Weberized Mumford-Shah Model with Bose-Einstein Photon Noise

@article{Shen2006WeberizedMM,
  title={Weberized Mumford-Shah Model with Bose-Einstein Photon Noise},
  author={Jianhong Shen and Yoon Mo Jung},
  journal={Applied Mathematics and Optimization},
  year={2006},
  volume={53},
  pages={331-358}
}
AbstractHuman vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber's Law. The current paper develops a new segmentation model based on the integration of Weber's Law and the celebrated Mumford-Shah segmentation model (Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989). Explained in… Expand

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References

SHOWING 1-10 OF 53 REFERENCES
Geometry-Driven Diffusion in Computer Vision
  • B. H. Romeny
  • Mathematics, Computer Science
  • Computational Imaging and Vision
  • 1994
TLDR
This paper presents a meta-analyses of differential Invariant Signatures and Flows in Computer Vision: a Symmetry Group approach P. Sapiro, A. Tannenbaum, and a Differential Geometric Approach to Anisotropic Diffusion. Expand
Euler's Elastica and Curvature-Based Inpainting
TLDR
A computational scheme based on numerical PDEs is presented, which allows the automatic handling of topologically complex inpainting domains and connects to the earlier works of Bertalmio, Sapiro, Caselles, and Ballester. Expand
Variational PDE models in image processing
TLDR
A broad picture of mathematical image processing is given through one of the most recent and very successful approaches - the variational PDE method, which discusses two crucial ingredients for image processing: image modeling or representation, and processor modeling. Expand
Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
TLDR
The resulting active contour model offers a tractable implementation of the original Mumford-Shah model to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner and leads to a novel PDE-based approach for simultaneous image magnification, segmentation, and smoothing. Expand
Total variation based image restoration with free local constraints
  • L. Rudin, S. Osher
  • Mathematics, Computer Science
  • Proceedings of 1st International Conference on Image Processing
  • 1994
TLDR
A new total variation based approach was developed by Rudin, Osher and Fatemi to overcome the basic limitations of all smooth regularization algorithms, using the L/sup 1/ norm of the magnitude of a gradient, thus making discontinuous and nonsmooth solutions possible. Expand
Optimal approximations by piecewise smooth functions and associated variational problems
Abstract : This reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamentalExpand
Retinal light adaptation—evidence for a feedback mechanism
TLDR
A family of horizontal-cell temporal frequency responses, measured at various mean light levels, could be accounted for by a negative feedback model in which the feedback strength is proportional to mean light level. Expand
Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
  • A. Chambolle
  • Mathematics, Computer Science
  • SIAM J. Appl. Math.
  • 1995
TLDR
This paper discusses the links between Mumford and Shah’s variational problem for (signal and) image segmentation, based on an energy functional of a continuous grey-level function, and the numerical algorithms proposed to solve it, which are based on a discrete functional. Expand
Mathematical Models for Local Nontexture Inpaintings
TLDR
The broad applications of the inpainting models are demonstrated through restoring scratched old photos, disocclusion in vision analysis, text removal, digital zooming, and edge-based image coding. Expand
A level set algorithm for minimizing the Mumford-Shah functional in image processing
  • T. Chan, L. Vese
  • Mathematics
  • Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision
  • 2001
We show how the piecewise-smooth Mumford-Shah segmentation problem can be solved using the level set method of Osher and Sethian (1988). The obtained algorithm can be simultaneously used to denoise,Expand
...
1
2
3
4
5
...