Steerable filters for multirate shape extraction

Multirate systems have achieved great success for image coding, and demonstrable success for the extraction of edge and line features. There have been no reports of multirate techniques for the extraction of more complex shape features, such as medial axes, or for the location of particular shapes, such as circles. Here, we show how adaptive, multirate filtering can be used to implement a threshold-free compact Hough transform. We use steerable, quadrature wavelets to generate feature fields at a number of sampling rates, then apply what we term “action at a distance wavelets” to synthesize shape detection kernels for generating accumulator spaces weighted by feature response. The technique is shown to work under different choices of feature detector and scale-space sampling, such as linear Gaussian scale space. Using a Bayesian formulation, we explicitly show the relationship between the choice of feature detectors and the corresponding shape kernels. The performance of the algorithm on some test images is presented and analysed