Applications of Chebyshev Bases to Cylindrical Volume Grids: Direct Section Computation and Robust Volume Reconstruction

With rapid advances in low-bitrate applications such as video-conferencing and interactive environments, much attention is being focussed on interaction and fusion between heterogeneous data streams from multiple sensors. Volumes often embody widely varying physical signals such as those acquired by X-rays, ultrasound sensors in addition to standard c.c.d. cameras. A large class of applications use image acquisition and volume reconstruction techniques in cylindrical grids; these include real-time 3D medical reconstruction, and reverse engineering. This paper presents the novel use of Chebyshev bases in such cylindrical grid-based volume applications. In particular, the paper covers the direct computation of cross-sectional plane from the original image data set without complete volume reconstruction as well as robust techniques for volume reconstruction. Chebyshev expansions have the benefits of fast convergence, bounded error, computational efficiency, and are optimal for cylindrical grids. In addition, our method exploits knowledge about the sampling strategy (e.g. position and trajectory of the sensor) used to acquire the original ensemble of images, which in turn makes the overall approach very amenable to internet-based visualization applications.