Graph Theoretical Measures for Land Development

Abstract

In the previous chapters, we concentrated on land use classification. This chapter extends this problem and casts it as measuring organization on land. Therefore, we introduce graph theoretical measures over panchromatic images here. We extract primitives from the image, calculate measures on these primitives, and fuse these measures to determine the final region type. Our primitives are lines extracted by line support regions; see Chap. 6). We represent each straight line segment as a vertex in a graph and define a neighborhood tolerance to construct edges between these vertices. We then compute measures on these graphs to infer the type of region. These measures generally increase with respect to the degree of organization in the image. To form these measures, we first consider unweighted graphs and use the circuit rank and degree (valency) sequence. Then, we consider weighted graphs and introduce measures based on graph partitioning and the graph spectrum. For our purposes, the level of development (or, roughly, the degree of organization) is based on the type and density of construction (buildings, streets, etc.) and its geometric regularity. Our measures are defined to infer this indirectly from the organization of lines in the image. We consider rural areas without buildings to be the least developed, proceeding through sparse residential, dense residential, commercial, industrial, to urban centers. We concede that the concept of “degree of organization” is not mathematically precise. This chapter represents a step toward quantifying this notion.