We present a new segmentation method for extracting thin structures embedded in three-dimensional medical images based on modern variational principles. We demonstrate the importance of the edge alignment and homogeneity terms in the segmentation of blood vessels and vascular trees. For that goal, the Chan-Vese minimal variance method is combined with the boundary alignment, and the geodesic active surface models. An efficient numerical scheme is proposed. In order to simultaneously detect a number of different objects in the image, a hierarchal approach is applied.
Abstract. We introduce a new method for segmentation of 3D medical data based on geometric variational principles. A minimal variance criterion is coupled with a geometric edge alignment measure and the geodesic active surface model. An efficient numerical scheme is proposed. In order to simultaneously detect a number of different objects in the image, a hierarchal method is presented. Finally, our method is compared with the multi-level set approach for segmentation of medical images.
Most patch based algorithms for completing missing parts of images fill in the absent regions by copying patches from the known part of the image into the unknown part, somewhat like plastic surgery. The criterion for deciding which patch to copy is compatibility of the copied patch with the vicinity of the region being completed. In this paper we propose introducing a new dimension to this compatibility criterion, namely, scale. The patch is thus chosen by evaluating its consistency with respect to a hierarchy of smoothed (less detailed) versions of the image, as well as its surroundings in the current version. Applied recursively, this approach results in a multi-scale framework that is shown to yield a dramatic improvement in the robustness of patch based image completion.
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