Mapping of hyperelastic deformable templates using the finite element method

In the current work we integrate well established techniques from finite deformation continuum mechanics with concepts from pattern recognition and image processing to develop a new finite element (FE) tool that combines image-based data with mechanics. Results track the deformation of material continua in the presence of unknown forces and/or material properties by using image-based data to provide the additional required information. The deformation field is determined from a variational problem that combines both the mechanics and models of the imaging sensors. A nonlinear FE approach is used to approximate the solution of the coupled problem. Results can be applied to (1) track the motion of deforming material and/or, (2) morphological warping of template images or patterns. 2D example results are provided for problems of the second type. One of the present examples was motivated primarily by a problem in medical imaging--mapping intersubject geometrical differences in human anatomical structures--with specific results given for the mapping 2D slices of the human distal femur based on X-ray computed tomographic images.

[1]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[2]  L. J. Thomas,et al.  A Matheematical Model for Positron-Emission Tomography Systems Having Time-of-Flight Measurements , 1981, IEEE Transactions on Nuclear Science.

[3]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[4]  E. Jaynes.  On the rationale of maximum-entropy methods , 1982, Proceedings of the IEEE.

[5]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

[6]  Y. Lanir.  Constitutive equations for fibrous connective tissues. , 1983, Journal of biomechanics.

[7]  R. Bajcsy,et al.  A computerized system for the elastic matching of deformed radiographic images to idealized atlas images. , 1983, Journal of computer assisted tomography.

[8]  W. Menke.  Geophysical data analysis : discrete inverse theory , 1984 .

[9]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[10]  M. Bronskill,et al.  Noise and filtration in magnetic resonance imaging. , 1985, Medical physics.

[11]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[12]  Ruzena Bajcsy,et al.  Multiresolution elastic matching , 1989, Comput. Vis. Graph. Image Process..

[13]  A. A. Vassiliou,et al.  Tomographic imaging in hydrocarbon reservoirs , 1989, Int. J. Imaging Syst. Technol..

[14]  D. Olbers,et al.  Determining Diffusivities from Hydrographic Data by Inverse Methods with Applications to the Circumpolar Current , 1989 .

[15]  D. Webb.  Assimilation of Data into Ocean Models , 1989 .

[16]  C. Gans,et al.  Biomechanics: Motion, Flow, Stress, and Growth , 1990 .

[17]  T. M. McGee,et al.  Seismic reverberations and the remote estimation of properties of underwater soils , 1991, Int. J. Imaging Syst. Technol..

[18]  Whirley.  DYNA3D: A nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics , 1993 .

[19]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[20]  Jun Zhang,et al.  Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation , 1994, IEEE Trans. Image Process..

[21]  R. Rabbitt,et al.  3D brain mapping using a deformable neuroanatomy. , 1994, Physics in medicine and biology.

[22]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..