Fast implementation of scale-space by interpolatory subdivision scheme

Abstract

While the scale-space approach has been widely used in computer vision, there has been a great interest in fast implementation of scale-space filtering. In this paper, we introduce an interpolatory subdivision scheme (ISS) for this purpose. In order to extract the geometric features in a scale-space representation, discrete derivative approximations are usually needed. Hence, a general procedure is also introduced to derive exact formulae for numerical differentiation with respect to this ISS. Then, from ISS, an algorithm is derived for fast approximation of scale-space filtering. Moreover, the relationship between the ISS and the Whittaker-Shannon sampling theorem and the commonly used spline technique is discussed. As an example of the application of ISS technique, we present some examples on fast implementation of λτ-spaces as introduced by Gokmen and Jain, which encompasses various famous edge detection filters. It is shown that the ISS technique demonstrates high performance in fast implementation of the scale-space filtering and feature extraction.