A Finite Element Model for 3 D Shape Reconstruction andNonrigid Motion

This paper presents a physics-based approach for recovering the 3D shape and tracking the motion of nonrigid objects using a 3D elastically deformable balloon model. The balloon model is based on a thin-plate under tension spline which deforms to t visual data according to internal forces stemming from the elastic properties of the surface and external forces which are produced from the data. We employ the nite element method to represent the model as a continuous surface. We use a \natural" nite element whose nodal variables comprise the position of the surface plus its rst and second partial derivatives, reeecting 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 diierential geometric properties of the tted surface. We apply the the balloon model to the reconstruction of 3D objects with irregular shape features and demonstrate its eeectiveness in extracting the left ventricu-lar surface and tracking its nonrigid motion in dynamic CT volume images.