Optimal filter design for volume reconstruction and visualization

Digital filtering is a crucial operation in volume reconstruction and visualization. Lowpass filters are needed for subsampling and minification. Interpolation filters are needed for registration and magnification, and to compensate for geometric distortions introduced by scanners. Interpolation filters are also needed in volume rendering for ray-casting and slicing. In this paper, we describe a method for digital filter design of interpolation filters based on weighted Chebyshev minimization. The accuracy of the resulting filters are compared with some commonly used filters defined by piecewise cubic polynomials. A significant finding of this paper is that although piecewise cubic interpolation has some computational advantages and may yield visually satisfactory results for some data, other data result in artifacts such as blurring. Furthermore, piecewise cubic filters are inferior for operations such as registration. Better results are obtained by the filters derived in this papers at only small increases in computation