A grammatical framework for building rooftop extraction

Roof detection has been studied for several decades, one of the big challenge is its structure and appearance diversity. In this paper, we present a grammatical framework to account for these diversities and a multiple way compositional algorithm to extract rooftops from aerial images. We represent rooftops by a context sensitive graph grammar consisting of 5 production rules and 3 types of commonly shared quadrilateral primitives. Each production rule includes a number of equations that constrain the attributes of a parent node and those of its children. In addition, a set of horizontal links are defined between peer nodes at the same level that account for spatial/appearance constraints. The graph grammar produces a large number of valid configurations and can be used to represent the wide structural variability of rooftops. Our rooftop extraction algorithm starts with a lower level bottom-up step that generates hypothesis of quadrilateral primitives by grouping edgelets hierarchically into bigger structures (straight lines, parallel lines and junctions). The grouping process repeats multiple times following alternative paths to reduce missing detections caused by partial occlusion and/or background clutter. Then the higher level relations served as context for lower level elements evaluates each hypothesis according to the graph grammar model and prunes incompatible ones to arrive at an optimal solution.