Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method

Michel Grediac 1 Frédéric Sur 2
2 MAGRIT - Visual Augmentation of Complex Environments
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : This paper deals with noise propagation from camera sensor to displacement and strain maps when the grid method is employed to estimate these quantities. It is shown that closed-form equations can be employed to predict the link between metrological characteristics such as resolution and spatial resolution in displacement and strain maps on the one hand and various quantities characterising grid images such as brightness, contrast and standard deviation of noise on the other hand. Various numerical simulations confirm first the relevance of this approach in the case of an idealised camera sensor impaired by a homoscedastic Gaussian white noise. Actual CCD or CMOS sensors exhibit, however, a heteroscedastic noise. A pre-processing step is therefore proposed to first stabilise noise variance prior to employing the predictive equations, which provide the resolution in strain and displacement maps due to sensor noise. This step is based on both a modelling of sensor noise and the use of the generalised Anscombe transform to stabilise noise variance. Applying this procedure in the case of a translation test confirms that it is possible to model correctly noise propagation from sensor to displacement and strain maps, and thus also to predict the actual link between resolution, spatial resolution and standard deviation of noise in grid images.
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Michel Grediac, Frédéric Sur. Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method. Strain, Wiley-Blackwell, 2014, 50 (1), pp.1-27. 〈http://onlinelibrary.wiley.com/doi/10.1111/str.12070/abstract〉. 〈10.1111/str.12070〉. 〈hal-00937972〉

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