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.<<ETX>>

[1]  Rachid Deriche,et al.  3D edge detection using recursive filtering: application to scanner images , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[2]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Demetri Terzopoulos,et al.  Multilevel computational processes for visual surface reconstruction , 1983, Comput. Vis. Graph. Image Process..

[4]  Rachid Deriche,et al.  3D edge detection using recursive filtering: Application to scanner images , 1991, CVGIP Image Underst..

[5]  Alistair A. Young,et al.  Non-rigid heart wall motion using MR tagging , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[6]  Dmitry B. Goldgof,et al.  Adaptive-size physically-based models for nonrigid motion analysis , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  Demetri Terzopoulos,et al.  Recursive estimation of shape and nonrigid motion , 1991, Proceedings of the IEEE Workshop on Visual Motion.

[8]  G. Touzot,et al.  The finite element method displayed , 1984 .

[9]  Demetri Terzopoulos,et al.  Reconstructing and visualizing models of neuronal dendrites , 1991 .

[10]  Yuan-Fang Wang,et al.  Surface Reconstruction Using Deformable Models with Interior and Boundary Constraints , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Nicholas Ayache,et al.  From voxel to curvature , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  Demetri Terzopoulos,et al.  Constraints on Deformable Models: Recovering 3D Shape and Nonrigid Motion , 1988, Artif. Intell..

[13]  Alex Pentland,et al.  Recovery of Nonrigid Motion and Structure , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Richard A. Robb,et al.  Imaging physiological functions: Experience with the dynamic spatial reconstructor , 1984 .

[15]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[16]  Katsushi Ikeuchi,et al.  Shape representation and image segmentation using deformable surfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[17]  Laurent D. Cohen,et al.  Introducing new deformable surfaces to segment 3D images , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.