Image processing via shift-twist invariant operations on orientation bundle functions

R. Duits, M.A. Almsick, van, M. Duits, E.M. Franken, L.M.J. Florack

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Abstract

Inspired by our own visual system we consider the construction of-and reconstruction from- an orientation bundle function (OBF) Uf : R2 ¿ S1 ¿C as a local orientation score of an image, f : R2 ¿ R, via a wavelet transform W¿ corresponding to a representation of the Euclidean motion group onto L2(R2) and oriented wavelet ¿ ¿L2(R2). This wavelet transform is a unitary mapping with stable inverse, which allows us to directly relate each operation ¿ on OBF’s to an operation ¿ on images in a robust manner. We examine the geometry of the domain of an OBF and show that the only sensible operations on OBF’s are non-linear and shift-twist invariant. As an example we consider all linear 2nd order shift-twist invariant evolution equations on OBF’s corresponding to stochastic processes on the Euclidean motion group in order to construct nonlinear shift-twist invariant operations on OBF’s. Given two such stochastic processes we derive the probability density that particles of the different processes collide. As an application we detect elongated structures in images and automatically close the gaps between them.
Original languageEnglish
Title of host publicationProceedings of the Tenth Annual Conference of the Advanced School for Computing and Imaging (ASCI 2004), Port Zélande, Ouddorp, The Netherlands, June 2-4, 2004
EditorsJ.J. Wijk, van, J.W.J. Heijnsdijk, K.G. Langendoen, R. Veltkamp
Place of PublicationDelft
PublisherAdvanced School for Computing and Imaging (ASCI)
Pages57-62
ISBN (Print)90-803086-9-2
Publication statusPublished - 2004
Event10th Annual Conference of the Advanced School for Computing and Imaging (ASCI 2004), Port Zélande, Ouddorp, June 2-4, 2004 - Port Zélande, Ouddorp, Netherlands
Duration: 2 Jun 20044 Jun 2004

Conference

Conference10th Annual Conference of the Advanced School for Computing and Imaging (ASCI 2004), Port Zélande, Ouddorp, June 2-4, 2004
Abbreviated titleASCI 2004
CountryNetherlands
CityOuddorp
Period2/06/044/06/04

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