The Taub Faculty of Computer Science Events and Talks

new framework is proposed for variational analysis and processing. It defines a functional-based nonlinear transform and inverse-transform. The framework is developed in the context of total-variation (TV), but it can be generalized to other one-homogeneous functionals.

An eigenfunction, with respect to the subdifferential of the functional, such as a disk in the TV case, yields an impulse in the transform domain. This can be viewed as a generalization of known spectral approaches, based on linear algebra, which are extensively used in image-processing, e.g. for segmentation.

Following the Fourier intuition, a spectrum can be computed to analyze dominant scales in the image. Moreover, new nonlinear low-pass, high-pass and band-pass filters can be designed with very precise scale selection.

Relations to sparse signals and to nonlocal-TV will be discussed. An example of a texture processing application will be shown, illustrating possible benefits of this new framework.