Climbing on Pyramids

TL;DR

This paper introduces a novel energy minimization method for identifying optimal cuts in hierarchical partitions, ensuring the energy increases with hierarchy level, applicable to various energy types.

Contribution

It proposes a new hierarchical energy minimization approach that guarantees scale-increasing properties for finding optimal cuts in hierarchies.

Findings

Effective in identifying optimal hierarchy cuts

Applicable to a broad class of energies including separable and supremum-composed energies

Ensures energy climbing property in hierarchical segmentation

Abstract

A new approach is proposed for finding the "best cut" in a hierarchy of partitions by energy minimization. Said energy must be "climbing" i.e. it must be hierarchically and scale increasing. It encompasses separable energies and those composed under supremum.