Direct methods for evaluating the planarity and rigidity of a surface using only 2D views

Novel algorithms for directly checking the planarity and the rigidity of object surfaces are described. Unlike the conventional methods, our algorithms need not recover the parameters included in the equations constraining the motion of the planar or the rigid surfaces. Instead, given the correspondences of the 2D image feature points over a small number of 2D images. They directly evaluate those properties by analyzing the shapes of the feature distributions in the feature space constructed by combining the 2D features. Then, they measure how well their shapes fit the types of those for planar or rigid surfaces that are underlyingly characterized by the conventional constraint equations. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed algorithms