# Copyright 2022 the Regents of the University of California, Nerfstudio Team and contributors. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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"""
Encoding functions
"""
import itertools
from abc import abstractmethod
from typing import Literal, Optional, Sequence
import numpy as np
import torch
import torch.nn.functional as F
from jaxtyping import Float, Int, Shaped
from torch import Tensor, nn
from nerfstudio.field_components.base_field_component import FieldComponent
from nerfstudio.utils.external import TCNN_EXISTS, tcnn
from nerfstudio.utils.math import components_from_spherical_harmonics, expected_sin, generate_polyhedron_basis
from nerfstudio.utils.printing import print_tcnn_speed_warning
[docs]class Encoding(FieldComponent):
"""Encode an input tensor. Intended to be subclassed
Args:
in_dim: Input dimension of tensor
"""
def __init__(self, in_dim: int) -> None:
if in_dim <= 0:
raise ValueError("Input dimension should be greater than zero")
super().__init__(in_dim=in_dim)
[docs] @classmethod
def get_tcnn_encoding_config(cls) -> dict:
"""Get the encoding configuration for tcnn if implemented"""
raise NotImplementedError("Encoding does not have a TCNN implementation")
[docs] @abstractmethod
def forward(self, in_tensor: Shaped[Tensor, "*bs input_dim"]) -> Shaped[Tensor, "*bs output_dim"]:
"""Call forward and returns and processed tensor
Args:
in_tensor: the input tensor to process
"""
raise NotImplementedError
[docs]class Identity(Encoding):
"""Identity encoding (Does not modify input)"""
[docs] def get_out_dim(self) -> int:
if self.in_dim is None:
raise ValueError("Input dimension has not been set")
return self.in_dim
[docs] def forward(self, in_tensor: Shaped[Tensor, "*bs input_dim"]) -> Shaped[Tensor, "*bs output_dim"]:
return in_tensor
[docs]class ScalingAndOffset(Encoding):
"""Simple scaling and offset to input
Args:
in_dim: Input dimension of tensor
scaling: Scaling applied to tensor.
offset: Offset applied to tensor.
"""
def __init__(self, in_dim: int, scaling: float = 1.0, offset: float = 0.0) -> None:
super().__init__(in_dim)
self.scaling = scaling
self.offset = offset
[docs] def get_out_dim(self) -> int:
if self.in_dim is None:
raise ValueError("Input dimension has not been set")
return self.in_dim
[docs] def forward(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
return self.scaling * in_tensor + self.offset
[docs]class NeRFEncoding(Encoding):
"""Multi-scale sinusoidal encodings. Support ``integrated positional encodings`` if covariances are provided.
Each axis is encoded with frequencies ranging from 2^min_freq_exp to 2^max_freq_exp.
Args:
in_dim: Input dimension of tensor
num_frequencies: Number of encoded frequencies per axis
min_freq_exp: Minimum frequency exponent
max_freq_exp: Maximum frequency exponent
include_input: Append the input coordinate to the encoding
"""
def __init__(
self,
in_dim: int,
num_frequencies: int,
min_freq_exp: float,
max_freq_exp: float,
include_input: bool = False,
implementation: Literal["tcnn", "torch"] = "torch",
) -> None:
super().__init__(in_dim)
self.num_frequencies = num_frequencies
self.min_freq = min_freq_exp
self.max_freq = max_freq_exp
self.include_input = include_input
self.tcnn_encoding = None
if implementation == "tcnn" and not TCNN_EXISTS:
print_tcnn_speed_warning("NeRFEncoding")
elif implementation == "tcnn":
assert min_freq_exp == 0, "tcnn only supports min_freq_exp = 0"
assert max_freq_exp == num_frequencies - 1, "tcnn only supports max_freq_exp = num_frequencies - 1"
encoding_config = self.get_tcnn_encoding_config(num_frequencies=self.num_frequencies)
self.tcnn_encoding = tcnn.Encoding(
n_input_dims=in_dim,
encoding_config=encoding_config,
)
[docs] @classmethod
def get_tcnn_encoding_config(cls, num_frequencies) -> dict:
"""Get the encoding configuration for tcnn if implemented"""
encoding_config = {"otype": "Frequency", "n_frequencies": num_frequencies}
return encoding_config
[docs] def get_out_dim(self) -> int:
if self.in_dim is None:
raise ValueError("Input dimension has not been set")
out_dim = self.in_dim * self.num_frequencies * 2
if self.include_input:
out_dim += self.in_dim
return out_dim
[docs] def pytorch_fwd(
self,
in_tensor: Float[Tensor, "*bs input_dim"],
covs: Optional[Float[Tensor, "*bs input_dim input_dim"]] = None,
) -> Float[Tensor, "*bs output_dim"]:
"""Calculates NeRF encoding. If covariances are provided the encodings will be integrated as proposed
in mip-NeRF.
Args:
in_tensor: For best performance, the input tensor should be between 0 and 1.
covs: Covariances of input points.
Returns:
Output values will be between -1 and 1
"""
scaled_in_tensor = 2 * torch.pi * in_tensor # scale to [0, 2pi]
freqs = 2 ** torch.linspace(self.min_freq, self.max_freq, self.num_frequencies, device=in_tensor.device)
scaled_inputs = scaled_in_tensor[..., None] * freqs # [..., "input_dim", "num_scales"]
scaled_inputs = scaled_inputs.view(*scaled_inputs.shape[:-2], -1) # [..., "input_dim" * "num_scales"]
if covs is None:
encoded_inputs = torch.sin(torch.cat([scaled_inputs, scaled_inputs + torch.pi / 2.0], dim=-1))
else:
input_var = torch.diagonal(covs, dim1=-2, dim2=-1)[..., :, None] * freqs[None, :] ** 2
input_var = input_var.reshape((*input_var.shape[:-2], -1))
encoded_inputs = expected_sin(
torch.cat([scaled_inputs, scaled_inputs + torch.pi / 2.0], dim=-1), torch.cat(2 * [input_var], dim=-1)
)
return encoded_inputs
[docs] def forward(
self, in_tensor: Float[Tensor, "*bs input_dim"], covs: Optional[Float[Tensor, "*bs input_dim input_dim"]] = None
) -> Float[Tensor, "*bs output_dim"]:
if self.tcnn_encoding is not None:
encoded_inputs = self.tcnn_encoding(in_tensor)
else:
encoded_inputs = self.pytorch_fwd(in_tensor, covs)
if self.include_input:
encoded_inputs = torch.cat([encoded_inputs, in_tensor], dim=-1)
return encoded_inputs
[docs]class FFEncoding(Encoding):
"""Fourier Feature encoding. Supports integrated encodings.
Args:
in_dim: Input dimension of tensor
basis: Basis matrix from which to construct the Fourier features.
num_frequencies: Number of encoded frequencies per axis
min_freq_exp: Minimum frequency exponent
max_freq_exp: Maximum frequency exponent
include_input: Append the input coordinate to the encoding
"""
def __init__(
self,
in_dim: int,
basis: Float[Tensor, "M N"],
num_frequencies: int,
min_freq_exp: float,
max_freq_exp: float,
include_input: bool = False,
) -> None:
super().__init__(in_dim)
self.num_frequencies = num_frequencies
self.min_freq = min_freq_exp
self.max_freq = max_freq_exp
self.register_buffer(name="b_matrix", tensor=basis)
self.include_input = include_input
[docs] def get_out_dim(self) -> int:
if self.in_dim is None:
raise ValueError("Input dimension has not been set")
assert isinstance(self.b_matrix, Tensor)
out_dim = self.b_matrix.shape[1] * self.num_frequencies * 2
if self.include_input:
out_dim += self.in_dim
return out_dim
[docs] def forward(
self,
in_tensor: Float[Tensor, "*bs input_dim"],
covs: Optional[Float[Tensor, "*bs input_dim input_dim"]] = None,
) -> Float[Tensor, "*bs output_dim"]:
"""Calculates FF encoding. If covariances are provided the encodings will be integrated as proposed
in mip-NeRF.
Args:
in_tensor: For best performance, the input tensor should be between 0 and 1.
covs: Covariances of input points.
Returns:
Output values will be between -1 and 1
"""
scaled_in_tensor = 2 * torch.pi * in_tensor # scale to [0, 2pi]
scaled_inputs = scaled_in_tensor @ self.b_matrix # [..., "num_frequencies"]
freqs = 2 ** torch.linspace(self.min_freq, self.max_freq, self.num_frequencies, device=in_tensor.device)
scaled_inputs = scaled_inputs[..., None] * freqs # [..., "input_dim", "num_scales"]
scaled_inputs = scaled_inputs.view(*scaled_inputs.shape[:-2], -1) # [..., "input_dim" * "num_scales"]
if covs is None:
encoded_inputs = torch.sin(torch.cat([scaled_inputs, scaled_inputs + torch.pi / 2.0], dim=-1))
else:
input_var = torch.sum((covs @ self.b_matrix) * self.b_matrix, -2)
input_var = input_var[..., :, None] * freqs[None, :] ** 2
input_var = input_var.reshape((*input_var.shape[:-2], -1))
encoded_inputs = expected_sin(
torch.cat([scaled_inputs, scaled_inputs + torch.pi / 2.0], dim=-1), torch.cat(2 * [input_var], dim=-1)
)
if self.include_input:
encoded_inputs = torch.cat([encoded_inputs, in_tensor], dim=-1)
return encoded_inputs
[docs]class RFFEncoding(FFEncoding):
"""Random Fourier Feature encoding. Supports integrated encodings.
Args:
in_dim: Input dimension of tensor
num_frequencies: Number of encoding frequencies
scale: Std of Gaussian to sample frequencies. Must be greater than zero
include_input: Append the input coordinate to the encoding
"""
def __init__(self, in_dim: int, num_frequencies: int, scale: float, include_input: bool = False) -> None:
if not scale > 0:
raise ValueError("RFF encoding scale should be greater than zero")
b_matrix = torch.normal(mean=0, std=scale, size=(in_dim, num_frequencies))
super().__init__(in_dim, b_matrix, 1, 0.0, 0.0, include_input)
[docs]class PolyhedronFFEncoding(FFEncoding):
"""Fourier Feature encoding using polyhedron basis as proposed by mip-NeRF360. Supports integrated encodings.
Args:
num_frequencies: Number of encoded frequencies per axis
min_freq_exp: Minimum frequency exponent
max_freq_exp: Maximum frequency exponent
basis_shape: Shape of polyhedron basis. Either "octahedron" or "icosahedron"
basis_subdivisions: Number of times to tesselate the polyhedron.
include_input: Append the input coordinate to the encoding
"""
def __init__(
self,
num_frequencies: int,
min_freq_exp: float,
max_freq_exp: float,
basis_shape: Literal["octahedron", "icosahedron"] = "octahedron",
basis_subdivisions: int = 1,
include_input: bool = False,
) -> None:
basis_t = generate_polyhedron_basis(basis_shape, basis_subdivisions).T
super().__init__(3, basis_t, num_frequencies, min_freq_exp, max_freq_exp, include_input)
[docs]class HashEncoding(Encoding):
"""Hash encoding
Args:
num_levels: Number of feature grids.
min_res: Resolution of smallest feature grid.
max_res: Resolution of largest feature grid.
log2_hashmap_size: Size of hash map is 2^log2_hashmap_size.
features_per_level: Number of features per level.
hash_init_scale: Value to initialize hash grid.
implementation: Implementation of hash encoding. Fallback to torch if tcnn not available.
interpolation: Interpolation override for tcnn hashgrid. Not supported for torch unless linear.
"""
def __init__(
self,
num_levels: int = 16,
min_res: int = 16,
max_res: int = 1024,
log2_hashmap_size: int = 19,
features_per_level: int = 2,
hash_init_scale: float = 0.001,
implementation: Literal["tcnn", "torch"] = "tcnn",
interpolation: Optional[Literal["Nearest", "Linear", "Smoothstep"]] = None,
) -> None:
super().__init__(in_dim=3)
self.num_levels = num_levels
self.min_res = min_res
self.features_per_level = features_per_level
self.hash_init_scale = hash_init_scale
self.log2_hashmap_size = log2_hashmap_size
self.hash_table_size = 2**log2_hashmap_size
levels = torch.arange(num_levels)
self.growth_factor = np.exp((np.log(max_res) - np.log(min_res)) / (num_levels - 1)) if num_levels > 1 else 1
self.scalings = torch.floor(min_res * self.growth_factor**levels)
self.hash_offset = levels * self.hash_table_size
self.tcnn_encoding = None
self.hash_table = torch.empty(0)
if implementation == "torch":
self.build_nn_modules()
elif implementation == "tcnn" and not TCNN_EXISTS:
print_tcnn_speed_warning("HashEncoding")
self.build_nn_modules()
elif implementation == "tcnn":
encoding_config = self.get_tcnn_encoding_config(
num_levels=self.num_levels,
features_per_level=self.features_per_level,
log2_hashmap_size=self.log2_hashmap_size,
min_res=self.min_res,
growth_factor=self.growth_factor,
interpolation=interpolation,
)
self.tcnn_encoding = tcnn.Encoding(
n_input_dims=3,
encoding_config=encoding_config,
)
if self.tcnn_encoding is None:
assert (
interpolation is None or interpolation == "Linear"
), f"interpolation '{interpolation}' is not supported for torch encoding backend"
[docs] def build_nn_modules(self) -> None:
"""Initialize the torch version of the hash encoding."""
self.hash_table = torch.rand(size=(self.hash_table_size * self.num_levels, self.features_per_level)) * 2 - 1
self.hash_table *= self.hash_init_scale
self.hash_table = nn.Parameter(self.hash_table)
[docs] @classmethod
def get_tcnn_encoding_config(
cls, num_levels, features_per_level, log2_hashmap_size, min_res, growth_factor, interpolation=None
) -> dict:
"""Get the encoding configuration for tcnn if implemented"""
encoding_config = {
"otype": "HashGrid",
"n_levels": num_levels,
"n_features_per_level": features_per_level,
"log2_hashmap_size": log2_hashmap_size,
"base_resolution": min_res,
"per_level_scale": growth_factor,
}
if interpolation is not None:
encoding_config["interpolation"] = interpolation
return encoding_config
[docs] def get_out_dim(self) -> int:
return self.num_levels * self.features_per_level
[docs] def hash_fn(self, in_tensor: Int[Tensor, "*bs num_levels 3"]) -> Shaped[Tensor, "*bs num_levels"]:
"""Returns hash tensor using method described in Instant-NGP
Args:
in_tensor: Tensor to be hashed
"""
# min_val = torch.min(in_tensor)
# max_val = torch.max(in_tensor)
# assert min_val >= 0.0
# assert max_val <= 1.0
in_tensor = in_tensor * torch.tensor([1, 2654435761, 805459861]).to(in_tensor.device)
x = torch.bitwise_xor(in_tensor[..., 0], in_tensor[..., 1])
x = torch.bitwise_xor(x, in_tensor[..., 2])
x %= self.hash_table_size
x += self.hash_offset.to(x.device)
return x
[docs] def pytorch_fwd(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
"""Forward pass using pytorch. Significantly slower than TCNN implementation."""
assert in_tensor.shape[-1] == 3
in_tensor = in_tensor[..., None, :] # [..., 1, 3]
scaled = in_tensor * self.scalings.view(-1, 1).to(in_tensor.device) # [..., L, 3]
scaled_c = torch.ceil(scaled).type(torch.int32)
scaled_f = torch.floor(scaled).type(torch.int32)
offset = scaled - scaled_f
hashed_0 = self.hash_fn(scaled_c) # [..., num_levels]
hashed_1 = self.hash_fn(torch.cat([scaled_c[..., 0:1], scaled_f[..., 1:2], scaled_c[..., 2:3]], dim=-1))
hashed_2 = self.hash_fn(torch.cat([scaled_f[..., 0:1], scaled_f[..., 1:2], scaled_c[..., 2:3]], dim=-1))
hashed_3 = self.hash_fn(torch.cat([scaled_f[..., 0:1], scaled_c[..., 1:2], scaled_c[..., 2:3]], dim=-1))
hashed_4 = self.hash_fn(torch.cat([scaled_c[..., 0:1], scaled_c[..., 1:2], scaled_f[..., 2:3]], dim=-1))
hashed_5 = self.hash_fn(torch.cat([scaled_c[..., 0:1], scaled_f[..., 1:2], scaled_f[..., 2:3]], dim=-1))
hashed_6 = self.hash_fn(scaled_f)
hashed_7 = self.hash_fn(torch.cat([scaled_f[..., 0:1], scaled_c[..., 1:2], scaled_f[..., 2:3]], dim=-1))
f_0 = self.hash_table[hashed_0] # [..., num_levels, features_per_level]
f_1 = self.hash_table[hashed_1]
f_2 = self.hash_table[hashed_2]
f_3 = self.hash_table[hashed_3]
f_4 = self.hash_table[hashed_4]
f_5 = self.hash_table[hashed_5]
f_6 = self.hash_table[hashed_6]
f_7 = self.hash_table[hashed_7]
f_03 = f_0 * offset[..., 0:1] + f_3 * (1 - offset[..., 0:1])
f_12 = f_1 * offset[..., 0:1] + f_2 * (1 - offset[..., 0:1])
f_56 = f_5 * offset[..., 0:1] + f_6 * (1 - offset[..., 0:1])
f_47 = f_4 * offset[..., 0:1] + f_7 * (1 - offset[..., 0:1])
f0312 = f_03 * offset[..., 1:2] + f_12 * (1 - offset[..., 1:2])
f4756 = f_47 * offset[..., 1:2] + f_56 * (1 - offset[..., 1:2])
encoded_value = f0312 * offset[..., 2:3] + f4756 * (
1 - offset[..., 2:3]
) # [..., num_levels, features_per_level]
return torch.flatten(encoded_value, start_dim=-2, end_dim=-1) # [..., num_levels * features_per_level]
[docs] def forward(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
if self.tcnn_encoding is not None:
return self.tcnn_encoding(in_tensor)
return self.pytorch_fwd(in_tensor)
[docs]class TensorCPEncoding(Encoding):
"""Learned CANDECOMP/PARFAC (CP) decomposition encoding used in TensoRF
Args:
resolution: Resolution of grid.
num_components: Number of components per dimension.
init_scale: Initialization scale.
"""
def __init__(self, resolution: int = 256, num_components: int = 24, init_scale: float = 0.1) -> None:
super().__init__(in_dim=3)
self.resolution = resolution
self.num_components = num_components
# TODO Learning rates should be different for these
self.line_coef = nn.Parameter(init_scale * torch.randn((3, num_components, resolution, 1)))
[docs] def get_out_dim(self) -> int:
return self.num_components
[docs] def forward(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
line_coord = torch.stack([in_tensor[..., 2], in_tensor[..., 1], in_tensor[..., 0]]) # [3, ...]
line_coord = torch.stack([torch.zeros_like(line_coord), line_coord], dim=-1) # [3, ...., 2]
# Stop gradients from going to sampler
line_coord = line_coord.view(3, -1, 1, 2).detach()
line_features = F.grid_sample(self.line_coef, line_coord, align_corners=True) # [3, Components, -1, 1]
features = torch.prod(line_features, dim=0)
features = torch.moveaxis(features.view(self.num_components, *in_tensor.shape[:-1]), 0, -1)
return features # [..., Components]
[docs] @torch.no_grad()
def upsample_grid(self, resolution: int) -> None:
"""Upsamples underyling feature grid
Args:
resolution: Target resolution.
"""
line_coef = F.interpolate(self.line_coef.data, size=(resolution, 1), mode="bilinear", align_corners=True)
self.line_coef = torch.nn.Parameter(line_coef)
self.resolution = resolution
[docs]class TensorVMEncoding(Encoding):
"""Learned vector-matrix encoding proposed by TensoRF
Args:
resolution: Resolution of grid.
num_components: Number of components per dimension.
init_scale: Initialization scale.
"""
plane_coef: Float[Tensor, "3 num_components resolution resolution"]
line_coef: Float[Tensor, "3 num_components resolution 1"]
def __init__(
self,
resolution: int = 128,
num_components: int = 24,
init_scale: float = 0.1,
) -> None:
super().__init__(in_dim=3)
self.resolution = resolution
self.num_components = num_components
self.plane_coef = nn.Parameter(init_scale * torch.randn((3, num_components, resolution, resolution)))
self.line_coef = nn.Parameter(init_scale * torch.randn((3, num_components, resolution, 1)))
[docs] def get_out_dim(self) -> int:
return self.num_components * 3
[docs] def forward(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
"""Compute encoding for each position in in_positions
Args:
in_tensor: position inside bounds in range [-1,1],
Returns: Encoded position
"""
plane_coord = torch.stack([in_tensor[..., [0, 1]], in_tensor[..., [0, 2]], in_tensor[..., [1, 2]]]) # [3,...,2]
line_coord = torch.stack([in_tensor[..., 2], in_tensor[..., 1], in_tensor[..., 0]]) # [3, ...]
line_coord = torch.stack([torch.zeros_like(line_coord), line_coord], dim=-1) # [3, ...., 2]
# Stop gradients from going to sampler
plane_coord = plane_coord.view(3, -1, 1, 2).detach()
line_coord = line_coord.view(3, -1, 1, 2).detach()
plane_features = F.grid_sample(self.plane_coef, plane_coord, align_corners=True) # [3, Components, -1, 1]
line_features = F.grid_sample(self.line_coef, line_coord, align_corners=True) # [3, Components, -1, 1]
features = plane_features * line_features # [3, Components, -1, 1]
features = torch.moveaxis(features.view(3 * self.num_components, *in_tensor.shape[:-1]), 0, -1)
return features # [..., 3 * Components]
[docs] @torch.no_grad()
def upsample_grid(self, resolution: int) -> None:
"""Upsamples underlying feature grid
Args:
resolution: Target resolution.
"""
plane_coef = F.interpolate(
self.plane_coef.data, size=(resolution, resolution), mode="bilinear", align_corners=True
)
line_coef = F.interpolate(self.line_coef.data, size=(resolution, 1), mode="bilinear", align_corners=True)
self.plane_coef, self.line_coef = torch.nn.Parameter(plane_coef), torch.nn.Parameter(line_coef)
self.resolution = resolution
[docs]class TriplaneEncoding(Encoding):
"""Learned triplane encoding
The encoding at [i,j,k] is an n dimensional vector corresponding to the element-wise product of the
three n dimensional vectors at plane_coeff[i,j], plane_coeff[i,k], and plane_coeff[j,k].
This allows for marginally more expressivity than the TensorVMEncoding, and each component is self standing
and symmetrical, unlike with VM decomposition where we needed one component with a vector along all the x, y, z
directions for symmetry.
This can be thought of as 3 planes of features perpendicular to the x, y, and z axes, respectively and intersecting
at the origin, and the encoding being the element-wise product of the element at the projection of [i, j, k] on
these planes.
The use for this is in representing a tensor decomp of a 4D embedding tensor: (x, y, z, feature_size)
This will return a tensor of shape (bs:..., num_components)
Args:
resolution: Resolution of grid.
num_components: The number of scalar triplanes to use (ie: output feature size)
init_scale: The scale of the initial values of the planes
product: Whether to use the element-wise product of the planes or the sum
"""
plane_coef: Float[Tensor, "3 num_components resolution resolution"]
def __init__(
self,
resolution: int = 32,
num_components: int = 64,
init_scale: float = 0.1,
reduce: Literal["sum", "product"] = "sum",
) -> None:
super().__init__(in_dim=3)
self.resolution = resolution
self.num_components = num_components
self.init_scale = init_scale
self.reduce = reduce
self.plane_coef = nn.Parameter(
self.init_scale * torch.randn((3, self.num_components, self.resolution, self.resolution))
)
[docs] def get_out_dim(self) -> int:
return self.num_components
[docs] def forward(self, in_tensor: Float[Tensor, "*bs 3"]) -> Float[Tensor, "*bs num_components featuresize"]:
"""Sample features from this encoder. Expects in_tensor to be in range [0, resolution]"""
original_shape = in_tensor.shape
in_tensor = in_tensor.reshape(-1, 3)
plane_coord = torch.stack([in_tensor[..., [0, 1]], in_tensor[..., [0, 2]], in_tensor[..., [1, 2]]], dim=0)
# Stop gradients from going to sampler
plane_coord = plane_coord.detach().view(3, -1, 1, 2)
plane_features = F.grid_sample(
self.plane_coef, plane_coord, align_corners=True
) # [3, num_components, flattened_bs, 1]
if self.reduce == "product":
plane_features = plane_features.prod(0).squeeze(-1).T # [flattened_bs, num_components]
else:
plane_features = plane_features.sum(0).squeeze(-1).T
return plane_features.reshape(*original_shape[:-1], self.num_components)
[docs] @torch.no_grad()
def upsample_grid(self, resolution: int) -> None:
"""Upsamples underlying feature grid
Args:
resolution: Target resolution.
"""
plane_coef = F.interpolate(
self.plane_coef.data, size=(resolution, resolution), mode="bilinear", align_corners=True
)
self.plane_coef = torch.nn.Parameter(plane_coef)
self.resolution = resolution
[docs]class KPlanesEncoding(Encoding):
"""Learned K-Planes encoding
A plane encoding supporting both 3D and 4D coordinates. With 3D coordinates this is similar to
:class:`TriplaneEncoding`. With 4D coordinates, the encoding at point ``[i,j,k,q]`` is
a n-dimensional vector computed as the elementwise product of 6 n-dimensional vectors at
``planes[i,j]``, ``planes[i,k]``, ``planes[i,q]``, ``planes[j,k]``, ``planes[j,q]``,
``planes[k,q]``.
Unlike :class:`TriplaneEncoding` this class supports different resolution along each axis.
This will return a tensor of shape (bs:..., num_components)
Args:
resolution: Resolution of the grid. Can be a sequence of 3 or 4 integers.
num_components: The number of scalar planes to use (ie: output feature size)
init_a: The lower-bound of the uniform distribution used to initialize the spatial planes
init_b: The upper-bound of the uniform distribution used to initialize the spatial planes
reduce: Whether to use the element-wise product of the planes or the sum
"""
def __init__(
self,
resolution: Sequence[int] = (128, 128, 128),
num_components: int = 64,
init_a: float = 0.1,
init_b: float = 0.5,
reduce: Literal["sum", "product"] = "product",
) -> None:
super().__init__(in_dim=len(resolution))
self.resolution = resolution
self.num_components = num_components
self.reduce = reduce
if self.in_dim not in {3, 4}:
raise ValueError(
f"The dimension of coordinates must be either 3 (static scenes) "
f"or 4 (dynamic scenes). Found resolution with {self.in_dim} dimensions."
)
has_time_planes = self.in_dim == 4
self.coo_combs = list(itertools.combinations(range(self.in_dim), 2))
# Unlike the Triplane encoding, we use a parameter list instead of batching all planes
# together to support uneven resolutions (especially useful for time).
# Dynamic models (in_dim == 4) will have 6 planes:
# (y, x), (z, x), (t, x), (z, y), (t, y), (t, z)
# static models (in_dim == 3) will only have the 1st, 2nd and 4th planes.
self.plane_coefs = nn.ParameterList()
for coo_comb in self.coo_combs:
new_plane_coef = nn.Parameter(
torch.empty([self.num_components] + [self.resolution[cc] for cc in coo_comb[::-1]])
)
if has_time_planes and 3 in coo_comb: # Time planes initialized to 1
nn.init.ones_(new_plane_coef)
else:
nn.init.uniform_(new_plane_coef, a=init_a, b=init_b)
self.plane_coefs.append(new_plane_coef)
[docs] def get_out_dim(self) -> int:
return self.num_components
[docs] def forward(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
"""Sample features from this encoder. Expects ``in_tensor`` to be in range [-1, 1]"""
original_shape = in_tensor.shape
assert any(self.coo_combs)
output = 1.0 if self.reduce == "product" else 0.0 # identity for corresponding op
for ci, coo_comb in enumerate(self.coo_combs):
grid = self.plane_coefs[ci].unsqueeze(0) # [1, feature_dim, reso1, reso2]
coords = in_tensor[..., coo_comb].view(1, 1, -1, 2) # [1, 1, flattened_bs, 2]
interp = F.grid_sample(
grid, coords, align_corners=True, padding_mode="border"
) # [1, output_dim, 1, flattened_bs]
interp = interp.view(self.num_components, -1).T # [flattened_bs, output_dim]
if self.reduce == "product":
output = output * interp
else:
output = output + interp
# Typing: output gets converted to a tensor after the first iteration of the loop
assert isinstance(output, Tensor)
return output.reshape(*original_shape[:-1], self.num_components)
[docs]class SHEncoding(Encoding):
"""Spherical harmonic encoding
Args:
levels: Number of spherical harmonic levels to encode.
"""
def __init__(self, levels: int = 4, implementation: Literal["tcnn", "torch"] = "torch") -> None:
super().__init__(in_dim=3)
if levels <= 0 or levels > 4:
raise ValueError(f"Spherical harmonic encoding only supports 1 to 4 levels, requested {levels}")
self.levels = levels
self.tcnn_encoding = None
if implementation == "tcnn" and not TCNN_EXISTS:
print_tcnn_speed_warning("SHEncoding")
elif implementation == "tcnn":
encoding_config = self.get_tcnn_encoding_config(levels=self.levels)
self.tcnn_encoding = tcnn.Encoding(
n_input_dims=3,
encoding_config=encoding_config,
)
[docs] @classmethod
def get_tcnn_encoding_config(cls, levels) -> dict:
"""Get the encoding configuration for tcnn if implemented"""
encoding_config = {
"otype": "SphericalHarmonics",
"degree": levels,
}
return encoding_config
[docs] def get_out_dim(self) -> int:
return self.levels**2
[docs] @torch.no_grad()
def pytorch_fwd(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
"""Forward pass using pytorch. Significantly slower than TCNN implementation."""
return components_from_spherical_harmonics(levels=self.levels, directions=in_tensor)
[docs] def forward(self, in_tensor: Float[Tensor, "*bs input_dim"]) -> Float[Tensor, "*bs output_dim"]:
if self.tcnn_encoding is not None:
return self.tcnn_encoding(in_tensor)
return self.pytorch_fwd(in_tensor)