DIC Challenge 2.0: Developing Images and Guidelines for Evaluating Accuracy and Resolution of 2D Analyses

Abstract

Background

The DIC Challenge 2.0 follows on from the work accomplished in the first Digital Image Correlation (DIC) Challenge Reu et al. (Experimental Mechanics 58(7):1067, 1). The second challenge was required to better quantify the spatial resolution of 2D-DIC codes.

Objective

The goal of this paper is to outline the methods and images for the 2D-DIC community to use to evaluate the performance of their codes and improve the implementation of 2D-DIC.

Methods

This paper covers the creation of the new challenge images and the analysis and discussion of the results. It proposes a method of unambiguously defining spatial resolution for 2D-DIC and explores the tradeoff between displacement and strain noise (or measurement noise) and spatial resolution for a wide variety of DIC codes by a combination of the images presented here and a performance factor called Metrological Efficiency Indicator (MEI).

Results

The performance of the 2D codes generally followed the expected theoretical performance, particularly in the measurement of the displacement. The comparison did however show that even with fairly uniform displacement performance, the calculation of the strain spatial resolution varied widely.

Conclusions

This work provides a useful framework for understanding the tradeoff and analyzing the performance of the DIC software using the provided images. It details some of the unique errors associated with the analysis of these images, such as the Pattern Induced Bias (PIB) and imprecision introduced through the strain calculation method. Future authors claiming improvements in 2D accuracy are encouraged to use these images for an unambiguous comparison.

Appendix

Comparison with Theory

For most implementations of DIC, the optimal displacement minimizes the SSD criterion on each subset. The corresponding optimal parameters $q^*$ satisfies:

$$\begin{aligned} q^*=\underset{q}{\mathrm{Argmin}} \sum _{x\in \Omega } \left( I_{ref}\left( x\right) -I_{cur}(x+v\left( x,q\right) )\right) ^2 \end{aligned}$$

(4)

where $I_{ref}$ (resp. $I_{cur}$) is the reference (resp. current) image and v(x, q) is a polynomial basis function that is either 1st order (affine) or 2nd order (quadratic). Let $u_{GT}$ be the ground truth displacement. Considering an infinite resolution texture that tracks the underlying material, $I_{ref}\left( x\right) =I_{cur}\left( x+u_{GT}\left( x\right) \right)$. Equation (4) can be rewritten as

$$\begin{aligned} q^*=\underset{q}{\mathrm{Argmin}} \sum _{x\in \Omega } \left( I_{def}\left( x+u_{GT}(x)\right) -I_{cur}(x+v\left( x,q\right) )\right) ^2 . \end{aligned}$$

(5)

For most implementations of DIC, assuming that the image pattern corresponds to the perfect information carrier, it drives the DIC algorithm to the best solution. The expected DIC solution simply results to the projection of the ground truth displacement to the DIC kinematics, thus neglecting the effect of $I_{cur}$ in equation (5). This leads to

$$\begin{aligned} q^*=\underset{q}{\mathrm{Argmin}}_q \sum _{x\in \Omega } \left( u_{GT}\left( x\right) -v\left( x,q\right) \right) ^2 . \end{aligned}$$

(6)

This result was introduced in [26], experimentally validated in [13, 27] and thoroughly mathematically demonstrated in [20]. It simply corresponds to the effect of the well-known Savitzky-Golay filter. Even though these results are shown only for the SSD, most unweighted criteria lead to the same solution at convergence [28].

These equations produced the expected DIC results for the DIC Challenge 2.0 Star image in Figs. 3, 6 and 8 and produced the curves in the Fig. 14 for affine (1st order) and quadratic (2nd order) shape functions.

Fig. 14

Expected DIC results for the DIC Challenge 2.0 Star images using a SSD criterion and affine or quadratic shape functions. Notation h corresponds to the subset size