Multiscale Analysis of Similarities between Images on Riemannian Manifolds

Multiscale Analysis of Similarities between Images on Riemannian Manifolds

Linear Multiscale Analysis of Similarities between Images on Riemannian Manifolds: Practical Formula and Affine Covariant Metrics

In this paper we study the problem of comparing two patches of images defined on Riemannian manifolds which in turn can be defined by each image domain with a suitable metric depending on the image. For that we single out one particular instance of a set of models defining image similarities that was earlier studied in [C. Ballester et al., Multiscale Model. Simul., 12 (2014), pp. 616–649], usi...

Multiscale Analysis for Images on Riemannian Manifolds

Abstract. In this paper we study multiscale analyses for images defined on Riemannian manifolds and extend the axiomatic approach proposed by Álvarez, Guichard, Lions, and Morel to this general case. This covers the case of twoand three-dimensional images and video sequences. After obtaining the general classification, we consider the case of morphological scale spaces, which are given in terms...

Harmonic Morphisms between Riemannian Manifolds

Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) twistor methods, (ii) harmonic morphisms with one-dimensional fibres; in particular we shall outline the co...

Multiresolution analysis on compact Riemannian manifolds

The problem of representation and analysis of manifold defined functions (signals, images, and data in general) is ubiquities in neuroscience, medical and biological applications. In the context of modeling the computations of the cortex, some twenty years ago, Mumford noted: “... the set of higher level concepts will automatically have geometric structure”. Indeed, in Vision input images can b...