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Chapter 3: Data Collection and Modeling 35where R represents the rotation matrix and t is the translation vector. The point y is thesame as x but in the global coordinate frame. Registration is the process of finding R andt. The registration process tries to interpret common geometric information from twocalibrated range images at two different poses (views).According to [Horn et al.,1988], given three or more pairs of non-coplanarcorresponding 3D points between views, the unknown rigid transformation of rotationand translation has a closed form solution. The registration problem can hence beapproached as a point matching problem. The most popular of registration algorithms isthe Iterative Closest Point (ICP) algorithm [Besl and McKay, 1992]. We have used theimplementation of ICP in Rapidform (a reverse modeler software package) for the taskof surface registration. It allows us to initialize the ICP algorithm by manual pointpicking. The three pairs of corresponding points so picked are iteratively refined up to aparticular threshold before merging the two point clouds.Having overcome the problem of occlusions by registering multiple views, we now needto integrate these views into a single surface representation. We consider the registeredrange data as a cloud of points and reconstruct the topology of that object from its rangesamples. A simple shape may require just a few views while a complicated object mayrequire significantly more. Page et al. [Page et al., 2003a] document this systematicprocedure in the literature as a method of reconstructing mechanical components.Figure 3.6(a) shows a part that we would like to reverse engineer. We present resultsof multiple view range image acquisition process in Figure 3.6(b). The point cloud inFigure 3.6(c) is the result of reconstruction that we triangulate to represent as a CADmodel in Figure 3.6(d). We use polygonal meshes to represent the CAD model.(a) (b) (c) (d)Figure 3.6: Model creation. (a) Photograph of the object. (b) Multiple-view rangemaps. (c) View integrated point cloud. (d) Rendered triangle mesh model.
Chapter 3: Data Collection and Modeling 36A polygonal mesh is a piece-wise linear surface that comprises vertices, edges andfaces. A vertex is a 3D point on the surface, edges are the connections between twovertices, and a face is a closed sequence of edges. In a polygonal surface mesh, anedge can be shared by, at most, two adjacent polygons and a vertex is shared by atleast two edges. We use triangle meshes to represent the discrete approximations to3D surfaces. A triangle mesh is a pair T= where ν={ν 1 ,ν 2 ,ν 3 ,….,ν n } is a set ofvertices, and τ ={τ 1 ,τ 2 ,…,τ m }is the set of triangles that approximate the surface.3.2.2 Modeling Automotive Scenes for Under Vehicle InspectionUnder ideal laboratory conditions, data collection with a range scanner isstraightforward. Underneath a vehicle however, we address several challenges. Themost significant of those is the design of the scanning mechanism. The field of view islimited by the ground clearance and the huge variation in size of the components thatmake up the scene under the vehicle. The distance (range) is too small for the use oftime-of-flight scanners and laser triangulation scanners but too large forphotogrammetric measurements.Real-time 3D data acquisition is a research challenge in computer vision. Before westart thinking of a robot mountable design for vehicle inspection, we would like tobriefly survey 3D data acquisition systems that optimize the process of digitization ofreal world scenes and objects for speed and accuracy. One such expensive effort is thedigitization of statues in the “Digital Michelangelo” project that involves the closescanning of statues for cultural heritage recording. Levoy et al. in [Levoy et al., 2000]suggest a configuration for high speed laser triangulation that involves a lightprojector recording video, that is processed later to fill holes and registered using theICP algorithm for the complete 3D model. The paper [Takatsuka et al., 1999] proposesa low cost interactive active monocular range finder. Davis and Chen [Davis andChen, 2001] present the design of a laser range scanner designed for minimumcalibration complexity. They specifically state that despite the simple geometry andcomponents, laser scanners must be engineered and calibrated with extremely highprecision. Champleboux et al. [Champleboux et al., 1992] examine the process ofregistration of multiple 3D data sets obtained with a laser range finder. They propose anew sensor calibration technique based on the conjunction of a mathematical cameramodel and further discuss an algorithm based on octree splines for recovering rigidtransformation, for rotational and translational rectification between two 3D data setsobtained from the range sensor. Having considered so many options and as a tradeoffbetween resolution and field of view we decided to jack the vehicle up by a meter anduse the inverted triangle mechanism for scanning. We calibrated the sensorarrangement as discussed in Section 3.1.2 and without disturbing it we inverted it andmoved the sensor arrangement on a conveyer belt to reconstruct the 3D scene.
Page 1 and 2: To the Graduate Council:I am submit
Page 3 and 4: Acknowledgementsii“Experience is
Page 5 and 6: Contents1 INTRODUCTION.............
Page 7 and 8: List of TablesviTable 2.1:Qualitati
Page 9 and 10: viiiFigure 5.2: Curvature analysis
Page 11 and 12: Chapter 1: Introduction 21.1 Motiva
Page 13 and 14: Chapter 1: Introduction 41.2 Propos
Page 15 and 16: Chapter 1: Introduction 6We then pe
Page 17 and 18: Chapter 2: Literature Review 8Shape
Page 19 and 20: Chapter 2: Literature Review 102.2.
Page 21 and 22: Chapter 2: Literature Review 12Bimb
Page 23 and 24: Chapter 2: Literature Review 14is f
Page 25 and 26: Chapter 2: Literature Review 16foun
Page 27 and 28: Chapter 2: Literature Review 18Kort
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Page 31 and 32: Chapter 2: Literature Review 22Gots
Page 33 and 34: Chapter 2: Literature Review 24Tabl
Page 35 and 36: Chapter 3: Data Collection and Mode
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Page 49 and 50: Chapter 4: Algorithm Overview 404.1
Page 51 and 52: Chapter 4: Algorithm Overview 42Tri
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Page 55 and 56: Chapter 4: Algorithm Overview 46The
Page 57 and 58: Chapter 4: Algorithm Overview 48of
Page 59 and 60: Chapter 4: Algorithm Overview 50∞
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Page 69 and 70: Chapter 5: Analysis and Results 60W
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Page 91 and 92: Chapter 6: Conclusions 82complexity
Page 93 and 94: Bibliography 84BIBLIOGRAPHY
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Bibliography 86[Biermann, 2001][Bel
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Bibliography 88[Cyr and Kimia, 2001
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Bibliography 90[Gourley, 1998][Gosh
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Bibliography 92[Joshi and Chang, 19
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Bibliography 94[Meyer, 2002][Morse,
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Bibliography 96[Safar et al., 2000]
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Bibliography 98parts,” IEEE Trans
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Vita 100VITASreenivas Rangan Sukuma
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