A Truncation method for computing slant transforms with applications to image processing

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=2ⁿ, the truncation method takes a time between O(N) and O(Nlog₂N), 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×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(N²) and O(N²log₂N). 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