Local Image Analysis Using Higher-Order Riesz Transforms
Ross Marchant, James Cook University / CSIRO Computational Informatics

Seminar • 04 November 2013 • BM 4.233

Abstract
The Riesz transform can be used to model local image structure as a superposition of sinusoids, where phase describes feature type (line or edge) and amplitude describes feature strength. Current models consist of one or two sinusoids and are derived analytically, limiting the order of Riesz transform used. In this talk, we introduce an expanded set of signal models. The single sinusoidal model of the monogenic signal is modified to have a residual component, allowing higher-order Reisz transforms to be included in the derivation. This improves the parameter estimation and leads to a new method of detecting junctions and corners. Following on, a multi-sinusoidal model consisting of any number of sinusoids is described, allowing features consisting of any number of lines or edges to be analysed. To find the model parameters, a recent method from super-resolution theory is applied. Finally, junctions and corners are not well modelled by sinusoids. To analyse these features we propose a model consisting of the superposition of a 2D steerable wavelet at multiple amplitudes and orientations. The component wavelet corresponds to either a line segment or an edge segment, depending on the feature of interest.