Combinatorial pyramids and discrete geometry for energy-minimizing segmentation

TL;DR

This paper introduces a hierarchical segmentation framework using combinatorial pyramids and discrete geometry to optimize energy-based partitioning, enabling precise geometric and photometric analysis for improved image segmentation.

Contribution

The paper presents a novel hierarchical segmentation framework combining combinatorial pyramids and discrete geometric estimators for energy minimization.

Findings

Effective hierarchical segmentation demonstrated on experiments

Precise geometric parameters improve segmentation quality

Energy minimization based on discrete measures enhances results

Abstract

This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of partitions. Secondly, discrete geometric estimators measure precisely some important geometric parameters of the regions. These measures combined with photometrical and topological features of the partition allows to design energy terms based on discrete measures. Our segmentation framework exploits these energies to build a pyramid of image partitions with a minimization scheme. Some experiments illustrating our framework are shown and discussed.