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Chapter 5: Analysis and Results 65Figure 5.4: Curvature analysis – Variation in curvature for surface description.
Chapter 5: Analysis and Results 66that makes use of an equation involving quartiles to output a single number as theoptimal bandwidth. We have observed that it sometimes gives us under-smoothed datacompared to the cross validation methods. We have decided to use the plug-in methodfor bandwidth optimization because we want our algorithm to be fully automaticwithout us having to interfere. Another important parameter with the densitydistribution that decides accuracy of the estimate is the number of points at which wecalculate the density.Another small but significant implementation issue that we would like to throw lightupon is the difference between continuous random variables and discrete randomvariables. The discrete density function is not a sampled form of the continuous densityfunction. We note that the density at each point of a discrete random variable is less thanor equal to one and the sum of the densities is unity.Since some values of the density function estimated are possibly zero and since we areusing a logarithmic information measure, we should get around the zero points of thedensity function. We do not compute entropy at the zero points.5.2 State-of-the-Art Shape DescriptorsThe analysis in this section is the backbone of our CVM algorithm. We haveimplemented a few state-of-the-art algorithms to better understand the process of shapeextraction from triangle meshes and also to know about the existing curvature-basedmetrics. Now that we have accurate measures of principle curvature and Gaussiancurvature, we are able to identify curvedness and shape index used by Dorai in her“COSMOS” framework for shape recognition on range images.In Figure 5.5 we show curvedness, shape index and the Gaussian curvature color codedmodels of the fan disk. (Model source of the fan disk: Hughes Hoppe, MicrosoftResearch.) By color coding we mean we have attributed color in the RGB spectrum toeach vertex of that model. The cosine color coding is proportional to the value of theparameter that we have computed at that vertex. For example, in Figure 5.5(d) eachvertex is color coded to Gaussian curvature. We have chosen the fan disk model becauseit is the one that has a combination of flat and curved surfaces and is not too simple ortoo complex.
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To the Graduate Council:I am submit
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Acknowledgementsii“Experience is
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Contents1 INTRODUCTION.............
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List of TablesviTable 2.1:Qualitati
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viiiFigure 5.2: Curvature analysis
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Chapter 1: Introduction 21.1 Motiva
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Chapter 1: Introduction 41.2 Propos
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Chapter 1: Introduction 6We then pe
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Chapter 2: Literature Review 8Shape
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Chapter 2: Literature Review 102.2.
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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
Page 101 and 102: Bibliography 92[Joshi and Chang, 19
Page 103 and 104: Bibliography 94[Meyer, 2002][Morse,
Page 105 and 106: Bibliography 96[Safar et al., 2000]
Page 107 and 108: Bibliography 98parts,” IEEE Trans
Page 109: Vita 100VITASreenivas Rangan Sukuma
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