A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm

TL;DR

This paper introduces a new Euler's Elastica based segmentation method that effectively handles noisy images by integrating the progressive hedging algorithm with advanced optimization techniques, improving boundary completion in noisy conditions.

Contribution

The paper develops a novel Euler's Elastica segmentation approach for noisy images, utilizing the progressive hedging algorithm with convex relaxation and acceleration techniques.

Findings

Significant improvement in segmentation quality on synthetic images.

Effective boundary completion in noisy real images.

Enhanced computational efficiency through FFT and soft thresholding.

Abstract

Euler's Elastica based unsupervised segmentation models have strong capability of completing the missing boundaries for existing objects in a clean image, but they are not working well for noisy images. This paper aims to establish a Euler's Elastica based approach that properly deals with random noises to improve the segmentation performance for noisy images. We solve the corresponding optimization problem via using the progressive hedging algorithm (PHA) with a step length suggested by the alternating direction method of multipliers (ADMM). Technically, all the simplified convex versions of the subproblems derived from the major framework of PHA can be obtained by using the curvature weighted approach and the convex relaxation method. Then an alternating optimization strategy is applied with the merits of using some powerful accelerating techniques including the fast Fourier transform (FFT) and generalized soft threshold formulas. Extensive experiments have been conducted on both synthetic and real images, which validated some significant gains of the proposed segmentation models and demonstrated the advantages of the developed algorithm.