| Summary: | 碩士 === 國立清華大學 === 電機工程學系 === 92 === Some calibration methods can estimate the relative positions of cameras and their intrinsic parameters using 3D coordinates of points on a known calibration target. However, it is nearly impossible to use the same calibration target for the wide range of vision tasks that require cameras with long focal length for magnification as well as short one for a larger field of view. Furthermore, many robotic applications demand cameras to be calibrated on-line, which makes it impossible to put a specific calibration target for different camera setups. Now some methods of self-calibration are reported, these methods have not bad effect [31]. If we know some information from the scene, we can exploit the information to improve reconstruction from the methods of self-calibration. By deeply exploring 3D projective geometry we can know that relative lengths are a very beneficial constraint to metric 3D reconstruction. Relative lengths can be easily acquired from geometrical shape such as circle and cubic.
In this thesis, we presented a camera self-calibration and 3D structure recovery algorithm by using the relative lengths which is an invariant property under the similarity transformation. From the studying of 3D geometry and camera model, it can be shown that there exists a homography matrix with its elements partly depending on the intrinsic parameters to be able to upgrade the projective reconstruction to the metric one. Based on the particular form of homography matrix, we can formulate an error function according to the invariance of relative lengths under the similarity transformation and hence camera calibration and 3D structure recovery can be achieved by minimizing this error function. In this way, the recovered structure will automatically satisfy the invariance constraint of metric stratum. Thus, a metric reconstruction of the scene is also achieved. In addition, the proposed method can effectively deal with the case with varying intrinsic parameters of camera for the homography matrix is uniquely determined for every views of the scene.
In this thesis, we have tested the proposed method on some synthetic and real data. The results are encouraging. The reconstructed 3D structures are visually perfect.
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