A finite element model for 3D shape reconstruction and nonrigid motion tracking

The authors present a physics-based approach for recovering the 3-D shape and tracking the motion of nonrigid objects using a 3-D elastically deformable balloon model. The balloon model is based on a thin-plate under tension spline which deforms to fit visual data according to internal forces stemming from the elastic properties of the surface and external forces which are produced from the data. The finite element method is used to represent the model as a continuous surface. A natural finite element is used whose nodal variables comprise the position of the surface plus its first and second partial derivatives, reflecting each of the partial derivatives that occur in the spline´s strain energy functional. Hence, the model directly estimates all the information needed to measure the differential geometric properties of the fitted surface. The balloon model was applied to the reconstruction of 3-D objects with irregular shape features. Its effectiveness is demonstrated in extracting the left ventricular surface and tracking its nonrigid motion in dynamic computerized tomography volume images