Estimate the tomographic system-matrix for rays in voxels.

## Project description

# Overlap of a ray and a volume cell (voxel)

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.

# Interface

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:

- 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 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 `python`

implementation.

## Authors

Sebastian A. Mueller,

ETH-Zurich, Switzerland (2014-2019),

MPI-Heidelberg, Germany (2019-)

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