Recognizing repeated structures from a single image by invariants

This thesis presents a new class of objects and derives geometric invariants for recognizing these objects. It also demonstrates that these geometric invariants enable model-based recognition systems to automatically identify these 3D objects from a single image with a natural background regardless of viewpoints as long as features are visible in the image.; The new objects contain duplicate copies of an entity, called a repeated structure. The system can recognize 3D repeated structures from a single image because the image provides same information that can be found in stereo images. The information includes corresponding features between repeated structures.; We derived geometric invariants based on two symmetric relationships: repeated structures that are related by a strict translation (TSs) or by a strict rotation (SORs) in space. These geometric invariants are defined as properties that hold true for a particular symmetry in space and in the image. Therefore, we can identify objects based on their own geometric invariants from an image.; Although geometric invariants must be derived based on known symmetry, using these geometric invariants does not limit the system to recognize only this type of symmetry. This was demonstrated by using our geometric invariants to automatically recognize TSs and SORs.; This thesis characterizes the stability of our geometric invariants. The result shows that the index invariants for both TSs and SORs can be used practically because their inaccuracy is approximately linear to the inaccuracy of features in an image.; In addition, this thesis emphasizes the efficiency of the entire recognition process and the time profiles of real images are presented.