Frontiers in Computer Science (Jun 2023)

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

  • Kevin Bui,
  • Yifei Lou,
  • Fredrick Park,
  • Jack Xin

DOI
https://doi.org/10.3389/fcomp.2023.1131317
Journal volume & issue
Vol. 5

Abstract

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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.

Keywords