Transfer function design for fourier volume rendering and implementation using GPU

Volume rendering is a technique for volume visualization. Given a set of N×N×N volume data, the traditional volume rendering methods generally need O(N³) rendering time. The FVR (Fourier Volume Rendering), that takes advantage of the Fourier slice theorem, takes O(N ² log N ) rendering time once the Fourier Transform of the volume data is available. Thus the FVR is favor to designing a real-time rendering algorithm with a preprocessing step. But the FVR has a disadvantage that resampling in the frequency domain causes artifacts in the spatial domain. Another problem is that the method for designing a transfer function is not obvious. In this paper, we report that by using the spatial domain zero-padding and tri-linear filtering can reduce the artifacts to an acceptable rendered image quality in spatial domain. To design the transfer function, we present a method that the user can define a transfer function by using a Bézier curve first. Based on the linear combination property of the Fourier transform and Bézier curve equation, the volume rendered result can be obtained by adding the weighted frequency domain signals. That mean, once a transfer function is given, we don't have to recompute the Fourier transform of the volume data after the transfer function applied. This technique makes real-time adjustment of transfer function possible.