Kernel Cuts: MRF meets Kernel & Spectral Clustering

TL;DR

This paper introduces Kernel Cut algorithms that combine Markov Random Field regularization with spectral clustering criteria like Normalized Cut, enabling improved segmentation and clustering by integrating high-order and pairwise constraints efficiently.

Contribution

It presents a novel framework that unifies MRF regularization and spectral clustering criteria through Kernel Cut algorithms, facilitating joint optimization in segmentation and clustering tasks.

Findings

Kernel Cut algorithms effectively combine MRF and spectral clustering energies.

The approach improves segmentation quality by integrating high-order and pairwise constraints.

The method is compatible with existing discrete and continuous solvers.

Abstract

We propose a new segmentation model combining common regularization energies, e.g. Markov Random Field (MRF) potentials, and standard pairwise clustering criteria like Normalized Cut (NC), average association (AA), etc. These clustering and regularization models are widely used in machine learning and computer vision, but they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation and combinatorial max-flow techniques. On the one hand, we show that many common applications using MRF segmentation energies can benefit from a high-order NC term, e.g. enforcing balanced clustering of arbitrary high-dimensional image features combining color, texture, location, depth, motion, etc. On the other hand, standard clustering applications can benefit from an inclusion of common pairwise or higher-order MRF constraints, e.g. edge alignment, bin-consistency, label cost, etc. To address joint energies like NC+MRF, we propose efficient Kernel Cut algorithms based on bound optimization. While focusing on graph cut and move-making techniques, our new unary (linear) kernel and spectral bound formulations for common pairwise clustering criteria allow to integrate them with any regularization functionals with existing discrete or continuous solvers.