The translation sensitivity of wavelet-based registration

This paper studies the effects of image translation on wavelet-based image registration. The main result is that the normalized correlation coefficien ts of low-pass Haar and Daubechies wavelet subbands are essentially insensi tive to translations for features larger than twice the wavelet blocksize. The third-level low-pass subbands produce a correlation peak that varies wi th translation from 0.7 and 1.0 with an average in excess of 0.9. Translati on sensitivity is limited to the high-pass subband and even this subband is potentially useful. The correlation peak for high-pass subbands derived fr om first and second-level low-pass subbands ranges from about 0.0 to 1.0 wi th an average of about 0.5 for Daubechies and 0.7 for Haar. We use a mathem atical model to develop these results, and confirm them on real data.