OPTIMAL STRUCTURE FROM MOTION
People	A. Chiuso, R. Brockett, S. Soatto.
References	"Optimal Structure From Motion", submitted to the Intl. J. of Comp. Vision, August 1998
Synopsis	"Structure From Motion" (SFM) refers to the problem of estimating spatial properties of a three-dimensional scene from the motion of its projection onto a two-dimensional surface, such as the retina or the surface of the CCD in a modern camera. In this research we emphasize the analysis of SFM from the point of view of noise, and seek for algorithms that are provably convergent and provably optimal with respect to a chosen norm. In particular, we cast SFM as the minimization of a high-dimensional quadratic cost function, and show how it is possible to reduce it to the minimization of a two-dimensional function whose stationary points are in one-to-one correspondence with those of the original cost function. As a consequence, we can plot the reduced cost function and characterize the configurations of structure and motion that result in local minima. As an example, we discuss two local minima that are associated with well-known visual illusions.  We also offer an experimental study of the distribution of the estimation error in the presence of noise in the measurements, and characterize the sensitivity of the algorithm using the structure of Fisher's Information matrix.