Stable Algebraic Surfaces for 3D Object Representation
T. Sahin, M. Unel
Journal of Mathematical Imaging and Vision
Linear ﬁtting techniques by implicit algebraic models usually suffer from global stability problems. Ridge regression regularization can be used to improve the stability of algebraic surface ﬁts. In this paper a Euclidean Invariant 3D ridge regression matrix is developed and applied to a particular linear algebraic surface ﬁtting method. Utilization of such a regularization in ﬁtting process makes it possible to globally stabilize 3D object ﬁts with surfaces of any degree. Robustness to noise and moderate levels of occlusion has also been enhanced signiﬁcantly. Experimental results are presented to verify the improvements in global stability and robustness of the resulting ﬁts.