A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recursive algorithms for implementing digital image filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
A cross difference approach to the analysis of subdivision algorithms
Neural, Parallel & Scientific Computations
λτ-Space Representation of Images and Generalized Edge Detector
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Derived From B-Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stationary Subdivision
A new approach to numerical differentiation and integration
Mathematical and Computer Modelling: An International Journal
Image representations using multiscale differential operators
IEEE Transactions on Image Processing
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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.