This paper proposes a method for automatic selection of beam orientations in non-coplanar cranial IMRT. Methods of computer vision, beam's eye view techniques and neural networks are used to define a new geometry-based methodology that leads to treatment plans for cranial lesions that are comparable in quality to those generated by experienced radiation physicists. The automatic beam selection (ABS) process can be carried out in clinically useful computation times, in 1 min or less for most cases. In the process of describing the ABS process, it is shown that the cranial beam orientation optimization problem is mathematically ill posed, with the expectation that a large number of solutions will lead to similar results. Nevertheless, there are better and worse solutions and we show that the proposed ABS process, by its design, has to lead to one of the better ones. We have carried out extensive tests with 14 patients with beam selection tasks ranging from the rather simple to quite complex. The ABS process has always yielded optimizations with results that are considered good for clinic use. Seven-beam coplanar optimizations for some of the patients have also been investigated. Comparisons with non-coplanar optimizations indicate in which cases the simpler coplanar plans can be used to advantage. Parameters used in the comparisons are dose-volume histograms, minimum and maximum PTV doses, equivalent uniform doses for the PTV and OARs, and treatment volume, conformity and normal tissue indices. It is felt that the current ABS methodology is ready for extensive clinical tests.