A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings

TL;DR

This paper introduces a novel topology-preserving segmentation network that uses quasiconformal mappings to accurately segment objects while maintaining their topological properties, even with limited or no labeled data.

Contribution

The paper presents a deformation-based segmentation framework that guarantees topology preservation through quasiconformal theory and can be trained unsupervised, advancing the state-of-the-art in topology-aware segmentation.

Findings

Outperforms existing models in segmentation accuracy

Maintains topological integrity of segmented objects

Effective in multi-object segmentation scenarios

Abstract

We propose the Topology-Preserving Segmentation Network, a deformation-based model that can extract objects in an image while maintaining their topological properties. This network generates segmentation masks that have the same topology as the template mask, even when trained with limited data. The network consists of two components: the Deformation Estimation Network, which produces a deformation map that warps the template mask to enclose the region of interest, and the Beltrami Adjustment Module, which ensures the bijectivity of the deformation map by truncating the associated Beltrami coefficient based on Quasiconformal theories. The proposed network can also be trained in an unsupervised manner, eliminating the need for labeled training data. This is achieved by incorporating an unsupervised segmentation loss. Our experimental results on various image datasets show that TPSN achieves better segmentation accuracy than state-of-the-art models with correct topology. Furthermore, we demonstrate TPSN's ability to handle multiple object segmentation.