Multi-step Diierential Approaches for the Localization of 3d Point Landmarks in Medical Images

In this contribution, we are concerned with the detection and reened subvoxel localization of 3D point landmarks. We propose multi-step differential approaches which are generalizations of an existing two-step approach for subpixel localization of 2D point landmarks. This two-step approach combines landmark detection by applying a diierential operator with reened localization through a diierential edge intersection approach. In this paper, we investigate the localization performance of this two-step approach for an analytical model of a Gaussian blurred L-corner as well as a Gaussian blurred ellipse. By varying the model parameters, diier-ently tapered and curved structures are represented. The results motivate the use of an analogous approach to 3D point landmark localization. We generalize the edge intersection approach to 3D and, by combining it with 3D diierential operators for landmark detection, we propose multi-step approaches for subvoxel localization of 3D point landmarks. The multi-step approaches are experimentally tested on 3D synthetic images and 3D MR images of the human head. We show that the multi-step approaches sig-niicantly improve the localization accuracy in comparison to applying a 3D detection operator alone.