This award funds an initial exploration of a theoretical basis for visual image structure, to aid in supporting queries to image archives. Digital image archives are proliferating, which raises the question of how to retrieve specific images from them. However, while queries are naturally posed in high-level, functional terms, the realizations of such queries are based on low-level image operators. An intermediate-level theory of visual structure is necessary to close this gap, which is precisely what this research addresses. Based on an interpretation of edge elements as tangent estimates, it is derived from geometric measure and complexity theory. Viewed from below, the theory provides an organization for edge elements according to dimension. They are either bound into extended (1-dimensional) groups, into (2-dimensional) structural classes that abstract different types of texture, or (0-dimensional) orientation discontinuities. Viewed from above, the representation induces equivalence classes of structure, such as bounding contours, texture flows for hair and grass patterns, and ``T''-junctions for points of occlusion. Thus queries involving forests can be differentiated from those involving fur patterns or turbulent water, and multiple, overlapping objects can be separated into components. Furthermore, images and drawings can be segmented from pages of text.
