Fast quasi-DCT algorithm for shape-adaptive DCT image coding

In this paper we develop a new variant of the shape-adaptive discrete cosine transform (SA-DCT) recently proposed by Sikora and Makai and currently considered for MPEG-4 as a texture compression engine. We are concerned with the computational complexity of the SA-DCT; although its complexity is acceptable in the context of 8 × 8 (boundary) blocks as proposed for MPEG-4, it is very high for a true region-based coding where complete regions (e.g., 100 by 100 pixels) need to be processed. We adapt the original SA-DCT scheme by replacing the usual DCT with a quasi-DCT for which some basis functions are identical and some similar to those of the DCT. We test the new method and compare it numerically in terms of the basis restriction error as well as subjectively on some natural images. We conclude that the new method's energy compaction performance is slightly inferior to that of the SA-DCT, but its computational complexity is highly reduced.