EVALUATION AND DESIGN OF FILTERS USING A TAYLOR-SERIES EXPANSION

We describe a new method for analyzing, classifying, and evaluating fi lters that can be applied to interpolation filters as well as to arbit rary derivative filters of any order. Our analysis is based on the Tay lor series expansion of the convolution sum. Our analysis shows the ne ed and derives the method for the normalization of derivative filter w eights. Under certain minimal restrictions of the underlying function, we are able to compute tight absolute error bounds of the reconstruct ion process. We demonstrate the utilization of our methods to the anal ysis of the class of cubic BC-spline filters. As our technique is not restricted to interpolation filters, we are able to show that the Catm ull-Rom spline filter and its derivative are the most accurate reconst ruction and derivative filters, respectively, among the class of BC-sp line filters. We also present a new derivative filter which features b etter spatial accuracy than any derivative BC-spline filter, and is op timal within our framework. We conclude by demonstrating the use of th ese optimal filters for accurate interpolation and gradient estimation in volume rendering.