Non-Linear Scale-Spaces Isomorphic to the Linear Case with Applications to Scalar, Vector and Multispectral Images

摘要

A 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.