This thesis discusses wavelet-based volume visualization and compression. Volume rendering is an important area in the field of scientific visualization, and it has become the most useful technique in medical imaging. With the rapid progress in medical techniques, more and more high-resolution 3D medical data are generated. Unfortunately, the sizes of these 3D data are usually beyond the ability of most of today's computers and networks. To effectively process these data, compression is needed.; A new lossless 3D wavelet-based volume compression algorithm is presented. This algorithm is a 3D extension of SPIHT algorithm in 2D image compression, and it has the property of embedded quantization. The algorithm is combined with a scan-converting volume rendering algorithm to achieve interactive visualization in medical imaging.; In order to process very high-resolution 3D medical data in a hierarchical way, a “lifting-up” scheme is introduced. This scheme sorts the wavelet coefficients not only according to their values, but also according to their spatial hierarchy in the multiresolutionally decomposed subbands. The wavelet coefficients with the lowest resolution are encoded/decoded first. Then, the coefficients at the next resolution level are transmitted. The refining process continues until all the coefficients at the finest resolution level are encoded/decoded. The performance of the new algorithm is presented.
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