A Bit on the Right, A Bit on the Left: Towards Logical Bundle Adjustment

This article proposes an innovative approach fully based on logic to determine the relative positions and orientations of objects in a scene photographed from different points of view as well as those of the cameras used to take the pictures. The proposal is absolutely not based on 2D feature extraction, projective geometry or least squares adjustment but on a logical approach based on an enumeration of simple relationships between the objects visible in the photos. It is an approach imitating a natural and unconscious reasoning that each of us makes by observing a scene: is this object more to the right than this one? And is this other one further away from me than the one who’s partially hiding it from me? It is therefore a question of approaching the problem by identifying and recognizing objects in photographs and not by measuring millions of points in space without having any idea of the object to which they belong. This article presents a ”proof of concept” based on virtual experimentation: in a discrete 3D space, a simple scene, composed of spheres of different colors and cameras, is modelled in a 3D format. In this work the positioning of the spheres and cameras is limited to a plane. Cameras are placed in the scene in order to see the spheres and then for each camera an image is generated. The application reads each image and deducts relationships between object and camera. These relationships based on the visible occlusions between the projections of the objects onto the photographs, are formalized according to Allen’s relationships. A knowledge base is implemented to allow an iterative process of SPARQL queries for qualitative spatial reasoning leading to a set of possible solutions. Finally, the system deduces the relative positions between objects and cameras and the result is imported and can be used within several photogrammetry software suites.