19.5 3D Compression

Many 3D-cube image compression techniques are generally extended directly from their 2-D counterparts. Two 3D-cube compression techniques of particular interest that will be used in this chapter are JPEG2000 Multicomponent (ISO, 2000b) that is an extension of wavelet-based 2D-JPEG2000 (Taubman and Marcellin, 2000) and 3D-SPIHT, which is extended by 2D-SPIHT developed by Said and Pearlman (1996).

19.5.1 3D-Multicomponent JPEG

JPEG2000 (Taubman and Marcellin, 2000; Rucker et al., 2005) is a new still image compression standard that has replaced the commonly used DCT-based JPEG. It is a wavelet-based compression technique that adds/improves features such as coding of regions of interest, progressive coding, scalability, etc. The entire coding can be divided into four stages: tiling, discrete wavelets transform (DWT), scalar quantization, and block coding. The image is divided into rectangular regions called tiles; each tile gets encoded separately. The purpose of dividing images into tiles is that the decoder needs to decode only certain parts of the image on demand, instead of decoding the entire image and also less memory will be needed by the decoder to decode the image. After dividing the image into tiles, a wavelet transform is applied to each tile. The wavelet transform is followed by scalar quantization to quantize the sub-bands. The scalar quantized sub-bands representing different scales are coded using embedded block coding with block truncation (EBCOT) (Taubman and Marcellin, 2000; Rucker et al., 2005; ISO, 2000a; ISO, 2000b; Taubman, 2000). For the case of hyperspectral imagery the Part II of JPEG2000 (ISO, 2000b) is implemented to allow multicomponent image compression that involves grouping of arbitrary subsets of components into component collections and applying point transforms along the spectral direction like wavelet transform. The postcompression rate-distortion optimizer of EBCOT is simultaneously applied to all code blocks across all the components.

19.5.2 3D-SPIHT Compression

Recently, an approach developed by Said and Pearlman (1996), called set partitioning in hierarchical trees (SPIHT) has become popular. Two main features introduced by Shapiro (1993) are used in the SPIHT algorithm. First, it utilizes a partial ordering of coefficients by magnitude and transmits the most significant bits first. Second, the ordering data are not explicitly transmitted. The decoder running the same algorithm can trace the ordering information from the transmitted information. Kim et al. (2000) later extended 2D-SPIHT to 3D-SPIHT for video compression in a relatively straightforward manner. There is no constraint imposed on the SPIHT algorithm regarding the dimensionality of the data. If all pixels are lined up in decreasing order of magnitude, 3D-SPIHT performs exactly the same as 2D-SPIHT. In the case of 3D sub-band structure, one can use a wavelet packet transform to allow a different number of decompositions between the spatial and spectral dimensions.