Mapping of hyperelastic deformable templates using the finite element method

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Abstract
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.

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