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

This is an substantially expanded and revised version of: Stone, LeMoigne, and McGuire. The translation sensitivity of wavelet-based registration. Proceedings of the 26th AIPR Workshop, Proceedings of the SPIE, Exploiting New Image Sources and Sensors 3240:116-125, 1997

@article{319263,
 author = {Harold S. Stone and Jacqueline Le Moigne and Morgan McGuire},
 title = {The Translation Sensitivity of Wavelet-Based Registration},
 journal = {IEEE Trans. Pattern Anal. Mach. Intell.},
 volume = {21},
 number = {10},
 year = {1999},
 issn = {0162-8828},
 pages = {1074--1081},
 doi = {http://dx.doi.org/10.1109/34.799911},
 publisher = {IEEE Computer Society},
 address = {Washington, DC, USA},
}