Gram polynomial image decimation and its application to non-rigid registration
Amir Badshah, Paul L. O'Leary, Matthew Harker · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
This paper presents a new approach to non-rigid registration. A hierarchical subdivision approach is applied, with local normalized phase correlation for patch registration. The major improvement is achieved by implementing a suitable decimation at each level. The decimation is implemented via a Gram polynomial basis. Both global and local polynomial approximation are considered and compared with the use of a Fourier basis. The issue of Gibbs error in polynomial decimation is examined. It is shown that the Gram basis is superior when applied to signals with strong gradient, i.e., a gradient which generates a significant Gibbs error with a Fourier basis. A bivariate Gram polynomial tensor product approximation is used to implement regularization. It is demonstrated that the new method performs well on both synthetic and real image data. The procedure requires approximately 1.3 sec. to register an image with 800 × 500 pixels.