Vector quantization and signal compression
Vector quantization and signal compression
A new formulation for fast image coding using quadtree representation
Pattern Recognition Letters
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Optimal variable-rate mean-gain-shape vector quantization for image coding
IEEE Transactions on Circuits and Systems for Video Technology
A generalization of quad-trees applied to image coding
Integrated Computer-Aided Engineering
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The optimal design of quadtree-based codecs is addressed. Until now,work in this area has focused on the optimization of the quadtreestructure for a given set of leaf quantizers while neglecting thedesign of the quantizers themselves. In cases where the leafquantizers have been considered, codebooks have been optimizedwithout regard to the ultimate quadtree segmentation. However, it isnot sufficient to consider each problem independently, as separateoptimization leads to an overall suboptimal solution. Rather, jointdesign of the quadtree structure and the leaf codebooks must beconsidered for overall optimality. The method we suggest is a“quadtree” constrained version of the entropy-constrainedvector quantization design method. To this end, a centroid conditionfor the leaf codebooks is derived that represents a necessaryoptimality condition for variable-rate quadtree coding. Thiscondition, when iterated with the optimal quadtree segmentationstrategy of Sullivan and Baker results in a monotonically descendingrate-distortion cost function, and consequently, an (at leastlocally) optimal quadtree solution.