A Primal-Dual Solver for Large-Scale Tracking-by-Assignment

TL;DR

This paper introduces a fast, scalable primal-dual solver for large-scale tracking-by-assignment problems, significantly improving speed and memory efficiency over traditional solvers like Gurobi, with applications in cell tracking.

Contribution

The paper presents a novel decomposable problem representation, a dual block-coordinate ascent optimization method, and primal heuristics for feasible solution reconstruction.

Findings

Up to 60 times faster than Gurobi

Significantly reduced memory usage

Effective on real-world cell tracking problems

Abstract

We propose a fast approximate solver for the combinatorial problem known as tracking-by-assignment, which we apply to cell tracking. The latter plays a key role in discovery in many life sciences, especially in cell and developmental biology. So far, in the most general setting this problem was addressed by off-the-shelf solvers like Gurobi, whose run time and memory requirements rapidly grow with the size of the input. In contrast, for our method this growth is nearly linear. Our contribution consists of a new (1) decomposable compact representation of the problem; (2) dual block-coordinate ascent method for optimizing the decomposition-based dual; and (3) primal heuristics that reconstructs a feasible integer solution based on the dual information. Compared to solving the problem with Gurobi, we observe an up to~60~times speed-up, while reducing the memory footprint significantly. We demonstrate the efficacy of our method on real-world tracking problems.