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

arXiv: https://arxiv.org/abs/2202.10115 · HTML: https://mlsanity.com/paper/2202.10115/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 97 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [A Scale Invariant Approach for Sparse Signal Recovery](https://mlsanity.com/paper/1812.08852/) (2018)
- [Limited-angle CT reconstruction via the L1/L2 minimization](https://mlsanity.com/paper/2006.00601/) (2020)
- [A Three-stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)](https://mlsanity.com/paper/1506.00060/) (2015)
- [The iterative convolution-thresholding method (ICTM) for image segmentation](https://mlsanity.com/paper/1904.10917/) (2019)
- [A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity](https://mlsanity.com/paper/1504.02206/) (2015)
- [A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation](https://mlsanity.com/paper/2005.04401/) (2020)
- [Minimizing L1 over L2 norms on the gradient](https://mlsanity.com/paper/2101.00809/) (2021)

## Built on by (most cited first, 2 of 2)

- [Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise](https://mlsanity.com/paper/2301.03393/) (2023)
- [MBO Scheme for Local Chan--Vese Segmentation](https://mlsanity.com/paper/2608.00893/) (2026)

## Abstract (arXiv)

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 ℓ1 -α ℓ2 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 TVp (0<p<1) counterparts, showcasing the qualitative and quantitative advantages of our proposed method.