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iiiAbstractIn this thesis, we present the Curvature Variation Measure (CVM) as ourinformational approach to shape description. We base our algorithm on shapecurvature, and extract shape information as the entropic measure of the curvature. Wepresent definitions to estimate curvature for both discrete 2D curves and 3D surfacesand then formulate our theory of shape information from these definitions.With focus on reverse engineering and under vehicle inspection, we document ourresearch efforts in constructing a scanning mechanism to model real world objects. Weuse a laser-based range sensor for the data collection and discuss view-fusion andintegration to model real world objects as triangle meshes. With the triangle mesh asthe digitized representation of the object, we segment the mesh into smooth surfacepatches based on the curvedness of the surface. We perform region-growing to obtainthe patch adjacency and apply the definition of our CVM as a descriptor of surfacecomplexity on each of these patches. We output the real world object as a graphnetwork of patches with our CVM at the nodes describing the patch complexity. Wedemonstrate this algorithm with results on automotive components.
Contents1 INTRODUCTION.......................................................................11.1 Motivation ............................................................................................................. 21.2 Proposed Approach ............................................................................................... 41.3 Document Organization......................................................................................... 62 LITERATURE REVIEW...........................................................72.1 Cognition and Computer Vision............................................................................ 72.2 Shape Analysis on 2D Images............................................................................... 82.2.1 Classification of Methods....................................................................................82.2.2 Contour-Based Description ...............................................................................102.2.3 Region-Based Description.................................................................................132.3 Shape Analysis on 3D Models ............................................................................ 162.3.1 Classification of Methods..................................................................................162.3.2 Feature Extraction .............................................................................................172.3.3 Descriptive Representation................................................................................192.3.4 Shape Histograms..............................................................................................202.3.5 Topology Description........................................................................................212.4 Summary ............................................................................................................. 233 DATA COLLECTION AND MODELING ............................263.1 Range Data Acquisition....................................................................................... 263.1.1 Range Acquisition Systems...............................................................................263.1.2 Range Sensing Using the IVP Range Scanner ..................................................273.2 Solid Modeling from Range Images.................................................................... 333.2.1 Modeling Automotive Components for Reverse Engineering...........................333.2.2 Modeling Automotive Scenes for Under Vehicle Inspection............................364 ALGORITHM OVERVIEW ...................................................394.1 Algorithm Description......................................................................................... 394.1.1 Informational Approach to Shape Description – Curvature Variation Measure404.1.2 Curvature-Based Automotive Component Description.....................................414.2 Building Blocks of the CVM algorithm .............................................................. 434.2.1 Differential Geometry of Curves and Surfaces .................................................434.2.2 Curvature Estimation.........................................................................................454.2.3 Density Estimation ............................................................................................484.2.4 Information Measure .........................................................................................565 ANALYSIS AND RESULTS....................................................595.1 Implementation Decisions on the Building Blocks ............................................. 595.1.1 Analysis of Curvature Estimation Methods.......................................................595.1.2 Density Estimation for Information Measure....................................................635.2 State-of-the-Art Shape Descriptors ..................................................................... 665.3 Results of our Informational Approach............................................................... 705.3.1 Intensity and Range Images...............................................................................705.3.2 Surface Ruggedness ..........................................................................................705.3.3 3D Mesh Models ...............................................................................................726 CONCLUSIONS........................................................................816.1 Contributions....................................................................................................... 81iv
Page 1 and 2: To the Graduate Council:I am submit
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Chapter 6: Conclusions 82complexity
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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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