5 Uncertainty Quantifications for Multiviewcorrelation 61 Introducing the tensor Tc = qc 1q c 2 g c 1/ qc 1 ec 1 ⊗ec 1 +g c 1/ qc 2 ec 2 ⊗ec 2 gives access to a compact expression for the uncertainty due to noise σ 2 u = 1 A c sc σc 2 ϕc · Tc · ϕc c 1 σc 2 ϕc · Tc · ϕc −2 (5.9) This tensor accounts for the change of brightness as the surface becomes more inclined and in particular its anisotropic features. Similarly, the weight of a given surface that varies with the projected area is included. The optimal weighting of each camera mitigates the effect of unfavorable geometry of the observed surface. 5.4 Conclusions The standard displacement resolution associated with the registration for a surface facet was derived within the framework of small perturbations due to Gaussian white noise. This type of result can be generalized to more complex surfaces, and to the effect of calibration errors and shape reconstruction uncertainties. Practical evaluations are to be performed in order to compare the theoretical predictions with practical cases. References 1. Sutton, M.A., Orteu, J.-J., Schreier, H.W.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. Springer, New York, NY (2009) 2. Dufour, J.-E., Hild, F., Roux, S.: Shape, displacement and mechanical properties from isogeometric multiview stereocorrelation. J. Strain Anal. Eng. Des. 50(7), 470–448 (2015) 3. Hild, F., Roux, S.: Comparison of local and global approaches to digital image correlation. Exp. Mech. 52(9), 1503–1519 (2012) 4. Leclerc, H., Périé, J.-N., Hild, F., Roux, S.: Digital volume correlation: what are the limits to the spatial resolution? Mech. Ind. 13, 361–371 (2012) 5. Hild, F., Roux, S.: Digital image correlation. In: Rastogi, P., Hack, E. (eds.) Optical Methods for Solid Mechanics. A Full-Field Approach, pp. 183–228. Wiely-VCH Verlag, Weinheim (2012)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==