Robust medical image elastic registration using global optimisation strategy in frequency domain

Abstract

A new global optimisation strategy in frequency domain (GOFD) is presented and applied in medical image elastic registration. The method is consists of a global optimisation phase for rough searching and a local optimisation phase for fine searching. Rough searching is based on the random sampling technique in the frequency domain. According to the sampling theory, when the sampling frequency is higher than twice the maximum frequency of a function, the function can be completely reconstructed from these finite sampling points. The maximum (or minimum) value of the function at these finite sampling points is approximately in the global extreme. To obtain the exact global extreme, fine searching is performed in the small neighbourhood of the point corresponding to the approximate global maximum value. The new method presented can theoretically ensure that the global optimisation solution is found. The experiments show that our new method is more robust and accurate than other elastic registration algorithms.

Keywords:

• Non-rigid image registration
• Global optimisation
• Frequency domain
• Random sampling theory
• Fourier transform
• B-spline

Acknowledgment

This work is partially supported by the National Science Foundation of China (Project No. 31000450 and 81101109) and the Major State Basic Research Development Program of China (973 Program, No. 2010CB732500). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.