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

Abstract

AbstractRecently, 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‐the‐fly 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.