Lie group distance based generic 3-d vehicle classification

This paper introduces a 3-d representation of vehicles as a space of scale and orientation transformations that define the shape of individual vehicle instances. This shape space forms a group, where the similarity of different vehicle observations can be evaluated using a distance measure defined by Lie group theory. A generic class of vehicles (e.g. SUV) is represented by a set of curves on the Lie group manifold, called geodesics. The classification of any given vehicle instance is achieved by finding the class with the smallest Lie distance between the geodesics and the vehicle shape. Vehicle recognition is carried out on 3-d LIDAR point clouds. The performance of the Lie classifier is evaluated against two other approaches and found to provide superior recognition performance, particularly with respect to the ability to generalize from a small number of labeled prototypes.