Math#
Math Helper Functions
- class nerfstudio.utils.math.Gaussians(mean: Float[Tensor, '*batch dim'], cov: Float[Tensor, '*batch dim dim'])[source]#
Bases:
objectStores Gaussians
- Parameters:
mean – Mean of multivariate Gaussian
cov – Covariance of multivariate Gaussian.
- nerfstudio.utils.math.columnwise_squared_l2_distance(x: Float[Tensor, '*M N'], y: Float[Tensor, '*M N']) Float[Tensor, 'N N'][source]#
Compute the squared Euclidean distance between all pairs of columns. Adapted from https://github.com/google-research/multinerf/blob/5b4d4f64608ec8077222c52fdf814d40acc10bc1/internal/geopoly.py
- Parameters:
x – tensor of floats, with shape [M, N].
y – tensor of floats, with shape [M, N].
- Returns:
tensor of floats, with shape [N, N].
- Return type:
sq_dist
- nerfstudio.utils.math.compute_3d_gaussian(directions: Float[Tensor, '*batch 3'], means: Float[Tensor, '*batch 3'], dir_variance: Float[Tensor, '*batch 1'], radius_variance: Float[Tensor, '*batch 1']) Gaussians[source]#
Compute gaussian along ray.
- Parameters:
directions – Axis of Gaussian.
means – Mean of Gaussian.
dir_variance – Variance along direction axis.
radius_variance – Variance tangent to direction axis.
- Returns:
Oriented 3D gaussian.
- Return type:
- nerfstudio.utils.math.conical_frustum_to_gaussian(origins: Float[Tensor, '*batch 3'], directions: Float[Tensor, '*batch 3'], starts: Float[Tensor, '*batch 1'], ends: Float[Tensor, '*batch 1'], radius: Float[Tensor, '*batch 1']) Gaussians[source]#
Approximates conical frustums with a Gaussian distributions.
Uses stable parameterization described in mip-NeRF publication.
- Parameters:
origins – Origins of cones.
directions – Direction (axis) of frustums.
starts – Start of conical frustums.
ends – End of conical frustums.
radius – Radii of cone a distance of 1 from the origin.
- Returns:
Approximation of conical frustums
- Return type:
- nerfstudio.utils.math.cylinder_to_gaussian(origins: Float[Tensor, '*batch 3'], directions: Float[Tensor, '*batch 3'], starts: Float[Tensor, '*batch 1'], ends: Float[Tensor, '*batch 1'], radius: Float[Tensor, '*batch 1']) Gaussians[source]#
Approximates cylinders with a Gaussian distributions.
- Parameters:
origins – Origins of cylinders.
directions – Direction (axis) of cylinders.
starts – Start of cylinders.
ends – End of cylinders.
radius – Radii of cylinders.
- Returns:
Approximation of cylinders
- Return type:
- nerfstudio.utils.math.expected_sin(x_means: Tensor, x_vars: Tensor) Tensor[source]#
Computes the expected value of sin(y) where y ~ N(x_means, x_vars)
- Parameters:
x_means – Mean values.
x_vars – Variance of values.
- Returns:
The expected value of sin.
- Return type:
torch.Tensor
- nerfstudio.utils.math.generate_polyhedron_basis(basis_shape: Literal['icosahedron', 'octahedron'], angular_tesselation: int, remove_symmetries: bool = True, eps: float = 0.0001) Tensor[source]#
Generates a 3D basis by tesselating a geometric polyhedron. Basis is used to construct Fourier features for positional encoding. See Mip-Nerf360 paper: https://arxiv.org/abs/2111.12077 Adapted from https://github.com/google-research/multinerf/blob/5b4d4f64608ec8077222c52fdf814d40acc10bc1/internal/geopoly.py
- Parameters:
base_shape – string, the name of the starting polyhedron, must be either ‘icosahedron’ or ‘octahedron’.
angular_tesselation – int, the number of times to tesselate the polyhedron, must be >= 1 (a value of 1 is a no-op to the polyhedron).
remove_symmetries – bool, if True then remove the symmetric basis columns, which is usually a good idea because otherwise projections onto the basis will have redundant negative copies of each other.
eps – float, a small number used to determine symmetries.
- Returns:
a matrix with shape [3, n].
- Return type:
basis
- nerfstudio.utils.math.intersect_aabb(origins: Tensor, directions: Tensor, aabb: Tensor, max_bound: float = 10000000000.0, invalid_value: float = 10000000000.0) Tuple[Tensor, Tensor][source]#
Implementation of ray intersection with AABB box
- Parameters:
origins – [N,3] tensor of 3d positions
directions – [N,3] tensor of normalized directions
aabb – [6] array of aabb box in the form of [x_min, y_min, z_min, x_max, y_max, z_max]
max_bound – Maximum value of t_max
invalid_value – Value to return in case of no intersection
- Returns:
t_min, t_max - two tensors of shapes N representing distance of intersection from the origin.
- nerfstudio.utils.math.intersect_obb(origins: Tensor, directions: Tensor, obb: OrientedBox, max_bound: float = 10000000000.0, invalid_value: float = 10000000000.0)[source]#
Ray intersection with an oriented bounding box (OBB)
- Parameters:
origins – [N,3] tensor of 3d positions
directions – [N,3] tensor of normalized directions
R – [3,3] rotation matrix
T – [3] translation vector
S – [3] extents of the bounding box
max_bound – Maximum value of t_max
invalid_value – Value to return in case of no intersection
- nerfstudio.utils.math.k_nearest_sklearn(x: Tensor, k: int, metric: str = 'euclidean') Tuple[Float[Tensor, '*batch k'], Int[Tensor, '*batch k']][source]#
Find k-nearest neighbors using sklearn’s NearestNeighbors.
- Parameters:
x – input tensor
k – number of neighbors to find
metric – metric to use for distance computation
- Returns:
distances to the k-nearest neighbors indices: indices of the k-nearest neighbors
- Return type:
distances
- nerfstudio.utils.math.masked_reduction(input_tensor: Float[Tensor, '1 32 mult'], mask: Bool[Tensor, '1 32 mult'], reduction_type: Literal['image', 'batch']) Tensor[source]#
Whether to consolidate the input_tensor across the batch or across the image :param input_tensor: input tensor :param mask: mask tensor :param reduction_type: either “batch” or “image”
- Returns:
reduced input_tensor
- Return type:
input_tensor
- nerfstudio.utils.math.normalized_depth_scale_and_shift(prediction: Float[Tensor, '1 32 mult'], target: Float[Tensor, '1 32 mult'], mask: Bool[Tensor, '1 32 mult'])[source]#
More info here: https://arxiv.org/pdf/2206.00665.pdf supplementary section A2 Depth Consistency Loss This function computes scale/shift required to normalizes predicted depth map, to allow for using normalized depth maps as input from monocular depth estimation networks. These networks are trained such that they predict normalized depth maps.
Solves for scale/shift using a least squares approach with a closed form solution: Based on: https://github.com/autonomousvision/monosdf/blob/d9619e948bf3d85c6adec1a643f679e2e8e84d4b/code/model/loss.py#L7 :param prediction: predicted depth map :param target: ground truth depth map :param mask: mask of valid pixels
- Returns:
scale and shift for depth prediction