Compassionately Conservative Balanced Cuts for Image Segmentation

TL;DR

This paper introduces Compassionately Conservative Balanced (CCB) Cut costs, a flexible family of graph partitioning objectives that improve image segmentation by balancing cluster size and connectivity, outperforming normalized cuts.

Contribution

The paper proposes CCB-Cut costs, a novel family of balanced cut functions, and an algorithm for their optimization, bridging graph partitioning with Piecewise Flat Embeddings for image segmentation.

Findings

CCB-Cut improves segmentation accuracy over NCut.

The method offers greater variability in region size.

Experimental results on BSDS500 show enhanced performance.

Abstract

The Normalized Cut (NCut) objective function, widely used in data clustering and image segmentation, quantifies the cost of graph partitioning in a way that biases clusters or segments that are balanced towards having lower values than unbalanced partitionings. However, this bias is so strong that it avoids any singleton partitions, even when vertices are very weakly connected to the rest of the graph. Motivated by the B\"uhler-Hein family of balanced cut costs, we propose the family of Compassionately Conservative Balanced (CCB) Cut costs, which are indexed by a parameter that can be used to strike a compromise between the desire to avoid too many singleton partitions and the notion that all partitions should be balanced. We show that CCB-Cut minimization can be relaxed into an orthogonally constrained $\ell_{\tau}$-minimization problem that coincides with the problem of computing Piecewise Flat Embeddings (PFE) for one particular index value, and we present an algorithm for solving the relaxed problem by iteratively minimizing a sequence of reweighted Rayleigh quotients (IRRQ). Using images from the BSDS500 database, we show that image segmentation based on CCB-Cut minimization provides better accuracy with respect to ground truth and greater variability in region size than NCut-based image segmentation.