One Step Further Beyond Trilinear Interpolation and Central Differences: Triquadratic Reconstruction and its Analytic Derivatives at the Cost of One Additional Texture Fetch

Abstract

Recently, it has been shown that the quality of GPU-based trilinear volume resampling can be significantly improved if the six additional trilinear samples evaluated for the gradient estimation also contribute to the reconstruction of the underlying function [Csé19]. Although this improvement increases the approximation order from two to three without any extra cost, the continuity order remains C0. In this paper, we go one step further showing that a C1 continuous triquadratic B-spline reconstruction and its analytic partial derivatives can be evaluated by taking only one more trilinear sample into account. Thus, our method is the first volume-resampling technique that is nearly as fast as trilinear interpolation combined with on-thefly central differencing, but provides a higher-quality reconstruction together with a consistent analytic gradient calculation. Furthermore, we show that our fast evaluation scheme can also be adapted to the Mitchell-Netravali [MN88] notch filter, for which a fast GPU implementation has not been known so far.