Nonlinear diffusion on the 2D Euclidean motion group

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

14 Citaten (Scopus)
84 Downloads (Pure)

Samenvatting

Linear and nonlinear diffusion equations are usually considered on an image, which is in fact a function on the translation group. In this paper we study diffusion on orientation scores, i.e. on functions on the Euclidean motion group SE(2). An orientation score is obtained from an image by a linear invertible transformation. The goal is to enhance elongated structures by applying nonlinear left-invariant diffusion on the orientation score of the image. For this purpose we describe how we can use Gaussian derivatives to obtain regularized left-invariant derivatives that obey the non-commutative structure of the Lie algebra of SE(2). The Hessian constructed with these derivatives is used to estimate local curvature and orientation strength and the diffusion is made nonlinearly dependent on these measures. We propose an explicit finite difference scheme to apply the nonlinear diffusion on orientation scores. The experiments show that preservation of crossing structures is the main advantage compared to approaches such as coherence enhancing diffusion.
Originele taal-2Engels
TitelProceedings of the First International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2007) 30 May - 2 June 2007, Ischia, Italy
RedacteurenF. Sgallari, A. Murli, N. Paragios
Plaats van productieBerlin, Germany
UitgeverijSpringer
Pagina's461-472
ISBN van geprinte versie978-3-540-72822-1
DOI's
StatusGepubliceerd - 2007
Evenementconference; SSVM 2007, Ischia, Italy; 2007-05-30; 2007-06-02 -
Duur: 30 mei 20072 jun 2007

Publicatie series

NaamLecture Notes in Computer Science
Volume4485
ISSN van geprinte versie0302-9743

Congres

Congresconference; SSVM 2007, Ischia, Italy; 2007-05-30; 2007-06-02
Periode30/05/072/06/07
AnderSSVM 2007, Ischia, Italy

Vingerafdruk Duik in de onderzoeksthema's van 'Nonlinear diffusion on the 2D Euclidean motion group'. Samen vormen ze een unieke vingerafdruk.

  • Citeer dit

    Franken, E. M., Duits, R., & Haar Romenij, ter, B. M. (2007). Nonlinear diffusion on the 2D Euclidean motion group. In F. Sgallari, A. Murli, & N. Paragios (editors), Proceedings of the First International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2007) 30 May - 2 June 2007, Ischia, Italy (blz. 461-472). (Lecture Notes in Computer Science; Vol. 4485). Springer. https://doi.org/10.1007/978-3-540-72823-8_40