The final per-ray composite radial distance, with shape [N, R, 1]. - `weights`: Per-point weight for integral, with shape [N, R, K, 1]. - `T_end`: The accumulated transmittance along the ray from the start point `p_s` to the end point `p_e` in the foreground scene. This can be interpreted as the probability of the ray travelling from `p_s` to `p_e` without hitting any other particles in the foreground scene. This variable is with shape [N, R, 1]. """ # Parse arguments. use_mid_point = kwargs.get('use_mid_point', self.use_mid_point) use_dist = kwargs.get('use_dist', self.use_dist) max_radial_dist = kwargs.get('max_radial_dist', self.max_radial_dist) density_noise_std = kwargs.get('density_noise_std', self.density_noise_std) density_clamp_mode = kwargs.get( 'density_clamp_mode', self.density_clamp_mode) color_clamp_mode = kwargs.get('color_clamp_mode', self.color_clamp_mode) normalize_color = kwargs.get('normalize_color', self.normalize_color) delta_modulate_scalar = kwargs.get( 'delta_modulate_scalar', self.delta_modulate_scalar) use_white_background = kwargs.get( 'use_white_background', self.use_white_background) scale_color = kwargs.get('scale_color', self.scale_color) normalize_radial_dist = kwargs.get( 'normalize_radial_dist', self.normalize_radial_dist) clip_radial_dist = kwargs.get('clip_radial_dist', self.clip_radial_dist) # Check inputs. assert colors.ndim == 4 N, R, K, _ = colors.shape assert densities.shape == (N, R, K, 1) assert radii.shape == (N, R, K, 1) density_clamp_mode = density_clamp_mode.lower() if density_clamp_mode not in _DENSITY_CLAMP_MODES: raise ValueError(f'Invalid clamp mode: `{density_clamp_mode}`!\n' f'Modes allowed: {_DENSITY_CLAMP_MODES}.') color_clamp_mode = color_clamp_mode.lower() if color_clamp_mode not in _COLOR_CLAMP_MODES: raise ValueError(f'Invalid clamp mode: `{color_clamp_mode}`!\n' f'Modes allowed: {_COLOR_CLAMP_MODES}.') # Compute distances between adjacent points on each ray. Such a distance # is termed as `delta` in the paper (Eq. (3)). deltas = radii[:, :, 1:, :] - radii[:, :, :-1, :] # [N, R, K-1, 1] if delta_modulate_scalar != 1: deltas = torch.ones_like(deltas) * delta_modulate_scalar if use_mid_point: # Using K-1 points on each ray. colors = (colors[:, :, :-1, :] + colors[:, :, 1:, :]) / 2 densities = (densities[:, :, :-1, :] + densities[:, :, 1:, :]) / 2 radii = (radii[:, :, :-1, :] + radii[:, :, 1:, :]) / 2 else: # Using K points on each ray. # Append a maximum distance to make sure all points have reference. delta_last = max_radial_dist * torch.ones_like(deltas[:, :, :1, :]) deltas = torch.cat([deltas, delta_last], dim=2) # [N, R, K, 1] ray_dirs = kwargs.get('ray_dirs') if ray_dirs is not None: # [N, R, 3] assert ray_dirs.shape == (N, R, 3) ray_dirs = ray_dirs.unsqueeze(-1) # [N, R, 3, 1] deltas = deltas * torch.norm(ray_dirs, dim=-2, keepdim=True) # [N, R, K, 1] if not use_dist: deltas[:] = 1 if 'bg_index' in kwargs: bg_index = F.one_hot(kwargs['bg_index'].squeeze(-1), num_classes=deltas.shape[-2]).to(torch.bool) bg_index = bg_index.unsqueeze(-1) deltas[bg_index] = max_radial_dist if density_noise_std > 0: densities = densities + density_noise_std * torch.randn_like( densities) if density_clamp_mode == 'relu': densities = F.relu(densities + 3) elif density_clamp_mode == 'softplus': densities = F.softplus(densities) elif density_clamp_mode == 'mipnerf': densities = F.softplus(densities - 1) else: raise ValueError(f'Not implemented clamping mode: ' f'`{density_clamp_mode}`!\n') if color_clamp_mode == 'widen_sigmoid': colors = torch.sigmoid(colors) * (1 + 2 * EPS) - EPS # Compute per-point alpha values. See Eq. (3) in the paper. alphas = 1 - torch.exp(- deltas * densities) if not use_mid_point and max_radial_dist > 0: alphas[:, :, -1, :] = 1 if 'is_valid' in kwargs: alphas = alphas * kwargs['is_valid'] # Compute per-point accumulated transmittance. See Eq. (3) in the paper. # Here, we shift `alpha` forward by one index, because the transmittance # of each point is only related to its previous points, excluding # itself. alphas_shifted = torch.cat( [torch.ones_like(alphas[:, :, :1, :]), 1 - alphas + 1e-10], dim=2) T = torch.cumprod(alphas_shifted, dim=2)[:, :, :-1, :] # Transmittance. # Compute per-point integral weights. weights = alphas * T weights_sum = weights.sum(dim=2) # Get per-ray color. composite_color = torch.sum(weights * colors, dim=2) if normalize_color: composite_color = composite_color / weights_sum if use_white_background: composite_color = composite_color + 1 - weights_sum if scale_color: composite_color = composite_color * 2 - 1 # Get per-ray radial distance. composite_radial_dist = torch.sum(weights * radii, dim=2) if normalize_radial_dist: composite_radial_dist = composite_radial_dist / weights_sum if clip_radial_dist: composite_radial_dist = torch.nan_to_num( composite_radial_dist, float('inf')) composite_radial_dist = torch.clip( composite_radial_dist, torch.min(radii), torch.max(radii)) results = { 'composite_color': composite_color, 'composite_radial_dist': composite_radial_dist, 'weight': weights, 'T_end': T[:, :, -1, :], 'opacity': weights_sum, } return results