Paper Info
Title
The Convex-Hull-Stripping Median Approximates Affine Curvature Motion.
Abstract
The median filter is one of the fundamental filters in image processing. Its standard realisation relies on a rank ordering of given data which is easy to perform if the given data are scalar values. However, the generalisation of the median filter to multivariate data is a delicate issue. One of the methods of potential interest for computing a multivariate median is the convex-hull-stripping median from the statistics literature. Its definition is of purely algorithmical nature, and it offers the advantageous property of affine equivariance. While it is a classic result that the standard median filter approximates mean curvature motion, no corresponding assertion has been established up to now for the convex-hull-stripping median. The aim of our paper is to close this gap in the literature. In order to provide a theoretical foundation for the convex-hull-stripping median of multivariate images, we investigate its continuous-scale limit. It turns out that the resulting evolution is described by the well-known partial differential equation of affine curvature motion. Thus we have established in this paper a relation between two important models from image processing and statistics. We also present some experiments that support our theoretical findings.
Year
DOI
Venue
2019
10.1007/978-3-030-22368-7_16
Lecture Notes in Computer Science
Keywords
DocType
Volume
Median filter,Convex hull stripping,Partial differential equations,Curve evolution
Conference
11603
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Martin Welk140437.36
Michael Breuß216825.45