Fig. 11

Ridge features from the original map. (a) The orange line indicates the ridge on the 2D function surface. All ridge points on the ridge line are the maxima in the directions perpendicular to the line (red arrows). The local maximum point (dark blue) is also a ridge point based on the definition. (b) For each given point on the contact map, we select local region (i.e. the grid points) to approximate a quadratic function. (c) On the quadratic function surface, we could identify the linear ridge and project it to the XY plane. (d) Direction of the ridge ϕ and distance from the original given point to the ridge d could be obtained from the projection. (e) We could also identify the principal curvature direction on the ridge and approximate the cross section curve with a Gaussian ridge. The height h and width w are defined as the height and the standard deviation of the Gaussian function. Details are given in the (Additional file 1: Text S1)