An application of numerical differentiation formulas to discontinuity curve detection from irregularly sampled data

We present a method to detect discontinuity curves, usually called faults, from a set of scattered data. The scheme first extracts from the data set a subset of points close to the faults. This selection is based on an indicator obtained by using numerical differentiation formulas with irregular centers for gradient approximation, since they can be directly applied to the scattered point cloud without intermediate approximations on a grid. The shape of the faults is reconstructed through local computations of regression lines and quadratic least squares approximations. In the final reconstruction stage, a suitable curve interpolation algorithm is applied to the selected set of ordered points previously associated with each fault.