On the computation of the 3-D DCT

The three-dimensional cosine transform (3-D DCT) is used for 3-D image compression and related applications. Its calculation involves a very large number of arithmetic operations and hence fast algorithms are needed for its computation. In this paper, the row-column-frame (RCF) and the 3-D vector radix (3-D VR) algorithms, which are usually used for the calculation of the 3-D DCT and its inverse, are investigated and compared based on their arithmetic operations and computer-run times. Both comparisons show that the 3-D VR algorithm is clearly faster and more efficient than the RCF approach.