Multiscale location equivalence and wavelet image transforms on the quincunx lattice

Work on wavelet based coding of images has relied almost completely on the use of the separable, ie. tensor wavelet transform. This method treats images as one-dimensional rows and columns. Treating images in a truely multidimensional way allows for much greater flexibility in the manipulation of the information. The quincunx lattice is a natural choice for applying non-separable filtering because it is the simplest non-separable lattice. Its diagonal cut-off gives it advantageous psychovisual properties. This paper shows how to determine spatial location equivalence across different levels of a wavelet decomposition on the quincunx lattice. This allows use of methods that use the continuity of features across scales such as embedded zero-tree coding and quadtree coding. A novel method of decomposition is outlined which significantly reduces resampling computational complexity