[1] O. Nemitz, M. Rumpf, T. Tasdizen, and R. Whitaker. Anisotropic curvature motion for structure enhancing smoothing of 3D MR angiography data. Journal of Mathematical Imaging and Vision, 27(3):217-229, 2007.
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We propose a novel concept of shape prior for the processing of tubular structures in 3D images. It is based on the notion of an anisotropic area energy and the corresponding geometric gradient flow. The anisotropic area functional incorporates a locally adapted template as a shape prior for tubular vessel structures consisting of elongated, ellipsoidal shape models. The gradient flow for this functional leads to an anisotropic curvature motion model, where the evolution is driven locally in direction of the considered template. The problem is formulated in a level set framework, and a stable and robust method for the identification of the local prior is presented. The resulting algorithm is able to smooth the vessels, pushing solution toward elongated cylinders with round cross sections, while bridging gaps in the underlying raw data. The implementation includes a finite-element scheme for numerical accuracy and a narrow band strategy for computational efficiency.