Scale-space derived from B-splines

Abstract

This paper proposes a scale-space theory based on B-spline kernels. Our aim is twofold: 1) present a general framework, and show how B-splines provide a flexible tool to design various scale-space representations. In particular, we focus on the design of continuous scale-space and dyadic scale-space frame representations. A general algorithm is presented for fast implementation of continuous scale-space at rational scales. In the dyadic case, efficient frame algorithms are derived using B-spline techniques to analyze the geometry of an image. The relationship between several scale-space approaches is explored. The behavior of edge models, the properties of completeness, causality, and other properties in such a scale-space representation are examined in the framework of B-splines. It is shown that, besides the good properties inherited from the Gaussian kernel, the B-spline derived scale-space exhibits many advantages for modeling visual mechanism including the efficiency, compactness, orientation feature and parallel structure.