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 i) track the motion of deforming material and/or, ii) morphological warping of template images or patterns. Two-dimensional (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 (CT) images.