A new generalised $\alpha$ scale spaces quadrature filters
Résumé
The $\alpha$ scale spaces is a recent theory that opens new possibilities of phase-based image processing. It is a parameterised class $(\alpha\in]0,1])$ of linear scale space representations, which allows a continuous connection beyond the well-known Gaussian scale space ($\alpha$=1). In this paper, we make use of this unified representation to derive new families of band pass quadrature filters, built from derivatives and difference of the $\alpha$ scale space generating kernels. This construction leads to \rev{generalised} $\alpha$ kernel filters including the commonly known families derived from the Gaussian and the Poisson kernels. The properties of each family are first studied and then experiments on one and two dimensional signals are shown to exemplify how the suggested filters can be used for edge detection. This work is complemented by an experimental evaluation, which demonstrates that the new proposed filters are a good alternative to the commonly used Log-Gabor filter.