A frequency-domain approach to registration estimation in 3-D space

Autonomous robotic systems require automatic registration of data collected by on-board sensors. Techniques requiring user intervention are unsuitable for autonomous robotic applications, while iterative-based techniques do not scale well as the dataset size increases, and additionally tend towards locally minimal solutions. To avoid the latter problem, an accurate initial estimation of the transformation is required for iterative algorithms to perform properly. The method presented in this paper does not require an initial estimation of the transformation, and avoids problems of the classical iterative techniques by employing the multi-dimensional Fourier transform, which decouples the estimation of rotational parameters from the estimation of the translational parameters. Using the magnitude of the Fourier transform, an axis of rotation is estimated by determining the line that contains the minimal energy differential between two rotated 3-D images. By using a coarse to fine approach, the angle of rotation is determined from the minimal sum squared difference between the two rotated image. As the Fourier transform introduces hermitical symmetry in the rotation, the proper solution is identified through the use of a phase-correlation technique, and the estimate of translation is simultaneously obtained Experimental results illustrate the accuracy that can be achieved by the proposed registration technique and performance is compared with that of the classical iterative closest point method.