Nonlinear diffusion of scalar images using well-posed differential operators

W.J. Niessen, B.M. Haar Romenij, ter, L.M.J. Florack, A.H. Salden, M.A. Viergever

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

5 Citations (Scopus)

Abstract

In recent years several nonlinear diffusion schemes have been introduced. In this paper we will discuss the numerical implementation of a number of current nonlinear evolution schemes, using the notion of well-posed differentiation by Gaussian kernels. The infinitesimal change of an image when increasing scale depends on the local differential invariants evaluated at the scale of the image considered, i.e. on terms of the local jet (the set of all spatial partial derivatives at that point). All these differential terms can be obtained in a well-posed fashion by a convolution of the original image with the family of the Gaussian and its derivatives. The nonlinear partial differential equation can thus be numerically approximated by an iterative calculation of the appropriate terms in the local jet. Examples are given for medical images.
Original languageEnglish
Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (ICPR 12), June 21-23, 1994, Jerusalem, Israel
Place of PublicationLos Alamitos, Calif.
PublisherIEEE Computer Society
Pages92-97
ISBN (Print)0-8186-6265-4
DOIs
Publication statusPublished - 1994
Eventconference; IAPR International Conference on Pattern Recognition (ICPR) ; 12 (Jerusalem) : June 21-23, 1994; 1994-06-21; 1994-06-23 -
Duration: 21 Jun 199423 Jun 1994

Conference

Conferenceconference; IAPR International Conference on Pattern Recognition (ICPR) ; 12 (Jerusalem) : June 21-23, 1994; 1994-06-21; 1994-06-23
Period21/06/9423/06/94
OtherIAPR International Conference on Pattern Recognition (ICPR) ; 12 (Jerusalem) : June 21-23, 1994

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