A new structure-from-motion ambiguity

Demonstrates the existence of an approximate, intrinsic ambiguity in Euclidean structure from motion (SFM) which occurs as generically as the bas-relief ambiguity but, unlike it, strengthens for scenes with more depth variation. The ambiguity does not occur in projective SFM, but the reasons for this make projective reconstructions more likely to have large errors. Our analysis gives a semiquantitative characterization of the least-squares error surface over a domain complementary to that analyzed by Jepson, Heeger, and Maybank. As part of our analysis, we show that the least-squares error for infinitesimal motion-the optical-flow error-gives a good approximation to the least-squares error for moderate finite motions. We propose that many high-error local minima occur for epipoles in or near the image. We also establish the existence of a new local minimum in minimizing over the rotation, given the translation direction.