Laplace-Dirichlet energy field specification for deformable models. An FEM approach to active contour fitting

The construction of large scale computer models for complex biological systems requires the fitting of curves or surfaces to anatomical data sets. Algorithms recently developed to perform this task are based on the displacement of an initial model contour. There are several problems associated with this approach. Here we present improvements which eliminate the (i) sensitivity to the initial model position and shape; (ii) existence of local minima or maxima in the field used to displace the model; and (iii) presence of multiple solutions in the rules governing model displacement. Key elements of our algorithm are first that both the energy field used to displace the model and the model displacement itself are governed by partial differential equations. Secondly, we approximate the model with a polygonal contour which facilitates accurate displacement. Tests performed against cases that are known to be problematic show that our algorithm can fit complex data sets entirely automatically.