PSI - Issue 37

Francisco Barros et al. / Procedia Structural Integrity 37 (2022) 880–887 Barros et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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parameters and the “optimal triangulation method” presented by Hartley and Zisserman (2003). Displacements between the two states were obtained directly through the subtraction of coordinates. The 3D case was intended from the beginning to be processed in a conventional DIC procedure due to the speckle like properties of the surface. The intention on the 2D case was initially to track a single notable point instead of a field over a region of interest, but it was verified that results were obtainable for any point on the surface, so a region of interest along the side of the bridge was also defined and its displacement field was computed. 3.3. Stereo matching In the 3D case, matching subsets across images from different cameras required an additional step, because the distortion due to perspective means that the same real-world area will, in general, be in different areas of the image in both cameras; besides, the subsets themselves can be distorted in ways that cannot be approximated by a rigid translation. In this case, since the surface is approximately flat, the change in shape of the whole surface from one camera to the other can be roughly described by a projective transformation in 2D. Finding this transformation makes it possible to warp one of the images such that the surface appears very similar in both images, as shown in Fig. 6. DIC computations were performed using this warped image and the inverse transformation was applied to the resulting image points in order to get their location in the original image.

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Fig. 6. Superposition of the reference images from camera A (magenta) and camera B (green): (a) before applying the projective transformation; (b) after applying the projective transformation.

The projective transformation was found through a feature detection and matching algorithm between both reference images, namely the scale-invariant feature transform (SIFT) method (Lowe, 2004), implemented with the VLFeat library (Vedaldi & Fulkerson, 2008), with a peak threshold of 7 and an edge threshold of 2. The point correspondences were used as an input to the Matlab function estimateGeometricTransform (The MathWorks, Inc., 2021), in order to obtain the desired transformation. 4. Results The displacement magnitude field for the 3D test, using a subset size of 50 px and a step size of 25 px, are presented in Fig. 7. The 2D test, with 100 px subsets, produced the results in Fig. 8, which include displacement magnitude and direction, after the elimination of outlier values.