Mathematical analysis of adaptive multiscale texture operators

Establish the mathematical analysis of nonlinear and spatially adaptive multiscale texture operators whose observation scale depends on spatial position or evolves according to local image features.

Background

The paper uses a globally prescribed scale parameter and an r-adic discretization to analyze texture persistence across scales. In practical images, however, the characteristic texture scale may vary from one spatial location to another.

The authors propose adaptive operators in which the observation scale depends on position or local image features. Because such operators are nonlinear and spatially adaptive, their analytical properties fall outside the theory established in the paper and are explicitly declared unresolved.