Journal ArticleDOI
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TLDR
The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.About:
This article is published in Journal of Computational Physics.The article was published on 1988-11-01. It has received 13020 citations till now. The article focuses on the topics: Equations of motion & Curvature.read more
Citations
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Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
Journal ArticleDOI
Active contours without edges
Tony F. Chan,Luminita A. Vese +1 more
TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
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User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability
Paul A. Yushkevich,Joseph Piven,Heather C. Hazlett,Rachel Gimpel Smith,Sean Ho,James C. Gee,Guido Gerig +6 more
TL;DR: The methods and software engineering philosophy behind this new tool, ITK-SNAP, are described and the results of validation experiments performed in the context of an ongoing child autism neuroimaging study are provided, finding that SNAP is a highly reliable and efficient alternative to manual tracing.
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Geodesic active contours
TL;DR: A novel scheme for the detection of object boundaries based on active contours evolving in time according to intrinsic geometric measures of the image, allowing stable boundary detection when their gradients suffer from large variations, including gaps.
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User’s guide to viscosity solutions of second order partial differential equations
TL;DR: The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorem, and continuous dependence may now be proved by very efficient and striking arguments as discussed by the authors.
References
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Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
ShuChi-Wang,OsherStanley +1 more
TL;DR: This work extends earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes by providing a new simplified expression for the ENO constructio...
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Uniformly high order accurate essentially non-oscillatory schemes, 111
TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
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