Dynamic Discrete Tomography

TL;DR

This paper addresses the challenge of reconstructing moving points over time using limited X-ray data, analyzing computational complexity, proposing algorithms, and exploring related flow and matching problems.

Contribution

It introduces and analyzes algorithmic models for dynamic discrete tomography, establishing complexity results and practical algorithms, with insights into related flow and matching problems.

Findings

Determined the computational complexity of dynamic discrete tomography.

Developed algorithms applicable in practical scenarios.

Provided new results on constrained min-cost flow and matching problems.

Abstract

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This particular particle tracking problem, with applications, e.g., in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.