Proceedings Article10.1109/CVPR.1992.223119
Segmentation by nonlinear diffusion. II
Jayant Shah
- 03 Jun 1991
- pp 644-647
66
TL;DR: An algorithm that systematically uses nonuniform smoothing to find boundary components in the form of connected, regularized curves is presented.
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Abstract: A global model which integrates three sequential steps for segmenting an image, namely, noise-filtering, local edge-detection, and integration of local edges into object boundaries, is described. The model overcomes some of the difficulties inherent in earlier global models, particularly their tendency to oversegment, and the lack of practical numerical algorithms for implementing them. The model consists of two coupled elliptic functionals, one for smoothing out the noise, and the other for boundary detection. The latter is obtained by regularizing the usual pointwise thresholding employed for boundary detection. The first variation of these functionals leads to coupled system of diffusion equations which are implemented by a simple finite difference scheme. The scheme may easily be converted into a parallel algorithm. >
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Citations
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Anisotropic diffusion in image processing
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109
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Multiscale geodesic active contours for ultrasound image segmentation using speckle reducing anisotropic diffusion
Weiming Wang,Lei Zhu,Jing Qin,Jing Qin,Yim-Pan Chui,Yim-Pan Chui,Bing Nan Li,Pheng-Ann Heng,Pheng-Ann Heng +8 more
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66
References
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Snakes : Active Contour Models
TL;DR: This work uses snakes for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest, and uses scale-space continuation to enlarge the capture region surrounding a feature.
Scale-space and edge detection using anisotropic diffusion
Pietro Perona,Jitendra Malik +1 more
TL;DR: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced, chosen to vary spatially in such a way as to encourage intra Region smoothing rather than interregion smoothing.
Optimal approximations by piecewise smooth functions and associated variational problems
David Mumford,Jayant Shah +1 more
TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.
Approximation of functional depending on jumps by elliptic functional via t-convergence
TL;DR: It is shown how it is possible to approximate the Mumford-Shah image segmentation functional by elliptic functionals defined on Sobolev spaces by ellipsoidal functionals, using the De Giorgi F-convergence.
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