In this paper, we have introduced a novel four-dimensional feature that describes the intrinsic geometrical relation between a pair of surflets, i.e., oriented surface points in 3D space. The statistical distribution of this feature as sampled from an object's surface captures both local and global aspects of shape. Empirically learned histograms of the feature distribution have here been demonstrated as a compact and efficient representation of arbitrary 3D shapes. This representation allows for rapid classification of shapes based on a single histogram per object model, independent of translation and rotation.
We have evaluated six different criteria for the shape classifier. The Kullback-Leibler and likelihood criteria have been found to perform equally well and superior to the others. They have shown nearly perfect classification under ideal sensing conditions and robust performance in the face of noise and occlusion. They are, moreover, largely independent of the resolution used for meshing surfaces of test objects. Considering its lower computational cost, we recommend using the maximum-likelihood classifier.
More specifically, the experiments clearly indicate that, for best performance, high noise during recognition should be reduced by spatial averaging, at the cost of a lower mesh resolution.
The more invariant a classifier, the less can be recovered from an act of classification. The present classifiers are by design invariant to object pose. Especially for robotic applications, however, it would be most desirable to obtain an estimate of the pose of an object, along with its identity. One direction of future research will hence be to augment the algorithm by a method for locating an object's data within a larger set that may comprise multiple objects. This would imply segmentation of the data into the objects' components.
To more firmly establish the potential of the proposed representation of shape, the dependence of classification performance on various design parameters, like feature quantization and subsampling rate, has to be investigated. Moreover, the database of objects will be extended in the future.
When moving to real data, we plan to use the DLR laser range-scanner [1] or some sort of stereo processing to acquire 3D-point clouds from a scene as a first processing step.
Apart from scene analysis, potential applications of the present shape classifiers include similarity search in a database of 3D object-models, e.g., on the Internet. In this context, normalization of the model dimensions will make the classifiers invariant to object scale.