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Title: Dynamic calibration and 3D reconstruction via homographic matrix in a structured light system
Other Titles: Jie gou guang xi tong zhong ji yu dan ying ju zhen de dong tai biao ding he san wei chong jian
Authors: Zhang, Bei Wei (張備偉)
Department: Dept. of Manufacturing Engineering and Engineering Management
Degree: Doctor of Philosophy
Issue Date: 2006
Publisher: City University of Hong Kong
Subjects: Calibration
Three-dimensional imaging
Notes: 149 leaves : ill. ; 30 cm.
CityU Call Number: TA1637.Z428 2006
Includes bibliographical references (leaves 131-149)
Thesis (Ph.D.)--City University of Hong Kong, 2006
Type: Thesis
Abstract: In this thesis, we investigate the problem of dynamic calibration and 3D reconstruction in a color-encoded structured light system. The problem is approached from different perspectives under different assumptions with the corresponding methods developed, namely the two-known-plane based, one-known-plane based and one-arbitrary-plane based methods. Here, the word ‘known’ means that the equation of a plane is known, rather than knowing any Euclidean structure from the plane. The first method explores the image-to-world transformation and its use in obtaining 3D structure of the scene. Herein, we assume that there are two known planar surfaces in the scene and the projector is calibrated. Our results show that the dynamic determination of this transformation is equivalent to the computation of the online image-to-light-plane Homography in our system. This method is proved to be computationally cheaper than the traditional approaches and therefore suitable for the time-critical tasks. In the second method, we assume that there is one known planar surface in the scene. Then the image-to-world transformation can also be determined online. Our results show that this task is equivalent to the process of first obtaining the unknown and variable intrinsic and extrinsic parameters and then computing the transformation from its formula. To initially calibrate the intrinsic parameters of the camera, a planar pattern containing an equilateral polygon with 2n sides (2>n) is suggested to be used. This pattern is very easy to produce and manipulate for the calibration since the position and metric size of the polygon can be arbitrary. In addition, it is easily detectable and identifiable, requiring no point correspondence between the pattern and the image. In the last method, we propose to resolve the extrinsic parameters of our system under the assumption of an arbitrary planar surface in the scene. The image-to-image Homographic matrix is first computed using the camera image and projector plane. Then over-constrained equations are established to determine the translation vector and the rotation matrix. By using matrix perturbation theory, we also investigate the error sensitivity of the estimated pose parameters with respect to the noise in the image points. Our results show that this algorithm is reliable and easy to be implemented. Hence, it promises wide applications for active vision systems, such as robot hand-eye calibration, mobile robot navigation and object recognition and localization. In these methods, the plane-based formulation is extensively studied and analytic solutions are provided. In the presence of noise, these techniques can be easily incorporated with redundancy in the data to improve the reliability of the estimations. Besides, they all feature the sufficiency of a single image, requiring no special calibration devices or targets. We hence call the process dynamic calibration. The first two methods consider the system as a collection of light planes and a camera, by solving the online image-to-world transformation to give a real Euclidean reconstruction. However, only the camera’s parameters are allowed to adjust freely. On the other hand, the last one regards the system as an active stereoscopic vision, by solving the relative pose problem to obtain a relative structure. Either the projector or the camera can be moved arbitrarily during working, which is more desirable for practical applications.
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