Globally Optimal TV-L1 Shape Prior Segmentation

Inffeldgasse 16, A-8010 Graz, Austria

Interpreting an image is a common and challenging task in computer vision. A human observer does not only use intensity or color information or other basic features when looking for region boundaries but also takes prior knowledge into account. This increases the robustness on the segmentation result for most images. The main intention of our work is to propose a globally optimal segmentation algorithm that incorporates prior knowledge in form of a geometric shape. The proposed energy is based on a weighted Total Variation energy and is optimized with fast numerical approaches like the projected gradient descent method. The GPU-based implementation is able to achieve real-time performance for the presented applications. We show the coherence of the proposed energy model to former variational methods like the well-known edge-preserving restoration model of Rudin, Osher and Fatemi and methods that incorporate prior information into classical segmentation models. Different applications are realized with the proposed energy. First of all a semi-automatic, interactive segmentation tool is implemented. The user can either define a shape prior on the fly using the weighted Total Variation as geodesic active contour or load a predefined geometric shape. Next the energy model can be used to align two shapes on each other or optimize the alignment of a shape to an underlying edge function. Consequentially a tracking approach was introduced with the ability to optimize the incorporated shape information according to consecutive frames. This position update is also used when processing 3D data sets with a 2D prior which is particularly useful for segmenting tubular structures in medical data sets with a single constraint on the first slice.

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