A theoretical framework for convex regularizers in PDE-based computation of image motion

Weickert, Joachim ; Schnörr, Christoph

2000_13.pdf - Published

Download (1MB)

URL: https://ub-madoc.bib.uni-mannheim.de/1841
URN: urn:nbn:de:bsz:180-madoc-18412
Document Type: Working paper
Year of publication: 2000
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Classification: MSC: 68U99 68U10 68T45 ,
Subject headings (SWD): Bildfolge , Diffusion , Anisotrope Diffusion
Keywords (English): optic flow , differential methods , regularization , diffusion filtering , well-posedness
Abstract: Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which reqires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
Additional information:

Dieser Eintrag ist Teil der Universitätsbibliographie.

Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.

Metadata export


+ Search Authors in

+ Download Statistics

Downloads per month over past year

View more statistics

You have found an error? Please let us know about your desired correction here: E-Mail

Actions (login required)

Show item Show item