학술논문
Evaluation and design of filters using a Taylor series expansion
Document Type
Periodical
Author
Source
IEEE Transactions on Visualization and Computer Graphics IEEE Trans. Visual. Comput. Graphics Visualization and Computer Graphics, IEEE Transactions on. 3(2):184-199 Jun, 1997
Subject
Language
ISSN
1077-2626
1941-0506
2160-9306
1941-0506
2160-9306
Abstract
We describe a new method for analyzing, classifying, and evaluating filters that can be applied to interpolation filters as well as to arbitrary derivative filters of any order. Our analysis is based on the Taylor series expansion of the convolution sum. Our analysis shows the need and derives the method for the normalization of derivative filter weights. Under certain minimal restrictions of the underlying function, we are able to compute tight absolute error bounds of the reconstruction process. We demonstrate the utilization of our methods to the analysis of the class of cubic BC-spline filters. As our technique is not restricted to interpolation filters, we are able to show that the Catmull-Rom spline filter and its derivative are the most accurate reconstruction and derivative filters, respectively, among the class of BC-spline filters. We also present a new derivative filter which features better spatial accuracy than any derivative BC-spline filter, and is optimal within our framework. We conclude by demonstrating the use of these optimal filters for accurate interpolation and gradient estimation in volume rendering.