Manually extracting 3D anatomical point landmarks from tomographic images is generally tedious and time-consuming. A semi-automatic procedure for landmark extraction, which allows for interactive control, offers the possibility to improve on this. The detection performance is decisive for the applicability of such a procedure. However, existing computational approaches to landmark detection often suffer from a larger number of false detections. A considerable number of false detections is caused by neighboring anatomical structures that are captured by the region-of-interest (ROI) at a landmark. In this paper, we present two different approaches to reducing false detections caused by neighboring structures. First, we present a statistical, differential approach to automatically selecting a suitable size for the 3D ROI. Second, we present a differential approach that incorporates additional prior knowledge of the intensity structure at a landmark. Combining both approaches with a robust 3D differential operator for landmark detection, we develop a new algorithm for landmark detection. In estimating the partial derivatives of the intensity function, we can cope with anisotropic voxel sizes using a scheme based on B-spline image interpolation. The new algorithm is applied within a semi-automatic procedure to extract anatomical point landmarks from 3D MR and CT images of the human head.