Automatic construction of eigenshape models by direct optimization

A new approach to the problem of automatic construction of eigenshape models is presented. Eigenshape models have proved to be successful in a variety of medical image analysis problems. However, automatic construction of eigenshape models has proved to be a difficult problem, and in many applications the models are built by hand—a painstaking process. We show that the fundamental problem is a choice of the correct pose and parametrization of each shape in the training set. Eigenshape models are not invariant under reparametrizations and pose transformations of the training shapes. Since there is no a priori correct choice for the pose and parametrization of each shape, their value should be chosen so as to produce a model that is compact and specific. This problem can be solved by finding an objective function that measures these properties and varying the pose and parametrization of each shape to optimize this function. We show that the appropriate objective function is the determinant of the covariance matrix. We go on to show how this objective function can be optimized by a genetic algorithm (GA) and thus give a practical method for building eigenshape models. The models produced are often better than hand-built ones. The advantages of a GA over other choices of optimization method are that no assumptions about the nature of the shapes being modelled is required and that the global minimum of the objective function can, in principle, be found.