Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise
This work addresses segmentation challenges in images degraded by blur and Poisson noise, which is an incremental improvement over existing smoothing-and-thresholding methods.
The paper tackles image segmentation under blur and Poisson noise by proposing a method that replaces Gaussian noise handling with a MAP term and uses a weighted difference of anisotropic and isotropic total variation for regularization, showing it outperforms several existing methods including the original SaT framework in numerical experiments.
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.