Physically-based models for three-dimensional surface reconstruction, representation, and recognition

In this dissertation, we propose to use physically-based models to accomplish three tasks in computer vision: (1) 3-D shape reconstruction, (2) 3-D shape representation for sensor data fusion, and (3) 3-D shape recognition.; In the first task, we make an observation that many existing shape-from-X techniques use an "observable" and a domain-specific prediction model in 3-D shape reconstruction. We show that all these "observable--prediction-model" types of techniques can be incorporated into our unification framework of energy constraint on a flexible, deformable image frame.; In the second task, we develop a 3-D modeling scheme which uses Kalman filter as the sensor data integration tool and hierarchical B-spline surface as the recording data structure. Hierarchical B-spline surface maintains high-order surface derivative continuity, may be adaptively refined, possesses desirable local control property, and is storage efficient.; In the third task, we propose a curved surface recognition process which uses local differential surface properties calculated from hierarchical B-spline representation. When two object structures--with one constructed from image data and the other chosen from a prestored database--are made available, we use shape index to establish correspondences between the two structures and register them by properly aligning their orientations and conforming their positions and scales. This registration process can be expedited by exploiting the spline surface representation and the shape hashing approach. Shape parameters of the two objects can be compared with one another in a scale and pose invariant manner.; This research is geared toward constructing a system that is capable of reconstructing 3-D shapes using a variety of image cues, representing complex 3-D structures efficiently, and classifying an imaged surface structure against a library of models.