1,721,106 research outputs found
Non-Linear scale-spaces isomorphic to the linear case with applications to scalar, vector and multispectral images
No full textA basic requirement of scale-space representations in general is that of scale causality, which states that local extrema in the image should not be enhanced when resolution is diminished. We consider a special class of nonlinear scale-spaces consistent with this constraint, which can be linearised by a suitable isomorphism in the grey-scale domain so as to reproduce the familiar Gaussian scale-space. We consider instances in which nonlinear representations may be the preferred choice, as well as instances in which they enter by necessity. We also establish their relation to morphological scale-space representations based on a quadratic structuring function
Scale space representations locally adapted to the geometry of base and target manifold
Get PDFWe 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
A Geometric Model for Cortical Magnification
No full textA Riemannian manifold endowed with a conformal metric is proposed as a geometric model for the cortical magnification that characterises foveal systems. The eccentricity scaling of receptive fields, the relative size of the foveola, as well as the fraction of receptive fields involved in foveal vision can all be deduced from it
Coarse-to-fine partitioning of signals
Get PDFAn empirically acquired signal can be analyzed in a multi-scale framework. Its multi-scale structure induces a hierarchical partitioning of the signal domain into topologically meaningful segments. A method is proposed to operationalize this using elementary results from singularity theory for certain generic solutions of the one-dimensional heat equatio
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