Interior Object Geometry via Fitted Frames (2407.14357v1)

Abstract: We describe a representation targeted for anatomic objects which is designed to enable strong locational correspondence within object populations and thus to provide powerful object statistics. The method generates fitted frames on the boundary and in the interior of objects and produces alignment-free geometric features from them. It accomplishes this by understanding an object as the diffeomorphic deformation of an ellipsoid and 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-the-art 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 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, is discussed.