A general framework for multiscale image representations using B-spline approaches

Scale is a basic aspect of image modeling. The Gaussian kernel has long been used in multiscale image analysis. This paper presents a general framework for mutiscale geometric representations using S-splines instead of the Gaussian. The following computational and statistical issues will be discussed. (a) The construction of wavelets using S-splines leads to computationally efficient algorithms. We show that for a class of wavelets, their masks can be factored into simple-B-spline factors. As a result, these wavelets can be implemented using fast filter bank algorithms, (b) The analysis of statistical properties of wavelet transforms can be facilitated using B-splines. We show how the statistical properties of the class of wavelet transforms that are derived from S-splines can be easily deduced from those of the Gaussian function since it approximates the -B-splines.