Planar Ultrametric Rounding for Image Segmentation

TL;DR

This paper introduces an efficient LP relaxation and dual cutting plane method for hierarchical clustering on planar graphs, specifically applied to improve image segmentation techniques.

Contribution

It presents a novel LP relaxation approach combined with a dual cutting plane scheme utilizing minimum cost perfect matching for planar graph clustering.

Findings

Efficient algorithm for hierarchical clustering on planar graphs.

Improved image segmentation results using the proposed method.

Scalable approach for large planar graph segmentation tasks.

Abstract

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation.