A truncation method for computing the slant transform is presented. The slant transform truncation (STT) algorithm uses the divide and conquer principle of hierarchical data structures to factorize coherent image data into sparse subregions. In one dimension with a data array of size N=2/sup n/, the truncation method takes a time between O(N) and O(Nlog/sub 2/N), degenerating to the performance of the fast slant transform (FST) method in its worst case. In two dimensions, for a data array of size N/spl times/N, the one-dimensional truncation method is applied to each row, then to each column of the array, to compute the transform in a time between O(N/sup 2/) and O(N/sup 2/log/sub 2/N). Coherence is a fundamental characteristic of digital images and so the truncation method is superior to the FST method when computing slant transforms of digital images. Experimental results are presented to justify this assertion.>

Transforms and quadtrees are both methods of representing information in an image in terms of the presence of information at differing length scales. This paper presents a mathematical relationship between these two approaches to describing images in the particular case when Walsh transforms are used. Furthermore, both methods have been used for the compression of images for transmission. This paper notes that under certain circumstances, quadtree compression produces identical results to Walsh transform coding, but requires less computational effort to do so. Remarks are also made about the differences between these approaches.