We introduce a new approach for the localization of 3D anatomical point landmarks based on 3D parametric intensity models which are directly fit to the image. We propose an analytic intensity model based on the Gaussian error function in conjunction with 3D rigid transformations as well as deformations to efficiently model tip-like structures of ellipsoidal shape. The approach has been successfully applied to accurately localize anatomical landmarks in 3D MR and 3D CT image data. We have also compared the experimental results with the results of a previously proposed 3D differential operator. It turns out that the new approach significantly improves the localization accuracy.