Multiscale location equivalence and wavelet image transforms on the quincunx lattice

Work on Wavelet based coding of images [1] has relied almost completely on the use of the separable, ie. Tensor Wavelet Transform. This method treats images as onedimensional 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 zerotree coding and quad-tree coding. A novel method of decomposition is outlined which significantly reduces resampling computational complexity.