Stable algebraic surfaces for 3D object representation

Abstract

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.