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Generalized laplacians for man-made object detection in satellite images

A discrete version of Bochner laplacian is used for man-made object detection in mostly-natural satellite images. This paper describes research made for studying in this context discrete versions of Bochner laplacian and Ricci curvature known from Riemannian geometry. These combinatorial operators act on cell-complexes instead of smooth manifolds - a concept originating in the work of Robin Forman, and adopts his more general concepts to images. The idea is that digital images are not the smooth manifolds we want them to be, but objects of discrete nature. Thus, referring an image as a cell-complex and using the appropriate operators is a more natural approach. This way there is no loss of information due to approximation made by the transition from the discrete to the continuous world. The discrete Bochner laplacian excels in other image processing tasks as well, such as sharpening and edge-detection, and can be used in diffusion processes.