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.
|Title of host publication||Mathematical Methods for Signal and Image Analysis and Representation|
|Editors||L.M.J. Florack, R. Duits, G. Jongbloed, M.N.M. Lieshout, van, P.L. Davies|
|Place of Publication||London|
|Publication status||Published - 2012|
|Name||Computational Imaging and Vision|
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