Beyond the epsilon band: polygonal modeling of gradation/uncertainty in area-class maps

A spatial modeling technique is proposed to represent boundary uncertainty or gradation on area class maps using a simple polygon tessellation with designated zones of indeterminacy, or transition zones. The transition zone can be conceptualized as a dual of the epsilon band, but is more flexible and allows for a wide range of polygonal configurations, including polygons with sinuous boundaries, spurs, three-way transition zones and null polygons. The model is specified using the medial axis to capture the general shape characteristics of a transition zone. Graph theoretic representation of an extended version of the medial axis captures key junctions in both shape and classification, and is used to identify well-formed transition zones that can be logically and unambiguously handled by the model. A multivariate classification surface is specified by first defining degrees or probabilities of membership at every point on the medial axis and transition zone boundary. Degrees or probabilities of membership at all other points are defined by linear interpolation. The technique is illustrated with an example of a complex transition zone, and a simple isoline representation that can be derived from the model is presented. The proposed modeling technique promises to facilitate expert characterization of soil formations, ecological systems, and other types of areal units where gradation and/or boundary uncertainty are prevalent.