Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise

TL;DR

This paper introduces a novel segmentation method for images degraded by blur and Poisson noise, combining anisotropic and isotropic total variation regularization within a MAP framework and solving it with ADMM, demonstrating superior performance.

Contribution

It proposes a new nonconvex model integrating AITV regularization and a MAP fidelity term for Poisson noise, with a tailored ADMM scheme and convergence proof.

Findings

Outperforms existing segmentation methods in various scenarios

Effective handling of Poisson noise with MAP fidelity term

Robust segmentation results on grayscale and color images

Abstract

In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by $k$-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.