Necessary conditions to attain performance bounds on structure and motion estimates of rigid objects

Analytic conditions that are necessary for the maximum likelihood estimate to become asymptotically unbiased and attain minimum variance are derived for estimation problems in computer vision. In particular, problems of estimating the parameters that describe the 3D structure of rigid objects or their motion are investigated. It is common practice to compute Cramer-Rao lower bounds (CRLB) to approximate the mean-square error in parameter estimation problems, but the CRLB is not guaranteed to be a tight bound and typically underestimates the true mean-square error. The necessary conditions for the Cramer-Rao lower bound to be a good approximation of the mean-squareerror are derived. The tightness of the bound depends on the noise level, the number of pixels on the surface of the object, and the texture of the surface. We examine our analytical results experimentally using polyhedral objects that consist of planar surface patches with various textures that move in 3D space. We provide necessary conditions for the CRLB to be attained that depend on the size, texture, and noise level of the surface patch.