.LP.BR QccSPIHT3DDecode2()provides the appropriate alternative interface to 3D-SPIHT decodingrequired if encoding was done via.BR QccSPIHT3DEncode2() .Essentially, .BR QccSPIHT3DDecode()is implemented by a call to.BR QccSPIHT3DDecode2()followed by an appropriate inverse 3D DWT.If.BR QccSPIHT3DDecode2()is used, it is the responsibility of the calling to routineto perform the appropriate inverse 3D DWT subsequent to the callto.BR QccSPIHT3DDecode2() .As noted above, most applications should use.BR QccSPIHT3DDecode()rather than.BR QccSPIHT3DDecode2() ..SH "DYADIC VS. WAVELET-PACKET TRANSFORMS AND ZEROTREES"As the first step in 3D-SPIHT coding, awavelet transform is deployed. As is usual for 2D images, the 3D DWT is implemented in a separable fashion, employing 1Dtransforms separately in the spatial-row, spatial-column, and temporal-frame directions.In a 3D wavelet transform, different decomposition orders can yield different results.For instance, we can perform one scale of decomposition along eachdirection, then do further decomposition in the lowpass subband, leading to the dyadic decomposition.RI ( transform_typeequal.BR QCCWAVSUBBANDPYRAMID3D_DYADIC ).This dyadic decomposition structure is the 3D generalization ofthe 2D dyadic decomposition used ubiquitously in 2D image coding.However, in 3D,we can alternatively use a so-called"wavelet-packet" transform in which we firstapply a 1D decomposition in the temporal direction and then followby decomposing each temporalframe using a separable 2D transform.With this approach, we employ a 1D decomposition of.IR temporal_num_levelsscales temporally followed by a 2D decomposition of.IR spatial_num_levelsscales spatially, where it is possiblefor.IR spatial_num_levels " and " temporal_num_levelsto be unequal.In comparing the two decomposition structures,the wavelet-packet transform is generally considered to be more flexible becausethe temporal decomposition can be better tailored to the dataat hand than in the dyadic transform..LPAfter the wavelet transform, the 3D-SPIHT algorithm employs a zerotree-basedbitplane-coding algorithm.In the case of a dyadic transform, the zerotree used is a straightforwardextension to 3D of the parent-child relationship of 2D zerotrees;that is, one coefficient is the parent to a 2x2x2 cube of eightoffspring coefficients in the next scale..LPIn the case of a wavelet-packet transform, there are several approachesto fitting a zerotree structure to the wavelet coefficients.The first, proposed by Kim.IR "et al" .,recognizes that wavelet-packet subbands appear as "split" versions oftheir dyadic counterparts, consequently, one should "split" the 2x2x2offspring nodes of the dyadic zerotree structure appropriately.Alternatively, one could employ a dyadic zerotree structuredirectly on the wavelet-packet subband decomposition obliviousto the differing structure.While the former "splitting" approach appears to be a more appropriatestructure, the latter dyadic approach, which results in the intermingling ofcoefficients from different spatial localities within a single 2x2x2offspring collection,is easier to implement and often resultsin slightly better rate-distortion performance.However, both of these zerotree structures apparently require that thewavelet-packet transform have the same number of temporal and spatialdecomposition levels..LPAn alternative zerotree structure for packet transforms was proposedoriginally by He.IR "et al" .,and was subsequently used by Cho and Pearlman.In essence, this zerotree structure consists of 2D zerotrees within each"slice" of the subband-pyramid volume, with parent-child relationshipssetup between the tree-root coefficients of the 2D trees.Cho and Pearlman called this alternative structure an"asymmetric" packet zerotree, with the original splitting-basedpacket structure of Kim.IR "et al" .then being a "symmetric" packet zerotree.The asymmetric structure usually offers slightly better rate-distortionperformance than either the symmetric packet or dyadic zerotree structures;additionally, the wavelet-packet transform can have the number oftemporal decomposition levels different from the number ofspatial decomposition levels when the asymmetric tree is used..LPThe QccPack implementation of 3D-SPIHT supports bothdyadic and packet transforms (as specified by.IR transform_type ).In the case that a wavelet-packet transform is used.RI ( transform_typeequal to.BR QCCWAVSUBBANDPYRAMID3D_PACKET ),one canindependently control whether a dyadic, symmetric-packet,or asymmetric-packet zerotree structure is used (as specified by.IR zerotree_type ).The asymmetric-packet zerotree structure.RI ( zerotree_typeequal to.BR QCCSPIHT3D_ZEROTREE_ASPACKET )is implemented by adopting the 2D zerotree offspring relationships,suitably altered at the tree roots; for an asymmetric-packet zerotree,.IR spatial_num_levelsand.IR temporal_num_levelscan differ.For the symmetric-packet zerotree structure.RI ( zerotree_typeequal to.BR QCCSPIHT3D_ZEROTREE_PACKET ),the splitting approach of Kim.IR "et al" .is implemented by reorganizing the wavelet coefficients with a call to.BR QccWAVSubbandPyramid3DPacketToDyadic (3)and then following through coding as though a dyadic transform was used.For the dyadic zerotree structure.RI ( zerotree_typeequal to.BR QCCSPIHT3D_ZEROTREE_DYADIC ),a zerotree of.IR spatial_num_levelsis employed directly on the wavelet-packet coefficients.In the case of either a symmetric-packet or dyadic zerotree,both.IR spatial_num_levelsand.IR temporal_num_levelsmust be the same.In the case that a dyadic DWT is used.RI ( transform_typeequal to.BR QCCWABSUBBANDPYRAMID3D_DYADIC ),only the dyadic zerotree structure is supported; i.e., .IR zerotree_typemust be.BR QCCSPIHT3D_ZEROTREE_DYADIC ,and both.IR spatial_num_levelsand.IR temporal_num_levelsmust be the same..SH "SHAPE-ADAPTIVE CODING"The usual way to handle arbitrarily shaped objects within 3D-SPIHT is tofollow the approach typically used for 2D zerotree-based coders;that is, permanently set transparent regions in the image to "insignificant" during the SA-DWT so that the 3D-SPIHT algorithmprocesses these transparent regions in a manner identical to that of otherinsignificant coefficients. This approach has been taken fora number of 2D zerotree-based coding algorithms; see Li and Li foran example of such.Minami.IR "et al" .go one step further on this basic approach by discarding allsets of coefficients that lie entirely within a transparent regionfrom the lists maintained by 3D-SPIHT. Although this refinement typicallyoffers a small gain in performance, the size of the gain is dependenton how much of the overall image is transparent.The QccPack implementation of 3D-SPIHT follows the approach byMinami.IR "et al" .for shape-adaptive coding..LPFinally, note that the concept ofshape-adaptive coding arose in the work surroundingthe MPEG-4 standard and wasnot considered in the original 2D-SPIHT work by Said and Pearlman, northe original extension to 3D by Kim, Pearlman, and Xiong..SH "SEE ALSO".BR spihtencode3d (1),.BR spihtdecode3d (1),.BR QccBitBuffer (3),.BR QccWAVSubbandPyramid3D (3),.BR QccWAVSubbandPyramid3DDWT (3),.BR QccWAVSubbandPyramid3DShapeAdaptiveDWT (3),.BR QccSPIHTEncode (3),.BR QccPackWAV (3),.BR QccPackIMG (3),.BR QccPack (3)B.-J. Kim, Z. Xiong, and W. A. Pearlman,"Low Bit-Rate Scalable Video Coding with 3-D Set Partitioningin Hierarchical Trees (3-D SPIHT),".IR "IEEE Transactions on Circuits and Systems for Video Technology" ,vol. 10, no. 8, pp. 1374-1387, December 2000..LPB.-J. Kim and W. A. Pearlman,"An Embedded Wavelet Video Coder Using Three-DimensionalSet Partitioning in Hierarchical Trees (SPIHT)," in.IR "Proceedings of the Data Compression Conference" ,J. A. Storer and M. Cohn, Eds., Snowbird, UT, March 1997, pp. 251-257..LPA. Said and W. A. Pearlman,"A New, Fast, and Efficient Image Codec Basedon Set Partitioning in Hierarchical Trees,".IR "IEEE Transactions on Circuits and Systems for Video Technology" ,vol. 6, no. 3, pp. 243-250, June 1996..LPC. He, J. Dong, Y. F. Zheng, and Z. Gao,"Optimal 3-D Coefficient Tree Structure for 3-D Wavelet Video Coding,".IR "IEEE Transactions on Circuits and Systems for Video Technology" ,vol. 13, no. 10, pp. 961-972, October 2003..LPS. Cho and W. P. Pearlman,"Error Resilient Video Coding With Improved 3-D SPIHT and Error Concealment,"in.IR "Image and Video Communications and Processing" ,B. Vasudev, T. R. Hsing, and A. G. Tescher, Eds.,Santa Clara, CA, January 2003, Proc. SPIE 5022, pp. 125-136.LPG. Minami, Z. Xiong, A. Wang, and S. Mehrota,"3-D Wavelet Coding of Video With Arbitrary Regions of Support,".IR "IEEE Transactions on Circuits and Systems for Video Technology" ,vol. 11, no. 9, pp. 1063-1068, September 2001..LPS. Li and W. Li, "Shape-Adaptive Discrete Wavelet Transforms forArbitrarily Shaped Visual Object Coding,".IR "IEEE Transactions on Circuits and Systems for Video Coding" ,vol. 10, pp. 725-743, August 2000..SH AUTHORCopyright (C) 1997-2008  James E. Fowler.SH LICENSEThe 3D Set Partitioning In Hierarchical Trees (3D-SPIHT) algorithm isprotected by US patents 5,764,807 and 6,674,911, and other patents pending.An implementation of the 3D-SPIHT algorithm is included herein (utilityprograms spihtencode3d and spihtdecode3d, and spiht3d.c in the QccPacklibrary) with the permission of PrimaComp, Inc., exclusive holder ofpatent rights. PrimaComp has graciously granted a license with certainrestrictions governing the terms and conditions for use, copying,distribution, and modification of the 3D-SPIHT algorithm implementationcontained herein. Specifically, only use in academic and non-commercialresearch is permitted, while all commercial use is prohibited.  Refer tothe file LICENSE-3D-SPIHT for more details.