Before revision:  We show that members of the Matern covariance family directly satisfy this linear PDE . Thus, our key contribution is the realisation that the regularised Eikonal equation can be simply solved by applying the logarithmic function to a GPIS formulation to recover the accurate EDF and, at the same time, the implicit surface .
After revision:  We show that members of the Matern covariance family directly satisfy this linear PDE .