Estimate the tomographic system-matrix for rays in voxels.
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 ray_voxel_overlap.estimate_overlap_of_ray_with_voxels? """ 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:
Create a system-matrix using scipy.sparse matrix which can be used for iterative tomographic reconstructions.
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.
import numpy as np import ray_voxel_overlap as rvo np.random.seed(0) N_RAYS = 100 supports = np.array([ np.random.uniform(-2.5, 2.5, N_RAYS), np.random.uniform(-2.5, 2.5, N_RAYS), np.zeros(N_RAYS) ]).T directions = np.array([ np.random.uniform(-0.3, 0.3, N_RAYS), np.random.uniform(-0.3, 0.3, N_RAYS), np.ones(N_RAYS) ]).T 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( supports=supports, directions=directions, 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
Sebastian A. Mueller,
ETH-Zurich, Switzerland (2014-2019),
MPI-Heidelberg, Germany (2019-)
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