From Gaussian scale-space to B-spline scale-space

The Gaussian kernel has long been used in the classical multiscale analysis. The purpose of the paper is to propose the uniform B-spline as an alternative for the visual modeling. A general framework for various scale-space representations is formulated using the B-spline approach. In particular, the evolution of the wavelet models can be well understood from such an approach. Most of the wavelet representations can be factored into B-spline bases and hence can be implemented efficiently using the spline technique. Besides, it is shown that the B-spline scale-space representations not only inherit most of the properties of the Gaussian scale-space but also have many advantages with respect to the efficiency, compactness and parallel structure.