Interior Object Geometry via Fitted Frames

We propose a means of computing fitted frames on the boundary and in the interior of objects and using them to provide the basis for producing geometric features from them that are not only alignment-free but most importantly can be made to correspond locally across a population of objects. We describe a representation targeted for anatomic objects which is designed to enable this strong locational correspondence within object populations and thus to provide powerful object statistics. It accomplishes this by understanding an object as the diffeomorphic deformation of the closure of the interior of an ellipsoid and by using a skeletal representation fitted throughout the deformation to produce a model of the target object, where the object is provided initially in the form of a boundary mesh. Via classification performance on hippocampi shape between individuals with a disorder vs. others, we compare our method to two state-of-theart methods for producing object representations that are intended to capture geometric correspondence across a population of objects and to yield geometric features useful for statistics, and we show notably improved classification performance by this new representation, which we call the evolutionary s-rep. The geometric features that are derived from each of the representations, especially via fitted frames, are discussed.