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To enable fast reliable feature matching or tracking in scenes, features need to be discrete and meaningful, and hence corner detection is often used for this purpose. However, to obtain a higher level description of an image, such as identification of objects, additional information such as edges is required, and more recently detectors have been proposed that find both edges and corners. Recently, finite-element based methods have been used to develop gradient operators for edge detection that have improved angular accuracy over standard techniques. We extend this work to corner detection, enabling edge and corner detection to be integrated. In addition we present a combined operator, enabling edge and corner detection to be achieved concurrently, and we demonstrate that accuracy is comparable to well- known existing corner detectors and edge detectors, and, as standard post-smoothing of the corner map is not required, significantly reduced computation time can be achieved.