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Estimate the tomographic system-matrix for rays in voxels.

Project description

Overlap of a ray and a volume cell (voxel) Build Status

Estimate the euclidean overlap passed by a ray within a rectangular volume cell (voxel).


For a given, rectangular space partitioning in 3D, and a given ray the overlap of all voxels with the ray is estimated. The figure shows a ray and its overlap with voxels. A brown overlap with voxel 3, a red overlap with voxel 0, a purple overlap with voxel 4, and a green overlap with voxel 5. The ray is defined by its support and direction vectors. The space-partitioning is defined by its bin-edges.


There is one core function:

import ray_voxel_overlap
Returns the voxel indices and overlap distances for one single ray
(defined by support and direction) with voxels defined by the bin_edges
in x,y and z.

support         3D support vector of ray.

direction       3D direction vector of ray.

x_bin_edges     voxel bin edge positions in x.

y_bin_edges     voxel bin edge positions in y.

z_bin_edges     voxel bin edge positions in z.

There are two more functions:

  • 2nd ray_voxel_overlap.estimate_system_matrix()

Create a system-matrix using scipy.sparse matrix which can be used for iterative tomographic reconstructions.

  • 3rd ray_voxel_overlap.estimate_overlap_of_ray_bundle_with_voxels()

Average the overlap of multiple rays representing a single read-out-channel. This is useful when a single ray is not representative enough for the geometry sensed by a read-out-channel in your tomographic setup, e.g. when there is a narrow depth-of-field.

Tomographic system-matrix

import numpy as np
import ray_voxel_overlap as rvo


N_RAYS = 100
supports = np.array([
    np.random.uniform(-2.5, 2.5, N_RAYS),
    np.random.uniform(-2.5, 2.5, N_RAYS),

directions = np.array([
    np.random.uniform(-0.3, 0.3, N_RAYS),
    np.random.uniform(-0.3, 0.3, N_RAYS),

norm_directions = np.linalg.norm(directions, axis=1)
directions[:, 0] /= norm_directions
directions[:, 1] /= norm_directions
directions[:, 2] /= norm_directions

N_X_BINS = 8
N_Y_BINS = 13
N_Z_BINS = 7
system_matrix = rvo.estimate_system_matrix(
    x_bin_edges=np.linspace(-100., 100., N_X_BINS+1),
    y_bin_edges=np.linspace(-100., 100., N_Y_BINS+1),
    z_bin_edges=np.linspace(0., 200., N_Z_BINS+1),

How it is done

To be fast, the production-code is written in C and wrapped in cython. But for development, there is a python implementation.


Sebastian A. Mueller,

ETH-Zurich, Switzerland (2014-2019),

MPI-Heidelberg, Germany (2019-)

Project details

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