A new criterion based on Gaussian fields is introduced and applied to the task of automatic rigid registration of point-sets. The method defines a simple energy function, which is always differentiable and convex in a large neighborhood of the alignment parameters; allowing for the use of powerful standard optimization techniques. We show that the size of the region of convergence can be extended 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. Analysis through several experimental results on real world datasets shows the practicality and points out the limits of the approach.