We present an algorithm for evaluating a linear “intersection transform” of a function defined on the lattice of subsets of an n-element set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in “down-closure time” relative to the support of the function and the evaluation domain. As an application, we develop an algorithm that, given as input a digraph ...

Discrete cosine transform (DCT) plays an important role in video coding. Integer DCTs which approximate the standard DCT– II have been developed for various sizes i.e., N = 4, 8, 16, etc. In this paper, a review of various integer DCTs used in H.264, AVSchina and VC-1 is provided. For a first order Markov process, with high adjacent correlation coefficient, ρ = 0.95 and N=8 properties like tran...

Let Fq be the finite field with q elements and let ! be a primitive n-th root of unity in an extension eld Fqd of Fq. Given a polynomial P 2 Fq[x] of degree less than n, we will show that its discrete Fourier transform (P (1); P (!); :::; P (!n¡1)) 2Fqd n can be computed essentially d times faster than the discrete Fourier transform of a polynomial Q 2 Fqd[x] of degree less than n, in many case...

The medial axis transform (MAT) of a set S is defined as the set of centers and radii of maximal disks that are contained in S. If S is a region of a binary image, the disks are defined as upright maximal squares of black pixels and the region S is the union of these maximal squares. In this paper, we present an O(1) time algorithm for computing the medial axis transform of an N N binary image ...