| Inferring 3D information from 2D images is a fundamental problem in computer vision and has many applications such as robotics, scene modeling, medical imaging, and augmented reality. While the basic geometric principles for typical imaging models have been established and are well understood, successful real world 3D vision systems are still scarce and their functionalities are still very limited, due to various practical challenges. For instance, the camera parameters may be unavailable, the image quality may be poor, and good feature detection may be difficult to achieve.;As a result, the designed algorithms are not only robust enough for coping with many challenges arising in practical problems, but also able to produce results with some desired properties such as no projective/affine distortion. Further, the intuitive geometry also leads to insightful understanding of the particular problems such as the analysis of degeneracy. For each of the chosen applications, we report extensive experiments that were designed and performed to compare the proposed approach with existing state-of-the-art techniques, demonstrating the effectiveness and advantages of the proposed methods.;In this dissertation, novel image rectification schemes are proposed in the context of exploring several practical 3D vision problems, i.e. image rectification for stereoscopic visualization, stereoscopic view synthesis from monocular endoscopic images, rapid cone and cylinder modeling from a single image, and monocular vision guided mobile robot navigation. For each problem, novel algorithms are proposed based on the rectification schemes as well as the domain knowledge of the particular problems. These novel schemes are all based on the concept of sequential virtual rotation, which has intuitive geometric meaning and can be estimated from basic image features. |
