PhD Thesis - Automated Recognition of 3D CAD Model Objects in ...

More documents

Recommendations

Info

New Approach 24 3.3 Step 2 - 3D Registration As discussed in Section 2.6.2, the project 3D model and 3D laser scans can be most effectively and efficiently registered in a common coordinate system by using benchmark-based project registration. This type of registration consists in identifying points (or benchmarks) in one data set and pairing them with their corresponding points in the second data set and then automatically calculate the transformation parameters (translations and rotations) to register the two data sets in the same coordinate system. This problem is generally referred to as the rigid registration between two sets of 3D points with known correspondence problem [58]. It defers from the general rigid registration between two sets of 3D points problem for which no point correspondence is a priori known [107]. When matching corresponding benchmark, it is unlikely that the points match exactly. As a result, the rigid registration between two sets of 3D points with known correspondence problem must be approached as an optimization problem. A good reference to this problem can be found in [58]. This problem is generally mathematically stated as: automatically identifying the rotation matrix (R), translation matrix (T ) and scaling factor (k) that minimize a cost function that measures the closeness between the two point sets with n corresponding points (n ≥ 3). The cost function is generally the mean squared error, ɛReg, of the Euclidean distances between each point in one set, xi and its corresponding point in the other set, yi, registered in the same coordinate frame, calculated as: ɛReg (k, R, T )= 1 n n� �yi − (kRxi + T )� 2 i=1 (3.1) Solutions to this problem are presented in [14] and [58], and a more robust refined one is presented in [120]. Iterative and noniterative algorithms for finding the solution are proposed in [61] and [59] respectively. In the case of the benchmark-based registration problem, it can however be noticed that there is no scaling issue, in which case k = 1. The problem is thus redefined here as identifying the rotation matrix (R) and translation matrix (T ) that minimize mean squared error, ɛReg calculated as: ɛReg (R, T )= 1 n n� �yi − (Rxi + T )� 2 i=1 (3.2) The Step 3 of the proposed 3D object recognition approach, presented in Section 3.4, requires the 3D model be registered in the scan’s spherical coordinate
New Approach 25 frame. Therefore, first of all, the matrices R and T calculated during the registration process are used to register each vertex of the STL-formatted 3D model into the laser scan’s Cartesian coordinate frame, and then the coordinates of each vertex are recalculated in the scan’s spherical coordinate frame. The algorithmic implementation of this process is presented in Algorithm 2. Appendix B details the spherical coordinate frame used here, as well as the transformation formulas between the Cartesian and this spherical coordinate frames. Data: Model, T , R for each Model.Object do for each Model.Object.Facet as F do for each F.Vertex do F.Vertex.[XYZ] Scan ←R(F.Vertex.[XY Z] Model )+T F.Vertex. −→ n ←R(F.Vertex. −→ n ) F.Vertex.[PTR] Scan ← CartesianToSpherical(F.Vertex.[XY Z] Scan ) // see Algorithm 11 in Appendix B end F. −→ n ←R(F. −→ n ) end end Algorithm 2: Procedure ReferenceInScan referencing the STL-formatted project 3D model in the scan’s spherical coordinate frame. The optimal (minimal) value of ɛReg provides some information about the overall quality of the registration optimization process. This value is thus used in Step 4 as aprioriinformation about the expected matching quality between each pair of as-built and as-planned points. In the rest of this thesis, this optimal value of ɛReg is referred to as the registration error or referencing error, and is also noted ɛReg. Finally, it is remined that the overall procedure for performing the rigid registration of two sets of 3D points consists in: (1) manually associate at least three benchmark points in the range point cloud to their corresponding benchmark points in the 3D model, and (2) run the registration algorithm to obtain the matrices R and T minimizing ɛReg and register the two point sets in the same coordinate frame. As a result, although this registration procedure is generally not time consuming, it is not fully automated.
Page 1 and 2: Automated Recognition of 3D CAD Mod
Page 3 and 4: Abstract There is shift in the Arch
Page 5 and 6: Dedication This thesis is dedicated
Page 7 and 8: 3.4 Step 3 - Calculation of the As-
Page 9 and 10: D Construction of the Bounding Volu
Page 11 and 12: 5.4 Progress recognition results fo
Page 13 and 14: 5.2 Example of a model and recogniz
Page 15 and 16: Chapter 1 Introduction 1.1 Backgrou
Page 17 and 18: Introduction 3 Sub-objectives are f
Page 19 and 20: Chapter 2 Literature Review This ch
Page 21 and 22: Literature Review 7 is also often i
Page 23 and 24: Literature Review 9 Figure 2.2: Tot
Page 25 and 26: Literature Review 11 minutes (at mo
Page 27 and 28: Literature Review 13 tigated here.
Page 29 and 30: Literature Review 15 the recognitio
Page 31 and 32: Literature Review 17 recognition of
Page 33 and 34: Literature Review 19 frame of the e
Page 35 and 36: Chapter 3 New Approach 3.1 Overview
Page 37: New Approach 23 Data: Model, Scan R
Page 41 and 42: New Approach 27 The complexity of t
Page 43 and 44: New Approach 29 are tested for inte
Page 45 and 46: New Approach 31 effectiveness of a
Page 47 and 48: New Approach 33 (a) 3D View. (b) To
Page 49 and 50: New Approach 35 Data: PB, BVH Resul
Page 51 and 52: New Approach 37 α, of each as-plan
Page 53 and 54: New Approach 39 Data: Scan,Model Re
Page 55 and 56: New Approach 41 where: α is the as
Page 57 and 58: New Approach 43 Furthermore, the ca
Page 59 and 60: Chapter 4 Experimental Analysis of
Page 61 and 62: Experimental Analysis of the Approa
Page 81 and 82: Chapter 5 Enabled Applications: Fea
Page 83 and 84: Enabled Applications: Feasibility A
Page 89 and 90:
Enabled Applications: Feasibility A
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Chapter 6 Conclusions and Recommend
Page 97 and 98:
Conclusions and Recommendations 83
Page 99 and 100:
Appendix A Description of the STL F
Page 101 and 102:
Appendix A 87 solid name facet norm
Page 103 and 104:
Appendix B 89 Figure B.1: Spherical
Page 105 and 106:
Appendix B 91 Data: [x, y, z] Resul
Page 107 and 108:
Appendix C 93 (a) 3D View. (b) Top
Page 109 and 110:
Appendix C 95 C.1.1 Bounding Pan An
Page 111 and 112:
Appendix C 97 Figure C.5: Illustrat
Page 113 and 114:
Appendix C 99 Data: ϕmintemp, ϕmi
Page 115 and 116:
Appendix C 101 Figure C.6: Example
Page 117 and 118:
Appendix C 103 Data: {Facet} Result
Page 119 and 120:
Appendix D Construction of the Boun
Page 121 and 122:
Appendix D 107 Figure D.1: Illustra
Page 123 and 124:
Appendix D 109 (a) MSABV not inters
Page 125 and 126:
Appendix D 111 It can be noted that
Page 127 and 128:
Appendix E Containment of a Ray in
Page 129 and 130:
Appendix E 115 Finally, in the case
Page 131 and 132:
Appendix F Calculation of the Range
Page 133 and 134:
Appendix F 119 second plane perpend
Page 135 and 136:
Appendix F 121 included in Algorith
Page 137 and 138:
Appendix G 123 Figure G.1: 3D CAD m
Page 139 and 140:
Appendix G 125 G.2.2 Step 2 - 3D mo
Page 141 and 142:
Appendix G 127 G.2.4 Step 4 - Recog
Page 143 and 144:
Appendix G 129 It can be seen in Fi
Page 145 and 146:
Appendix G 131 Column 7: Whether th
Page 147 and 148:
Appendix G 133 Table G.1 - continue
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Appendix H 143 Table H.1 - continue
Page 159 and 160:
Appendix H 145 Table H.2 - continue
Page 161 and 162:
Appendix H 147 [11] J. Amanatides.
Page 163 and 164:
Appendix H 149 [35] G. S. Coleman a
Page 165 and 166:
Appendix H 151 [57] B. Hofmann-Well
Page 167 and 168:
Appendix H 153 [81] A. S. Mian, M.
Page 169 and 170:
Appendix H 155 [104] L. M. Sheppard
show all

PhD Thesis - Automated Recognition of 3D CAD Model Objects in ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?