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 Title: Determining Three-Dimensional Motion and Structure of a Rigid Body Using Point and Straight Line Correspondences (Stereo, Graphics, Vector) Author(s): Yen, Robert Louis Department / Program: Electrical Engineering Discipline: Electrical Engineering Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Engineering, Electronics and Electrical Abstract: The problem is the determination of the 3D motion and structure of a 3D object, using central projections of 3D points and 3D straight lines over a sequence of images. Over 2 frames, the 3D motion parameters to be determined are a 3D rotation and unit translation. Object structure can be determined as a map of relative depths of 3D points/lines. From point correspondences (PCs) and line correspondences (LCs) (which are assumed to be given), equations in terms of the 3D motion parameters are obtained and solved. A geometrical approach is taken, by using the unit sphere as the surface of projection and a homogeneous coordinate representation of points on it. For the case of PC methods, improvements and further insights are given. A simple derivation is shown for 2 basic equations. An improved linear method is given, for 3D objects with surfaces of arbitrary geometry. 2 new methods for determining a relative depth map of 3D points are described. For the case of LC methods, totally new and important results are described. It is important to note that a LC method can be applied as a PC method. A method over 2 frames is described (requiring the solution of non-linear equations), where the relative orientation of the 3D lines is known. A linear method over 2 frames is described, where the 3D lines lie on parallel planes. A method over 3 frames is described (requiring the solution of non-linear equations), where there is no constraint on the 3D motion or 3D line configuration. A linear method over 3 frames is described, where the 3D lines lying on parallel planes undergo a parallel screw motion over 3 frames. Given that rotation has been determined, a solution region to the unit translation can be determined as a patch on the unit sphere. If the unit translation can be uniquely determined, a map of relative depths of 3D lines can be determined. Simulation results are described for some of the PC and LC methods, including the effects on errors due to image quantization. Issue Date: 1984 Type: Text Description: 267 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984. URI: http://hdl.handle.net/2142/69286 Other Identifier(s): (UMI)AAI8422181 Date Available in IDEALS: 2014-12-15 Date Deposited: 1984
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