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Fast Implementation of Scale-Space by Interpolatory Subdivision Scheme
September 1999 (vol. 21 no. 9)
pp. 933-939

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 $\lambda \tau$-spaces as introduced by Gökmen and Jain [12], 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.

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Index Terms:
Scale-space, interpolatory subdivision scheme, $B$-splines, edge detection, image representation.
Citation:
Yu-Ping Wang, Ruibin Qu, "Fast Implementation of Scale-Space by Interpolatory Subdivision Scheme," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 9, pp. 933-939, Sept. 1999, doi:10.1109/34.790434
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