A Maximum-A-Posteriori Framework for Statistical Appearance Models with Probabilistic Correspondences

The identication of one-to-one correspondences in a training set is a key aspect of building statistical models. But the determination of these corresponding landmarks is the most challenging part of such methods. Hufnagel et al. [1] developed an alternative method using correspondence probabilities for statistical shape models. We propose the use of probabilistic correspondences for statistical appearance models by incorporating appearance information into the framework. A sparse representation is generated representing image structures by a set of vectors assembling positions and appearances. Using probabilistic correspondences Between these multi-dimensional feature vectors eliminates the need for extensive preprocessing to nd corresponding landmarks and reduces the dependence of the generated model on the landmark positions.
Then, a maximum-a-posteriori approach is used to derive a single global optimization criterion with respect to model parameters and observation dependent parameters that aects shape and appearance information of the considered structures. Model generation and tting can be expressed by optimizing the same criterion. This framework describes the modeling process in a concise and exible mathematical framework and allows for additional constraints as topological regularity in the modeling process. In a rst evaluation we apply the model to hand X-ray images demonstrating the feasibility of the model to reconstruct contours and landmarks for unseen images. Furthermore, we compare our model to a classical Active Shape Model and an Active Appearance Model.