Multi-Scale Classification of 3D Objects

We describe an approach to the classification of 3-D objects using a multi-scale representation. This approach starts with a smoothing algorithm for representing objects at different scales. In a way similar to the classical scale space representations, larger amount of smoothing removes more details from the surfaces. Smoothing is applied in curvature space directly, thus avoiding the usual shrinkage problems and allowing for efficient implementations. A 3-D similarity measure that integrates the representations of the objects at multiple scales is introduced. This similarity measure is designed to give higher weight to the coarse scale representations, while ignoring the finer scale details of the surfaces. Given a library of models, objects that are similar based on this multi-scale measure are grouped together into classes. We show how shapes in a given class can be combined into a single prototype object. This is achieved by using a powerful property, introduced earlier, of inverse mapping from representation to shape. Finally, the prototypes are used for hierarchical recognition by first comparing the scene representation to the prototypes and then matching it only to the objects in the most likely class rather than to the entire library of models. Beyond its application to object recognition, this approach provides an attractive implementation of the intuitive notions of scale and approximate similarity for 3-D shapes.