Fast implementation of scale-space by interpolatory subdivision scheme

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. 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 (1997), 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