This project is developing algorithms to recognize objects in wide- angle images using local symmetries. A new mathematical model of imaging geometry, based on stereographic projection, provides a more accurate model of real wide-angle lenses than traditional perspective projection. It also creates a simple mathematical relationship between local symmetries of round objects and their outlines in 2D images: symmetries project onto symmetries. Finally, projection of small objects is approximately orthographic, so that existing algorithms for detecting skew symmetries (symmetries of flat 3D objects) can be adapted to wide fields of view. An object recognition system is being constructed, using both skew and non-skew symmetries, a calibrated camera/lens system, and a canonical frame construction. Faster algorithms are being developed to detect symmetries so they can be used to group edges in complex wide-angle images. This project is evaluating techniques for using additional views of an object to verify or disambiguate possible symmetries, such as imposing depth constraints on the initial search for symmetries and confirming that the apparent shape of the object changes appropriately between two views. The frequency of local symmetries in real objects, and their stability across changes in viewpoint, is also being studied.
