Thorsten Beier

Probabilistic image segmentation with closedness constraints

We propose a novel graphical model for probabilistic image segmentation that contributes both to aspects of perceptual grouping in connection with image segmentation, and to globally optimal inference with higher-order graphical models. We represent image partitions in terms of cellular complexes in order to make the duality between connected regions and their contours explicit. This allows us to formulate a graphical model with higher-order factors that represent the requirement that all contours must be closed. The model induces a probability measure on the space of all partitions, concentrated on perceptually meaningful segmentations. We give a complete polyhedral characterization of the resulting global inference problem in terms of the multicut polytope and efficiently compute global optima by a cutting plane method. Competitive results for the Berkeley segmentation benchmark confirm the consistency of our approach.

Multicut brings automated neurite segmentation closer to human performance

Reference EPFL-ARTICLE-226946doi:10.1038/nmeth.4151View record in Web of Science Record created on 2017-03-27, modified on 2017-07-13

Fusion moves for correlation clustering

Correlation clustering, or multicut partitioning, is widely used in image segmentation for partitioning an undirected graph or image with positive and negative edge weights such that the sum of cut edge weights is minimized. Due to its NP-hardness, exact solvers do not scale and approximative solvers often give unsatisfactory results. We investigate scalable methods for correlation clustering. To this end we define fusion moves for the correlation clustering problem. Our algorithm iteratively fuses the current and a proposed partitioning which monotonously improves the partitioning and maintains a valid partitioning at all times. Furthermore, it scales to larger datasets, gives near optimal solutions, and at the same time shows a good anytime performance.

Cut, Glue, & Cut: A Fast, Approximate Solver for Multicut Partitioning

Recently, unsupervised image segmentation has become increasingly popular. Starting from a superpixel segmentation, an edge-weighted region adjacency graph is constructed. Amongst all segmentations of the graph, the one which best conforms to the given image evidence, as measured by the sum of cut edge weights, is chosen. Since this problem is NP-hard, we propose a new approximate solver based on the move-making paradigm: first, the graph is recursively partitioned into small regions (cut phase). Then, for any two adjacent regions, we consider alternative cuts of these two regions defining possible moves (glue & cut phase). For planar problems, the optimal move can be found, whereas for non-planar problems, efficient approximations exist. We evaluate our algorithm on published and new benchmark datasets, which we make available here. The proposed algorithm finds segmentations that, as measured by a loss function, are as close to the ground-truth as the global optimum found by exact solvers. It does so significantly faster then existing approximate methods, which is important for large-scale problems.

The lazy flipper: efficient depth-limited exhaustive search in discrete graphical models

We propose a new exhaustive search algorithm for optimization in discrete graphical models. When pursued to the full search depth (typically intractable), it is guaranteed to converge to a global optimum, passing through a series of monotonously improving local optima that are guaranteed to be optimal within a given and increasing Hamming distance. For a search depth of 1, it specializes to ICM. Between these extremes, a tradeoff between approximation quality and runtime is established. We show this experimentally by improving approximations for the non-submodular models in the MRF benchmark [1] and Decision Tree Fields [2].

An Efficient Fusion Move Algorithm for the Minimum Cost Lifted Multicut Problem

Many computer vision problems can be cast as an optimization problem whose feasible solutions are decompositions of a graph. The minimum cost lifted multicut problem is such an optimization problem. Its objective function can penalize or reward all decompositions for which any given pair of nodes are in distinct components. While this property has many potential applications, such applications are hampered by the fact that the problem is NP-hard. We propose a fusion move algorithm for computing feasible solutions, better and more efficiently than existing algorithms. We demonstrate this and applications to image segmentation, obtaining a new state of the art for a problem in biological image analysis.

Improving 3D EM data segmentation by joint optimization over boundary evidence and biological priors

We present a new automated neuron segmentation algorithm for isotropic 3D electron microscopy data. We cast the problem into the asymmetric multiway cut framework. The latter combines boundary-based segmentation (clustering) with region-based segmentation (semantic labeling) in a single problem and objective function. This joint formulation allows us to augment local boundary evidence with higherlevel biological priors, such as membership to an axonic or dendritic neurite. Joint optimization enforces consistency between evidence and priors, leading to correct resolution of many difficult boundary configurations. We show experimentally on a FIB/SEM dataset of mouse cortex that the new approach outperforms existing hierarchical segmentation and multicut algorithms which only use boundary evidence.

MAP-Inference on Large Scale Higher-Order Discrete Graphical Models by Fusion Moves

Many computer vision problems can be cast into optimization problems over discrete graphical models also known as Markov or conditional random fields. Standard methods are able to solve those problems quite efficiently. However, problems with huge label spaces and or higher-order structure remain challenging or intractable even for approximate methods.

Asymmetric Cuts: Joint Image Labeling and Partitioning

For image segmentation, recent advances in optimization make it possible to combine noisy region appearance terms with pairwise terms which can not only discourage, but also encourage label transitions, depending on boundary evidence. These models have the potential to overcome problems such as the shrinking bias. However, with the ability to encourage label transitions comes a different problem: strong boundary evidence can overrule weak region appearance terms to create new regions out of nowhere. While some label classes exhibit strong internal boundaries, such as the background class which is the pool of objects. Other label classes, meanwhile, should be modeled as a single region, even if some internal boundaries are visible.

Parallel multicut segmentation via dual decomposition

We propose a new outer relaxation of the multicut polytope, along with a dual decomposition approach for correlation clustering and multicut segmentation, for general graphs. Each subproblem is a minimum st-cut problem and can thus be solved efficiently. An optimal reparameterization is found using subgradients and affords a new characterization of the basic LP relaxation of the multicut problem, as well as informed decoding heuristics. The algorithm we propose for solving the problem distributes the computation and is amenable to a parallel implementation.