Classification and local error estimation of interpolation and derivative filters for volume rendering

We describe a new method for analyzing, classifying, and evaluating filters, which can be applied to interpolation filters, and derivative filters. Our analysis is based on the Taylor series expansion of a convolution sum and some assumptions on the behavior of the data function. As a result of our analysis, we derive the need and the method for normalization of derivative filter coefficients. As an example, we demonstrate the utilization of our methods to the analysis of the class of cardinal cubic filters. Since our technique is not restricted to interpolation filters, we can show that the Catmull-Rom spline filter and its derivative are the most accurate reconstruction and derivative filter among this class of filters. We show that the derivative filter has a much higher impact on the rendered volume than the interpolation filter. We demonstrate the use of these optimal filters for accurate interpolation and gradient estimation in volume rendering.