# Source code for pytorch3d.renderer.implicit.raymarching

```
# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.
# pyre-unsafe
import warnings
from typing import Optional, Tuple, Union
import torch
[docs]
class EmissionAbsorptionRaymarcher(torch.nn.Module):
"""
Raymarch using the Emission-Absorption (EA) algorithm.
The algorithm independently renders each ray by analyzing density and
feature values sampled at (typically uniformly) spaced 3D locations along
each ray. The density values `rays_densities` are of shape
`(..., n_points_per_ray)`, their values should range between [0, 1], and
represent the opaqueness of each point (the higher the less transparent).
The feature values `rays_features` of shape
`(..., n_points_per_ray, feature_dim)` represent the content of the
point that is supposed to be rendered in case the given point is opaque
(i.e. its density -> 1.0).
EA first utilizes `rays_densities` to compute the absorption function
along each ray as follows::
absorption = cumprod(1 - rays_densities, dim=-1)
The value of absorption at position `absorption[..., k]` specifies
how much light has reached `k`-th point along a ray since starting
its trajectory at `k=0`-th point.
Each ray is then rendered into a tensor `features` of shape `(..., feature_dim)`
by taking a weighed combination of per-ray features `rays_features` as follows::
weights = absorption * rays_densities
features = (rays_features * weights).sum(dim=-2)
Where `weights` denote a function that has a strong peak around the location
of the first surface point that a given ray passes through.
Note that for a perfectly bounded volume (with a strictly binary density),
the `weights = cumprod(1 - rays_densities, dim=-1) * rays_densities`
function would yield 0 everywhere. In order to prevent this,
the result of the cumulative product is shifted `self.surface_thickness`
elements along the ray direction.
"""
[docs]
def __init__(self, surface_thickness: int = 1) -> None:
"""
Args:
surface_thickness: Denotes the overlap between the absorption
function and the density function.
"""
super().__init__()
self.surface_thickness = surface_thickness
[docs]
def forward(
self,
rays_densities: torch.Tensor,
rays_features: torch.Tensor,
eps: float = 1e-10,
**kwargs,
) -> torch.Tensor:
"""
Args:
rays_densities: Per-ray density values represented with a tensor
of shape `(..., n_points_per_ray, 1)` whose values range in [0, 1].
rays_features: Per-ray feature values represented with a tensor
of shape `(..., n_points_per_ray, feature_dim)`.
eps: A lower bound added to `rays_densities` before computing
the absorption function (cumprod of `1-rays_densities` along
each ray). This prevents the cumprod to yield exact 0
which would inhibit any gradient-based learning.
Returns:
features_opacities: A tensor of shape `(..., feature_dim+1)`
that concatenates two tensors along the last dimension:
1) features: A tensor of per-ray renders
of shape `(..., feature_dim)`.
2) opacities: A tensor of per-ray opacity values
of shape `(..., 1)`. Its values range between [0, 1] and
denote the total amount of light that has been absorbed
for each ray. E.g. a value of 0 corresponds to the ray
completely passing through a volume. Please refer to the
`AbsorptionOnlyRaymarcher` documentation for the
explanation of the algorithm that computes `opacities`.
"""
_check_raymarcher_inputs(
rays_densities,
rays_features,
None,
z_can_be_none=True,
features_can_be_none=False,
density_1d=True,
)
_check_density_bounds(rays_densities)
rays_densities = rays_densities[..., 0]
absorption = _shifted_cumprod(
(1.0 + eps) - rays_densities, shift=self.surface_thickness
)
weights = rays_densities * absorption
features = (weights[..., None] * rays_features).sum(dim=-2)
opacities = 1.0 - torch.prod(1.0 - rays_densities, dim=-1, keepdim=True)
return torch.cat((features, opacities), dim=-1)
[docs]
class AbsorptionOnlyRaymarcher(torch.nn.Module):
"""
Raymarch using the Absorption-Only (AO) algorithm.
The algorithm independently renders each ray by analyzing density and
feature values sampled at (typically uniformly) spaced 3D locations along
each ray. The density values `rays_densities` are of shape
`(..., n_points_per_ray, 1)`, their values should range between [0, 1], and
represent the opaqueness of each point (the higher the less transparent).
The algorithm only measures the total amount of light absorbed along each ray
and, besides outputting per-ray `opacity` values of shape `(...,)`,
does not produce any feature renderings.
The algorithm simply computes `total_transmission = prod(1 - rays_densities)`
of shape `(..., 1)` which, for each ray, measures the total amount of light
that passed through the volume.
It then returns `opacities = 1 - total_transmission`.
"""
def __init__(self) -> None:
super().__init__()
[docs]
def forward(
self, rays_densities: torch.Tensor, **kwargs
) -> Union[None, torch.Tensor]:
"""
Args:
rays_densities: Per-ray density values represented with a tensor
of shape `(..., n_points_per_ray)` whose values range in [0, 1].
Returns:
opacities: A tensor of per-ray opacity values of shape `(..., 1)`.
Its values range between [0, 1] and denote the total amount
of light that has been absorbed for each ray. E.g. a value
of 0 corresponds to the ray completely passing through a volume.
"""
_check_raymarcher_inputs(
rays_densities,
None,
None,
features_can_be_none=True,
z_can_be_none=True,
density_1d=True,
)
rays_densities = rays_densities[..., 0]
_check_density_bounds(rays_densities)
total_transmission = torch.prod(1 - rays_densities, dim=-1, keepdim=True)
opacities = 1.0 - total_transmission
return opacities
def _shifted_cumprod(x, shift: int = 1):
"""
Computes `torch.cumprod(x, dim=-1)` and prepends `shift` number of
ones and removes `shift` trailing elements to/from the last dimension
of the result.
"""
x_cumprod = torch.cumprod(x, dim=-1)
x_cumprod_shift = torch.cat(
[torch.ones_like(x_cumprod[..., :shift]), x_cumprod[..., :-shift]], dim=-1
)
return x_cumprod_shift
def _check_density_bounds(
rays_densities: torch.Tensor, bounds: Tuple[float, float] = (0.0, 1.0)
) -> None:
"""
Checks whether the elements of `rays_densities` range within `bounds`.
If not issues a warning.
"""
with torch.no_grad():
if (rays_densities.max() > bounds[1]) or (rays_densities.min() < bounds[0]):
warnings.warn(
"One or more elements of rays_densities are outside of valid"
+ f"range {str(bounds)}"
)
def _check_raymarcher_inputs(
rays_densities: torch.Tensor,
rays_features: Optional[torch.Tensor],
rays_z: Optional[torch.Tensor],
features_can_be_none: bool = False,
z_can_be_none: bool = False,
density_1d: bool = True,
) -> None:
"""
Checks the validity of the inputs to raymarching algorithms.
"""
if not torch.is_tensor(rays_densities):
raise ValueError("rays_densities has to be an instance of torch.Tensor.")
if not z_can_be_none and not torch.is_tensor(rays_z):
raise ValueError("rays_z has to be an instance of torch.Tensor.")
if not features_can_be_none and not torch.is_tensor(rays_features):
raise ValueError("rays_features has to be an instance of torch.Tensor.")
if rays_densities.ndim < 1:
raise ValueError("rays_densities have to have at least one dimension.")
if density_1d and rays_densities.shape[-1] != 1:
raise ValueError(
"The size of the last dimension of rays_densities has to be one."
+ f" Got shape {rays_densities.shape}."
)
rays_shape = rays_densities.shape[:-1]
# pyre-fixme[16]: `Optional` has no attribute `shape`.
if not z_can_be_none and rays_z.shape != rays_shape:
raise ValueError("rays_z have to be of the same shape as rays_densities.")
if not features_can_be_none and rays_features.shape[:-1] != rays_shape:
raise ValueError(
"The first to previous to last dimensions of rays_features"
" have to be the same as all dimensions of rays_densities."
)
```