Measuring congruence of spatial objects

This article develops and tests an algorithm of spatial congruence based on geometric congruity of two spatial areal objects in the Euclidean plane. Spatial congruence is defined and thus evaluated as an increasing continuous function of congruity in the position, orientation, size, and shape of spatial objects, dependent upon scaling, translation, and rotation. Expansion-based geometric matching is used to seek the best match between the two objects of interest for the examination and differentiation of the congruence effects of their spatial and geometric properties, while the expansion-inflated size effect is deflated or filtered out accordingly. The use of both expansion and deflation not only allows for a trade-off between size and position, both of which are found substitutable for each other in congruence measurement, but also enables the congruence algorithm to be highly sensitive to differences or changes in these properties. Three geographical objects (the states of Texas, Mississippi, and Louisiana) are used to show how trade-offs among the four properties are manipulated by the congruence algorithm in a geographic information system (GIS) environment, ArcGIS®. In addition, three regular geometric objects are used to demonstrate how the congruence algorithm is sensitive even to small changes in each of the four properties of objects. The results show that the proposed congruence algorithm is capable of quantifying the extent of congruity between two spatial objects regardless of how they are related as described in topological relations.