METHOD FOR COMPUTING TWO-DIMENSIONAL TRANSFORM WITHOUT TRANSPOSING LARGE SCALE IMAGE DATA.

Abstract

Two-dimensional transforms, such as Fourier and Hadamard transforms, are indispensable tools for digital image processing. These two-dimensional transforms can be decomposed into rowwise transforms of data matrix followed by columnwise transforms. Since the size of data matrix of an image is usually large, the data has to be stored, say row by row, in an auxiliary storage. Then the rowwise transform is easily done, but the columnwise transform is incompatible with the row access data. A conventional solution to this difficulty is first transposing the intermediate data matrix and then performing another rowwise transform. Unfortunately, this solution has many drawbacks. This paper first presents a new algorithm, which does not require the transposing of a data matrix. Next it is shown that the new algorithm can perform the two-dimensional Fourier transform of a real image with one-half the time and memory capacity. Finally applications of the new algorithm to two-dimensional convolution and correlation between images are described.