Image selective smoothing and edge detection by nonlinear diffusion. II

Luis ALVAREZ; Pierre Louis LIONS; Jean-Michel MOREL

doi:10.1137/0729052

Image selective smoothing and edge detection by nonlinear diffusion. II

Luis ALVAREZ^*
, Pierre Louis LIONS
, Jean-Michel MOREL

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

1085 Citations (Scopus)

Abstract

A stable algorithm is proposed for image restoration based on the 'mean curvature motion' equation. Existence and uniqueness of the 'viscosity' solution of the equation are proved, a L^∞ stable algorithm is given, experimental results are shown, and the subjacent vision model is compared with those introduced recently by several vision researchers. The algorithm presented appears to be the sharpest possible among the multiscale image smoothing methods preserving uniqueness and stability.

Original language	English
Pages (from-to)	845-866
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	29
Issue number	3
DOIs	https://doi.org/10.1137/0729052
Publication status	Published - Jun 1992
Externally published	Yes

Keywords

mean curvature motion of level sets
image restoration
viscosity solutions
multiscale vision models

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10.1137/0729052

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title = "Image selective smoothing and edge detection by nonlinear diffusion. II",

abstract = "A stable algorithm is proposed for image restoration based on the 'mean curvature motion' equation. Existence and uniqueness of the 'viscosity' solution of the equation are proved, a L∞ stable algorithm is given, experimental results are shown, and the subjacent vision model is compared with those introduced recently by several vision researchers. The algorithm presented appears to be the sharpest possible among the multiscale image smoothing methods preserving uniqueness and stability.",

keywords = "mean curvature motion of level sets, image restoration, viscosity solutions, multiscale vision models",

author = "Luis ALVAREZ and LIONS, \{Pierre Louis\} and Jean-Michel MOREL",

year = "1992",

month = jun,

doi = "10.1137/0729052",

language = "English",

volume = "29",

pages = "845--866",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

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T1 - Image selective smoothing and edge detection by nonlinear diffusion. II

AU - ALVAREZ, Luis

AU - LIONS, Pierre Louis

AU - MOREL, Jean-Michel

PY - 1992/6

Y1 - 1992/6

N2 - A stable algorithm is proposed for image restoration based on the 'mean curvature motion' equation. Existence and uniqueness of the 'viscosity' solution of the equation are proved, a L∞ stable algorithm is given, experimental results are shown, and the subjacent vision model is compared with those introduced recently by several vision researchers. The algorithm presented appears to be the sharpest possible among the multiscale image smoothing methods preserving uniqueness and stability.

AB - A stable algorithm is proposed for image restoration based on the 'mean curvature motion' equation. Existence and uniqueness of the 'viscosity' solution of the equation are proved, a L∞ stable algorithm is given, experimental results are shown, and the subjacent vision model is compared with those introduced recently by several vision researchers. The algorithm presented appears to be the sharpest possible among the multiscale image smoothing methods preserving uniqueness and stability.

KW - mean curvature motion of level sets

KW - image restoration

KW - viscosity solutions

KW - multiscale vision models

UR - https://www.scopus.com/pages/publications/0026883886

U2 - 10.1137/0729052

DO - 10.1137/0729052

M3 - Journal Article (refereed)

AN - SCOPUS:0026883886

SN - 0036-1429

VL - 29

SP - 845

EP - 866

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 3

ER -

Image selective smoothing and edge detection by nonlinear diffusion. II

Abstract

Keywords

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