A 3D Laplacian-Driven Parametric Deformable Model

3D parametric deformable models have been used to extract volumetric object boundaries and they generate smooth boundary surfaces as results. However, in some segmentation cases, such as cerebral cortex with complex folds and creases, and human lung with high curvature boundary, parametric deformable models often suffer from over-smoothing or decreased mesh quality during model deformation. To address this problem, we propose a 3D Laplacian-driven parametric deformable model with a new internal force. Derived from a Mesh Laplacian, the internal force exerted on each control vertex can be decomposed into two orthogonal vectors based on the vertex's tangential plane. We then introduce a weighting function to control the contributions of the two vectors based on the model mesh's geometry. Deforming the new model is solving a linear system, so the new model can converge very efficiently. To validate the model's performance, we tested our method on various segmentation cases and compared our model with Finite Element and Level Set deformable models.