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"""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
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