The Perona-Malik paradox

被引：165

作者：

Kichenassamy, S

机构：

[1] School of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis, MN 55455-0487, 206 Church St., S.E.

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1997年 / 57卷 / 05期

关键词：

Perona-Malik equation; computer vision; ill-posed equations; nonlinear diffusions; scale-space;

D O I：

10.1137/S003613999529558X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Perona-Malik equation is a formally ill-posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable. After discussing the background of this paradox in computer vision, this paper shows the nonexistence of weak solutions even in those cases where computations are successful, and introduces a notion of generalized solutions for this equation, which do evolve smoothly and possess many of the features of numerical calculations.

引用

页码：1328 / 1342

页数：15

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