Lifting-based variational multiclass segmentation algorithm: design, convergence analysis, and implementation with applications in medical imaging

TL;DR

This paper introduces a novel variational multiclass segmentation method that leverages lifting into higher-dimensional feature spaces, with proven convergence and stability, demonstrated on medical imaging tasks like brain abscess and tumor classification.

Contribution

The paper presents a new lifting-based variational segmentation algorithm with theoretical guarantees and practical applications in medical imaging, including convergence analysis and implementation details.

Findings

Effective segmentation of medical images demonstrated

Proven existence of global minimizers and stability

Promising results in brain abscess and tumor classification

Abstract

We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions by minimizing an energy functional combining information from different channels. Multichannel image data can be obtained by lifting the image into a higher dimensional feature space using specific multichannel filtering or may already be provided by the imaging modality under consideration, such as an RGB image or multimodal medical data. Experimental results show that the proposed method performs well in various scenarios. In particular, promising results are presented for two medical applications involving classification of brain abscess and tumor growth, respectively. As main theoretical contributions, we prove the existence of global minimizers of the proposed energy functional and show its stability and convergence with respect to noisy inputs. In particular, these results also apply to the special case of binary segmentation, and these results are also novel in this particular situation.