On Error Assessment in Stereo-based Deformation Measurements: Part I: Theoretical Developments for Quantitative Estimates

Using the basic equations for stereo-vision with established procedures for camera calibration, the error propagation equations for determining both bias and variability in a general 3D position are provided. The results use recent theoretical developments that quantified the bias and variance in image plane positions introduced during image plane correspondence identification for a common 3D point (e.g., pattern matching during measurement process) as a basis for preliminary application of the developments for estimation of 3D position bias and variability. Extensive numerical simulations and theoretical analyses have been performed for selected stereo system configurations amenable to closed-form solution. Results clearly demonstrate that the general formulae provide a robust framework for quantifying the effect of various stereo-vision parameters and image-plane matching procedures on both the bias and variance in an estimated 3D object position.