Gradient Estimation from Irregularly Spaced Data Sets

Topographic data sets are often composed of terrain samples arranged in irregular meshes. Many gradient estimation methods require the data to be arranged in a regular mesh; irregular meshes present a difficulty for them. This paper presents a novel method of estimating surface gradients from irregularly spaced inputs. The method is derived using directional derivatives and is shown to be a generalization of traditional finite difference methods. Analytical tests were used to evaluate the method, which was shown to be accurate and robust.