Fast implementation of scale-space by interpolatory subdivision scheme

While the scale-space approach has been widely used in computer vision, the re has been a great interest in fast implementation of scale-space filterin g. In this paper, we introduce an interpolatory subdivision scheme (ISS) fo r this purpose. In order to extract the geometric features in a scale-space representation, discrete derivative approximations are usually needed. Hen ce, a general procedure is also introduced to derive exact formulae for num erical differentiation with respect to this ISS. Then, from ISS, an algorit hm is derived for fast approximation of scale-space filtering. Moreover, th e relationship between the ISS and the Whittaker-Shannon sampling theorem a nd the commonly used spline technique is discussed. As an example of the ap plication of ISS technique, we present some examples on fast implementation of lambda tau-spaces as introduced by Gokmen and Jain [12], which encompas ses various famous edge detection filters. It is shown that the ISS techniq ue demonstrates high performance in fast implementation of the scale-space filtering and feature extraction.