Segmentation of Three-dimensional Images with Parametric Active Surfaces and Topology Changes

TL;DR

This paper presents a new parametric method for 3D image segmentation that automatically handles topology changes like splitting and merging of surfaces, with applications to medical imaging.

Contribution

It introduces a novel parametric approach with topology change detection and an efficient finite element scheme for 3D image segmentation.

Findings

Successfully detects topology changes in artificial images

Effectively segments medical 3D images

Handles splitting, merging, and genus changes of surfaces

Abstract

In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.