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This paper presents a system for fully automatic recognition and reconstruction of 3D objects in image databases. We pose the object recognition problem as one of finding consistent matches between all images, subject to the constraint that the images were taken from a perspective camera. We assume that the objects or scenes are rigid. For each image, we associate a camera matrix, which is parameterised by rotation, translation and focal length. We use invariant local features to find matches between all images, and the RANSAC algorithm to find those that are consistent with the fundamental matrix. Objects are recognised as subsets of matching images. We then solve for the structure and motion of each object, using a sparse bundle adjustment algorithm. Our results demonstrate that it is possible to recognise and reconstruct 3D objects from an unordered image database with no user input at all.