Title :
Comments on "A translation- and scale-invariant adaptive wavelet transform"
Author_Institution :
Digimarc Corp., Tualatin, OR, USA
Abstract :
H. Xiong et al. (see ibid., vol.9, p.2100-8, 2000) presented a translationand scale-invariant adaptive wavelet transform. We show that their renormalized signal (pre-wavelet transform) is already translation- and scale-invariant. Thus, it is not just invariant under the wavelet transform. We give a necessary and sufficient condition for renormalized signals to be affine transform invariant.
Keywords :
signal processing; wavelet transforms; affine transform invariant; renormalized signal; scale-invariant adaptive wavelet transform; translation-invariant adaptive wavelet transform; Adaptive filters; Discrete transforms; Discrete wavelet transforms; Multiresolution analysis; Polynomials; Signal processing; Sufficient conditions; Wavelet analysis; Wavelet coefficients; Wavelet transforms;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2003.815255
