Active reconstruction of three-dimensional (3D) surfaces deals with the control of camera view-points to minimize error and uncertainty in the reconstructed shape of an object. In this paper, we develop a mathematical relationship between the setup and focal lengths of a stereo camera system and the corresponding error in 3D reconstruction of a given surface. We explicitly model the noise in the image plane, which can be interpreted as pixel noise or as uncertainty in the localization of corresponding point features. The results can be used to plan sensor positioning, e.g., using information theoretic concepts for optimal sensor data selection.
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