Multiphase Segmentation For Simultaneously Homogeneous and Textural Images

TL;DR

This paper introduces a novel multiphase segmentation model capable of simultaneously identifying homogeneous and textural regions in natural images, addressing limitations of existing models.

Contribution

It proposes a bi-level constrained minimization framework with new norms in Banach spaces for improved multiphase segmentation of complex images.

Findings

The model effectively segments natural images with both texture and homogeneous regions.

Theoretical analysis supports the segmentation approach and its decomposition capabilities.

Demonstrations show improved segmentation quality on real-world images.

Abstract

Segmentation remains an important problem in image processing. For homogeneous (piecewise smooth) images, a number of important models have been developed and refined over the past several decades. However, these models often fail when applied to the substantially larger class of natural images that simultaneously contain regions of both texture and homogeneity. This work introduces a bi-level constrained minimization model for simultaneous multiphase segmentation of images containing both homogeneous and textural regions. We develop novel norms defined in different functional Banach spaces for the segmentation which results in a non-convex minimization. Finally, we develop a generalized notion of segmentation delving into approximation theory and demonstrating that a more refined decomposition of these images results in multiple meaningful components. Both theoretical results and demonstrations on natural images are provided.