An algorithm to extract critical points from lattice height data

The data measured on areal surface texture instruments often takes the form of height values on a discrete rectangular lattice. The definitions of critical points (peak, pit and saddle points) for this type of data is a very important issue for definitions and stable algorithms of areal texture parameters. Many of the published algorithms for critical points fail to meet some very simple topological properties which are always true for continuous data. Thus the collection of critical points produced from these published algorithms could not have come from a genuine continuous surface giving difficulties with interpretation of the results. An algorithm for critical points from lattice height data is presented which satisfies these topological properties and represents genuine features from the measured surface.