A Frequency Domain Approach to Registration Estimation in Three-Dimensional Space

Autonomous robotic systems require automatic registration of data that are collected by on-board sensors. Techniques requiring user intervention are unsuitable for autonomous robotic applications, whereas iterative-based techniques do not scale well as the data set size increases and, additionally, tend toward locally minimal solutions. To avoid the latter problem, an accurate initial estimation of the transformation is required for iterative algorithms to properly perform. However, in some situations, an initial estimate of the transformation may not be readily available; hence, a method that does not require such an initial estimate nor descends into local minima is desirable. The method presented in this paper takes advantage of the multidimensional Fourier transform, which inherently decouples the estimation of the rotational parameters from the estimation of the translational parameters, to compute 3-D registration between range images without requiring an initial estimation of the transformation and avoiding problems of the classical iterative techniques. 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. A coarse-to-fine approach is used to determine the angle of rotation from the minimal sum of the squared difference between the two rotated images. Due to the Hermitian symmetry introduced by the Fourier transform, two possible solutions for the angle of rotation exist. The proper solution is identified through the use of a phase-correlation technique, and the estimate of translation is simultaneously obtained. Experimental results and an extended performance evaluation illustrate the accuracy that can be achieved by the proposed registration technique on simulated and on real range images. Last, a comparison of computational stability with that of the classical iterative closest point method is presented.