# A Three-stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)

arXiv: https://arxiv.org/abs/1506.00060 · HTML: https://mlsanity.com/paper/1506.00060/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2015.

## Built on by (most cited first, 9 of 9)

- [Classification of Hyperspectral Images Using SVM with Shape-adaptive Reconstruction and Smoothed Total Variation](https://mlsanity.com/paper/2203.15619/) (2022)
- [A 3-stage Spectral-spatial Method for Hyperspectral Image Classification](https://mlsanity.com/paper/2204.09294/) (2022)
- [Semi-supervised Change Detection of Small Water Bodies Using RGB and Multispectral Images in Peruvian Rainforests](https://mlsanity.com/paper/2206.09365/) (2022)
- [Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation](https://mlsanity.com/paper/2307.09052/) (2023)
- [An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation](https://mlsanity.com/paper/2202.10115/) (2022)
- [An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation](https://mlsanity.com/paper/2203.09036/) (2022)
- [A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Models](https://mlsanity.com/paper/2209.01375/) (2022)
- [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 propose a SLaT (Smoothing, Lifting and Thresholding) method with three stages for multiphase segmentation of color images corrupted by different degradations: noise, information loss, and blur. At the first stage, a convex variant of the Mumford-Shah model is applied to each channel to obtain a smooth image. We show that the model has unique solution under the different degradations. In order to properly handle the color information, the second stage is dimension lifting where we consider a new vector-valued image composed of the restored image and its transform in the secondary color space with additional information. This ensures that even if the first color space has highly correlated channels, we can still have enough information to give good segmentation results. In the last stage, we apply multichannel thresholding to the combined vector-valued image to find the segmentation. The number of phases is only required in the last stage, so users can choose or change it all without the need of solving the previous stages again. Experiments demonstrate that our SLaT method gives excellent results in terms of segmentation quality and CPU time in comparison with other state-of-the-art segmentation methods.