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This paper introduces a new and simple criterion for rigid registration based on Gaussian fields. The criterion is always differentiable and convex in a large neighborhood of the alignment parameters; allowing for the use of well-proven optimization techniques. Using this method we can extend the size of the region of convergence so that no close initialization is needed, thus overcoming local convergence problems of Iterative Closest Point algorithms. Furthermore, the Gaussian energy function can be evaluated with linear complexity using the fast Gauss transform, which permits efficient implementation of the registration algorithm. Experimental analysis on real-world data sets shows the usefulness and points the limits of the approach. [Copyright &y& Elsevier]