Comparing several spectral methods used to extract displacement fields from checkerboard images

Michel Grediac 1 Benoît Blaysat 1 Frédéric Sur 2
2 MAGRIT-POST - Augmentation visuelle d'environnements complexes
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : Checkerboard represents the best pattern for in-plane displacement measurement in terms of sensor noise propagation because this pattern maximizes image gradient. It also exhibits other interesting properties in terms of pattern-induced bias for instance. Digital Image Correlation (DIC) is not the best option to extract displacement fields from such periodic patterns, and spectral methods should be used instead. In this paper, it is shown that three different spectral techniques initially developed for classic bidimensional grids can be adapted to process checkerboard images. These three techniques are the Geometric Phase Analysis (GPA), the windowed version of the Geometric Phase Analysis (WGPA), and the Localized Spectrum Analysis (LSA), which can be regarded as the ultimate version of WGPA. The main features of these three techniques as well as the link between them are given in this paper. Their metrological performance are compared in terms of displacement resolution, spatial resolution and bias. Synthetic checkerboard images deformed with a suitable reference displacement field are considered for this purpose. It is shown that GPA is the fastest method. According to the metric used in this paper, the best metrological performance is obtained with WGPA with suitable settings. LSA followed by a deconvolution algorithm is just behind, but the calculation time is approximately 10 times lower than that of WGPA for the examples considered in this paper, which makes it a reasonable choice for the determination of in-plane displacement fields from checkerboard images.
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Michel Grediac, Benoît Blaysat, Frédéric Sur. Comparing several spectral methods used to extract displacement fields from checkerboard images. Optics and Lasers in Engineering, Elsevier, 2020, 127, pp.1-33. ⟨10.1016/j.optlaseng.2019.105984⟩. ⟨hal-02436572⟩

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