Scale space representations locally adapted to the geometry of base and target manifold

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Abstract

We generalize the Gaussian multi-resolution image paradigm for a Euclidean domain to general Riemannian base manifolds and also account for the codomain by considering the extension into a fibre bundle structure. We elaborate on aspects of parametrization and gauge, as these are important in practical applications. We subsequently scrutinize two examples that are of interest in bio-mathematical modeling, viz. scale space on the unit sphere, used among others for codomain regularization in the context of high angular resolution diffusion imaging (HARDI), and retino-cortical scale space, proposed as a biologically plausible model of the human visual pathway from retina to striate cortex.
Original languageEnglish
Title of host publicationMathematical Methods for Signal and Image Analysis and Representation
EditorsL.M.J. Florack, R. Duits, G. Jongbloed, M.N.M. Lieshout, van, P.L. Davies
Place of PublicationLondon
PublisherSpringer
Pages159-171
ISBN (Print)978-1-4471-2352-1
DOIs
Publication statusPublished - 2012

Publication series

NameComputational Imaging and Vision
Volume41
ISSN (Print)1381-6446

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Florack, L. M. J. (2012). Scale space representations locally adapted to the geometry of base and target manifold. In L. M. J. Florack, R. Duits, G. Jongbloed, M. N. M. Lieshout, van, & P. L. Davies (Eds.), Mathematical Methods for Signal and Image Analysis and Representation (pp. 159-171). (Computational Imaging and Vision; Vol. 41). London: Springer. https://doi.org/10.1007/978-1-4471-2353-8_9