The spatial relationship of DCT coefficients between a block and its sub-blocks

At present, almost all digital images are stored and transferred in their compressed format in which discrete cosine transform (DCT)-based compression remains one of the most important data compression techniques due to the efforts from JPEG. In order to save the computation and memory cost, it is desirable to have image processing operations such as feature extraction, image indexing, and pattern classifications implemented directly in the DCT domain. To this end, we present in this paper a generalized analysis of spatial relationships between the DCTs of any block and its sub-blocks. The results reveal that DCT coefficients of any block can be directly obtained from the DCT coefficients of its sub-blocks and that the interblock relationship remains linear. It is useful in extracting global features in compressed domain for general image processing tasks such as those widely used in pyramid algorithms and image indexing. In addition, due to the fact that the corresponding coefficient matrix of the linear combination is sparse, the computational complexity of the proposed algorithms is significantly lower than that of the existing methods.