Reened Localization of Three-dimensional Anatomical Point Landmarks Using Multi-step Diierential Approaches

In this contribution, we are concerned with the detection and re ned localization of 3D point landmarks. We propose multi-step di erential procedures which are generalizations of an existing two-step procedure for subpixel localization of 2D point landmarks. This two-step procedure combines landmark detection by applying a di erential operator with re ned localization through a di erential edge intersection approach. In this paper, we theoretically analyze the localization performance of this procedure for analytical models of a Gaussian blurred L-corner as well as a Gaussian blurred ellipse. By varying the model parameters di erently tapered and curved structures are represented. The results motivate the use of an analogous procedure for 3D point landmark localization. We generalize the edge intersection approach to 3D and, by combining it with 3D di erential operators for landmark detection, we propose three multi-step procedures for subvoxel localization of 3D point landmarks. The multi-step procedures are experimentally tested for 3D synthetic images and 3D MR images of the human head. We show that the multi-step procedures signi cantly improve the localization accuracy in comparison to applying a 3D detection operator alone.