Cramer-Rao Bounds for Nonparametric Surface Reconstruction from Range Data

The Cramer-Rao error bound provides a fundamental limit on the expected performance of a statistical estimator. The error bound depends on the general properties of the system, but not on the specific properties of the estimator or the solution. The Cramer-Rao error bound has been applied to scalarand vector-valued estimators and recently to parametric shape estimators. However, nonparametric, lowlevel surface representations are an important tool in 3D reconstruction, and are particularly useful for representing complex scenes with arbitrary shapes and topologies. This paper presents a generalization of the Cramer-Rao error bound to nonparametric shape estimators. Specifically, we derive the error bound for the full 3D reconstruction of scenes from multiple range images.