Co-clustering of image segments using convex optimization applied to EM neuronal reconstruction

Abstract

This paper addresses the problem of jointly clustering two segmentations of closely correlated images. We focus in particular on the application of reconstructing neuronal structures in over-segmented electron microscopy images. We formulate the problem of co-clustering as a quadratic semi-assignment problem and investigate convex relaxations using semidefinite and linear programming. We further introduce a linear programming method with manageable number of constraints and present an approach for learning the cost function. Our method increases computational efficiency by orders of magnitude while maintaining accuracy, automatically finds the optimal number of clusters, and empirically tends to produce binary assignment solutions. We illustrate our approach in simulations and in experiments with real EM data.

Segmentation fusion for connectomics

“…It is believed that the automatic, high-throughput analysis of such images can lead to a better understanding of the mammalian brain, as well as provide new insight into other important areas of neuroscience, such as the study of the biological basis of learning or memory [7]. Besides its scientific applications, connectomics also provides great opportunities for the computer vision community, as is evident in the fast growing vision literature addressing problems such as neuron segmentation [8,9,20,5], sparse tomographic reconstruction [19], and the design of features for connectomics [12].…”

Region-Based Particle Filter for Video Object Segmentation

“…This is a Quadratic Semi-Assignment Problem (QSAP) [26] for which a Linear Programming relaxation was presented by [8] imposing distances between regions based on the triangular inequality. Further relaxation approaches ( [26], [13]) make use of distances defined over cliques in a region adjacency graph.…”

“…Further relaxation approaches ( [26], [13]) make use of distances defined over cliques in a region adjacency graph. Considering these relaxations, this optimization can be stated as:…”

Segmenting Planar Superpixel Adjacency Graphs w.r.t. Non-planar Superpixel Affinity Graphs

“…Recent work on the multicut problem for computer vision application has afforded an exact cutting plane algorithm for general graph that is applicable if edge weights are strong [3], efficient greedy algorithms suitable for large problems and problems where edge weights are weak [6], as well as diverse linear programming (LP) relaxations [9,10,12,15,17]. The Lagrangian decomposition we propose in this paper is built on [17] which considers optimal multicuts of planar graphs.…”

“…The formalization of the image segmentation problem as a multicut problem has recently attracted considerable attention [2,3,6,9,10,15,17]. This problem consists in finding a partition of a weighted superpixel adjacency graph into connected components (segments) such that the set of edges that straddle different segments (the multicut) has minimum total weight.…”