Multi-scale classification of 3-D 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. 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. Given a library of models, objects that are similar based on this multi-scale measure are grouped together into classes. The objects that are in the same class are combined into a single prototype object. 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.