Invariant recognition and segmentation of 3D object using Lie algebra models

Representation models used for 3D object recognition are desired because their invariants can be easily extracted under Euclidean and affine transformations, the shapes can be easily synthesized from these invariants and they have enough representation ability. For currently used 3D models such as generalized cylinders or super-quadratics, it is usually difficult to find the invariant features, especially to find the complete set of invariants in order to uniquely determine and reproduce the objects. The Lie algebra models which have been proposed by these authors to represent 3D objects are known to have above features. This paper presents algorithms to extract invariants of the linear Lie algebra model from 3D objects. In particular, we apply the Hough transformation to find accurate estimates of the normal vectors. Moreover, we show an efficient segmentation algorithm for 3D objects using the invariants of the linear Lie algebra. These algorithms can be applied effectively in 3D object recognition, synthesis and image coding