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This paper first presents robust algorithms to extract invariants of the linear Lie algebra model from 3D objects. In particular, an extended 3D Hough transform is presented to extract accurate estimates of the normal vectors. Least squares fitting is used to find normal vectors and representation matrices. Then a segmentation algorithm for 3D objects is shown using the invariants of linear Lie algebra. Distributions of invariants, both in the invariant space and on the object surface, are used to produce clusters and edge detection.