An information geometry approach to shape density Minimum Description Length model selection

For advantages such as a richer representation power and inherent robustness to noise, probability density functions are becoming a staple for complex problems in shape analysis. We consider a principled and geometric approach to selecting the model order for a class of shape density models where the square-root of the distribution is expanded in an orthogonal series. The free parameters associated with these estimators can then be rigorously selected using the Minimum Description Length (MDL) criterion for model selection. Under these models, it is shown that the MDL has a closed-form representation, atypical for most applications of MDL in density estimation. We provide a straightforward application of our derivations by using this closed-from MDL criterion to select the optimal multiresolution level(s) for a class of square-root, wavelet density estimators. Experimental evaluation of our technique is conducted on one and two dimensional density estimation problems in shape analysis, with comparative analysis against other popular model selection criteria such as Bayesian and Akaike information criteria.