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We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic… (More)

- Stanley Osher, Ronald Fedkiw
- Applied mathematical sciences
- 2003

- Yunyun Yang, Chunming Li, Chiu-Yen Kao, Stanley Osher
- IEEE Transactions on Image Processing
- 2008

Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in… (More)

- Xavier Bresson, Selim Esedoglu, Pierre Vandergheynst, Jean-Philippe Thiran, Stanley Osher
- Journal of Mathematical Imaging and Vision
- 2007

The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of local… (More)

We develop a fast method to localize the level set method of Osher and Sethian (1988, J. Comput. Phys. 79, 12) and address two important issues that are intrinsic to the level set method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reset the level set function to be a signed distance… (More)

- Guy Gilboa, Stanley Osher
- Multiscale Modeling & Simulation
- 2008

We propose the use of nonlocal operators to define new types of flows and functionals for image processing and elsewhere. A main advantage over classical PDE-based algorithms is the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional… (More)

The point at which they meet (the triple junction) has prescribed angles which can be shown [12] to be defined by A coupled level set method for the motion of multiple junctions (of, e.g., solid, liquid, and grain boundaries), which follows the gradient flow for an energy functional consisting of surface tension (proportional to length) and bulk energies… (More)

- Leonid I. Rudin, Stanley Osher
- ICIP
- 1994

The two main plagues of image restoration are oscillations and smoothing. Traditional image restoration techniques prevent parasitic oscillations by resorting to smooth regularization. Hence, singular image features and oscillatory textures cannot be restored. The usefulness of images obtained by smooth regularization is very limited. Regularized faces and… (More)

- Stanley Osher, Martin Burger, Donald Goldfarb, Jinjun Xu, Wotao Yin
- Multiscale Modeling & Simulation
- 2005

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, by using total variation regularization. We obtain rigorous convergence results, and… (More)

- Luminita A. Vese, Stanley Osher
- J. Sci. Comput.
- 2003

This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, we decompose a given (possible textured) image f into a sum of two functions u+v, where u ¥ BV is a function of… (More)