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Chapter 4: Algorithm Overview 41BoundaryContourCurvatureEstimationDensityEstimationEntropyComputationShapeInformationFigure 4.2: Block diagram of our CVM as the informational approach to shapedescription.We use curvature because it is an information preserving feature, invariant to rotationand possesses an intuitively pleasing correspondence to the perceptive property ofsimplicity. Curvature completely parameterizes the boundary contour for efficientshape description of 2D curves and boundary contours. We counter the inverserelation to symmetry by using information theory. Symmetry does not contribute tomore shape information (entropy) but rather reduces it.4.1.2 Curvature-Based Automotive Component DescriptionOur CVM measure of shape on geometric curves is the entropy of curvature along theboundary contour. Curvature along the boundary provides us with sufficient detail inthe 2D case but with 3D models and surfaces, it is not enough. We extend our idea ofshape information on 3D meshes to describe surface variation of the smooth surfacepatches that make up the object and store the list of connected patches. We assumethat we can reasonably describe most objects as a unique network of smooth patches.Then, the uniqueness of our description is to measure the variation in curvature acrosseach of these patches.We describe the algorithm in a pictorial fashion with a block diagram in Figure 4.3.Our description which could be used for purposes such as reverse engineering andinspection takes triangle meshes as the input. We take the example of the disc brakeagain. We break down the triangle mesh into surface patches based on the Dorai’s[Dorai, 1997] definition of curvedness. Curvedness identifies sharp edges and abruptsurface changes. We perform a simple region growing segmentation by identifying apoint and collecting the vertices whose face normal deviation is less than a particularangle. This angle is a free parameter. We have used 85 degrees as the maximumthreshold angle before we meet an edge in the growing procedure. We save theconnectivity information of each of these surface patches. Our segmentation is a crude
Chapter 4: Algorithm Overview 42Triangle MeshSurface PatchDecompositionComputeCurvednessSegment byRegion GrowingConnectivity ofSurface PatchesCurvature VariationMeasureCurvatureComputationDensityEstimationInformationMeasure0.01 0.11 0.0010.11CVM= 0.001Graph RepresentationFigure 4.3:Block diagram of curvature-based vehicle component descriptionalgorithm including path decomposition and CVM computation.
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
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Page 35 and 36: Chapter 3: Data Collection and Mode
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Page 91 and 92: Chapter 6: Conclusions 82complexity
Page 93 and 94: Bibliography 84BIBLIOGRAPHY
Page 95 and 96: Bibliography 86[Biermann, 2001][Bel
Page 97 and 98: Bibliography 88[Cyr and Kimia, 2001
Page 99 and 100: 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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