To the Graduate Council: I am submitting herewith a thesis written by ...

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