Image processing

For each trial, strains in the contact area were computed from the images as described in Delhaye et al., 2016 (Figure 1C). Briefly, the contact region was first extracted semiautomatically from each image of the sequence. Second, equally spaced features were sampled in the contact area of the initial frame and then tracked from frame to frame to measure the displacement field in the contact using the optical flow technique (Lucas and Kanade, 1981) implemented in the OpenCV online computer vision toolbox (Bradski, 2008). Third, the tracked features were triangulated (Delaunay triangulation), and Green-Lagrange strains were computed for each triangle by calculating the gradient of the displacement field. This operation yielded a 2-by-2 symmetric strain matrix for each triangle and each pair of consecutive frames. Axial strains, that is, the diagonal elements of the strain matrix, were denoted exx and eyy and shear strain (off-diagonal) was denoted exy. The x-axis was aligned to the radial-ulnar orientation (Figure 1B). Strains were filtered, first spatially (using Smooth Triangulated mesh from Matlab FEX, https://mathworks.com/matlabcentral/fileexchange/26710-smooth-triangulated-mesh), and then temporally (median filtering over three strain values). By using the term 'strain' throughout the article, we refer to the elements of the strain tensor computed between two consecutive images and expressed in percent per second, that is, strain rates.

The principal strain components denoted e1 and e2 were then obtained by an eigenvalue/eigenvector decomposition of the strain matrix. The principal strains e1 and e2 correspond to the maximum compressive and tensile strains at the location where the strain tensor is measured. The eigenvalue decomposition is equivalent to a rotation of the reference frame so that the shear strain is canceled and only axial strains remain, which thus corresponds to the maximum local compression and/or dilation. Therefore, the principal strains are not necessarily aligned with the axes of the x-y reference frame defined above and their orientation is potentially different for each local strain tensor. Therefore, the matrix components of the local strain tensor e are solely given by the axial and shear strains along the x-y plane (exx, eyy, and exy). Besides, given the high stiffness of the outer layer of the skin (Wang and Hayward, 2007), it is reasonable to assume that the area of local patches of skin is conserved after deformation. Under this hypothesis, it can be shown that e1 and e2 have opposite signs. This means that if one of the principal strain is compressive, the other one is dilative and vice versa. Moreover, we follow the convention to sort the eigenvalues by ascending order. Therefore, e1 will always be smaller than e2. Under the hypothesis of area conservation, this implies that e1 will be negative and thus compressive, whereas e2 will be positive and thus tensile. This hypothesis has been verified in practice on the data.

To assess the strains taking place at each given point of the contact area across different trials, we interpolated the strains on an arbitrary rectangular grid, the ‘strain grid’. First, an easily identifiable feature of the fingerprint located near the center of contact was manually spotted on the first image of each trial and used to precisely align all trials. Given the precise repeatability of the trials, the spotted feature only moved by a few pixels from trial to trial. Then, the contact area was centered on the grid using its geometric center on the first image. The feature coordinates on the first image were then used to interpolate the strains over the entire trial on the given grid using MATLAB’s scatteredInterpolant function. The ‘strain grid’ spacing was set to 10 pixels (~200 um) and was composed of 120-by-90 elements (1200 × 900 pixels).

The local fingerprint orientation was also estimated as described previously (Delhaye et al., 2016) by computing the image gray-level gradients (Bazen and Gerez, 2000) over a 60-by-60 pixels window.