Foundations of topological characterization of surface texture

More than a hundred years ago Maxwell proposed dividing a landscape into regions consisting of hills or alternatively consisting of dales. A hill is a set of points from which maximum uphill paths lead to one particular peak, and a dale is the set of points from which maximum downhill paths lead to one particular pit. Starting with Maxwell's ideas this paper sets out to develop the foundations of topological characterization of surface texture. This leads to a system of surface texture characterization which is complementary to published areal parameters based on the mean line system. In a similar manner that R&W system is complementary to the mean line system for profiles (the dale is the areal equivalent of a motif on a profile). An important example of a true areal characterization contained within this system is the connectability of surface valleys. This is important for applications such as lubrication and paintability of a surface. It is also important for characterizing extruded aluminium that has been anodized. The anodizing has cracks (connected valleys) and isolated pits, both of which require characterizing separately for production control.