An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

TL;DR

This paper introduces a fast, multi-stage image segmentation framework called SaT that combines weighted anisotropic and isotropic total variation, effectively handling noisy and blurred images with high accuracy.

Contribution

The paper proposes a novel segmentation method using a weighted AITV regularizer within a Mumford-Shah model, solved efficiently with ADMM, and demonstrates superior performance over existing TV-based methods.

Findings

Efficient segmentation within seconds for grayscale and color images.

Robustness to noise and blur in input images.

Quantitative and qualitative improvements over traditional TV methods.

Abstract

In this paper, we design an efficient, multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation (AITV). The segmentation framework generally consists of two stages: smoothing and thresholding, thus referred to as SaT. In the first stage, a smoothed image is obtained by an AITV-regularized Mumford-Shah (MS) model, which can be solved efficiently by the alternating direction method of multipliers (ADMM) with a closed-form solution of a proximal operator of the $\ell_1 -\alpha \ell_2$ regularizer. Convergence of the ADMM algorithm is analyzed. In the second stage, we threshold the smoothed image by $K$-means clustering to obtain the final segmentation result. Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images, efficient in producing high-quality segmentation results within a few seconds, and robust to input images that are corrupted with noise, blur, or both. We compare the AITV method with its original convex TV and nonconvex TV$^p (0<p<1)$ counterparts, showcasing the qualitative and quantitative advantages of our proposed method.