Stefan Haller

Lisa Hutschenreiter, Stefan Haller, Lorenz Feineis et al.

We contribute to approximate algorithms for the quadratic assignment problem also known as graph matching. Inspired by the success of the fusion moves technique developed for multilabel discrete Markov random fields, we investigate its applicability to graph matching. In particular, we show how fusion moves can be efficiently combined with the dedicated state-of-the-art dual methods that have recently shown superior results in computer vision and bio-imaging applications. As our empirical evaluation on a wide variety of graph matching datasets suggests, fusion moves significantly improve performance of these methods in terms of speed and quality of the obtained solutions. Our method sets a new state-of-the-art with a notable margin with respect to its competitors.

Stefan Haller, Mangal Prakash, Lisa Hutschenreiter et al.

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.

Stefan Haller, Paul Swoboda, Bogdan Savchynskyy

We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous Sherali-Adams hierarchy), which naturally define lower bounds for its optimum. This family always contains a tight relaxation and we give an algorithm able to find it and therefore, solve the initial non-relaxed NP-hard problem. The relaxations we consider decompose the original problem into two non-overlapping parts: an easy LP-tight part and a difficult one. For the latter part a combinatorial solver must be used. As we show in our experiments, in a number of applications the second, difficult part constitutes only a small fraction of the whole problem. This property allows to significantly reduce the computational time of the combinatorial solver and therefore solve problems which were out of reach before.