ARBITRARY SHAPE WAVELET TRANSFORM WITH PHASE ALIGNMENT

An arbitrary shape wavelet transform with phase alignment (ASWP) is used to transform an arbitrary shaped object in an image. The phase of an odd tap wavelet filter is aligned so that a low pass filter is always centered at an even index, and a high pass filter is always centered at an odd index. The phase of an even tap wavelet filter is aligned so that the low pass filter and the high pass filter are both centered at index 2i+0.5, i.e., a half index past the even index. The objects for odd tap wavelet filters are each separately symmetrically extended by mirroring the objects from the opposite ends but not mirroring the end pixels. The objects for the even tap filter is symmetrically extended by mirroring the pixels from the opposite ends of the objects including mirroring the end pixels. The phase adjusted-symmetrically extended objects are then transformed.