Shape Ambiguities in Structure from Motion

This technical report examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape. Our results for orthographic cameras show that the bas-relief ambiguity is significant even with many images, unless a large amount of rotation is present. Similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction.