An algorithm for minimizing the Mumford-Shah functional

T Pock, D Cremers, H Bischof… - 2009 IEEE 12th …, 2009 - ieeexplore.ieee.org
In this work we revisit the Mumford-Shah functional, one of the most studied variational
approaches to image segmentation. The contribution of this paper is to propose an algorithm …

A two-stage image segmentation method using a convex variant of the Mumford--Shah model and thresholding

X Cai, R Chan, T Zeng - SIAM Journal on Imaging Sciences, 2013 - SIAM
The Mumford--Shah model is one of the most important image segmentation models and
has been studied extensively in the last twenty years. In this paper, we propose a two-stage …

Two-stage image segmentation based on nonconvex ℓ2− ℓp approximation and thresholding

T Wu, J Shao, X Gu, MK Ng, T Zeng - Applied Mathematics and …, 2021 - Elsevier
Image segmentation is of great importance in image processing. In this paper, we propose a
two-stage image segmentation strategy based on the nonconvex ℓ 2− ℓ p approximation of …

A two-stage image segmentation method for blurry images with poisson or multiplicative gamma noise

R Chan, H Yang, T Zeng - SIAM Journal on Imaging Sciences, 2014 - SIAM
In this paper, a two-stage method for segmenting blurry images in the presence of Poisson
or multiplicative Gamma noise is proposed. The method is inspired by a previous work on …

A Gaussian hypermodel to recover blocky objects

D Calvetti, E Somersalo - Inverse problems, 2007 - iopscience.iop.org
The paper discusses inverse problems in which the unknown is a function that is assumed to
be piecewise smooth with discontinuities of unknown location and size. If the locations of the …

[PDF][PDF] Image segmentation via Fischer-Burmeister total variation and thresholding

T Wu, Y Zhao, Z Mao, L Shi, Z Li, Y Zeng - Adv. Appl. Math. Mech, 2022 - doc.global-sci.org
Image segmentation is a significant problem in image processing. In this paper, we propose
a new two-stage scheme for segmentation based on the Fischer-Burmeister total variation …

Existence of infinitely many solutions for the one-dimensional Perona-Malik model

K Zhang - Calculus of Variations and Partial Differential …, 2006 - Springer
We establish the existence of infinitely many weak solutions for the the one-dimensional
version of the well-known and widely used Perona-Malik anisotropic diffusion equation …

A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional

M Gobbino, N Picenni - Transactions of the American Mathematical Society, 2023 - ams.org
We consider the Perona-Malik functional in dimension one, namely an integral functional
whose Lagrangian is convex-concave with respect to the derivative, with a convexification …

[PDF][PDF] Non-convex and convex coupling image segmentation via TGpV regularization and thresholding

T Wu, J Shao - Adv. Appl. Math. Mech, 2020 - researchgate.net
In this paper, we propose a non-convex and convex coupling variational model for image
segmentation. We design the non-convex and convex regularization terms based on total …

From Mumford–Shah to Perona–Malik in image processing

B Kawohl - Mathematical methods in the applied sciences, 2004 - Wiley Online Library
In mathematical image processing we are often presented with amazing examples of image
enhancement algorithms. Yet, when applied to different noisy images, they can produce …