Arbitrary Shape Wavelet Transform with Phase Alignment

We propose a wavelet transform for an arbitrary shape object. Compared with previous schemes, the proposed transform generates exactly the same number of coefficients as that of the original object. What is more, the phase of the horizontal wavelet filter is aligned so that the subsequent vertical transform is applied on coefficients with coherent phases and thus the transform efficiency is improved. We denote the scheme as the arbitrary shape wavelet transform with phase alignment (ASWP). The scheme was proposed at the MPEG4 meeting at Stockholm in July 1997, and was adopted by MPEG4 CD version 1 for wavelet transform of an arbitrary shape object.