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Chapter 5: Analysis and Results 69(a) (b) (c) (d)(e) (f) (g) (h)Figure 5.7: Shape Distributions and its uniqueness in description. (a) Model of afandisk. (b) Model of a disc brake. (c) Model of a Toyota muffler. (d) Model of aVolvo muffler. (e) Shape Distribution of model in (a). (f) Shape Distribution ofmodel in (b). (g) Shape Distribution of model in (c). (h) Shape Distribution of modelin (d).
Chapter 5: Analysis and Results 705.3 Results of our Informational ApproachIn Chapter 4 we discussed our CVM algorithm that quantifies surface shapecomplexity. We compute curvature based on the method suggested by [Abidi, 1995]and measure boundary complexity as the Shannon’s entropy of curvature on 2Dcontours. We have presented these results in [Page et al., 2003b]. We discuss someimportant results on X-ray and range images. We also analyze some limitations ofusing Shannon entropy and the need for a normalized information measure beforediscussing the results of our graph representation on automotive components.5.3.1 Intensity and Range ImagesIn Figure 5.8(a) we show results on simple curves. We have made a few importantassumptions with these curves. These curves are of the same resolution and areuniformly sampled. We have computed the Shannon entropy of the turning angle ateach point on the boundary as the shape complexity measure (SCM). We note thatSCM and CVM are similar measures but are not equivalent.SCM inspired thedevelopment of CVM, and CVM represents the evolution of SCM from lessonslearned on scaling and resolution We would like to emphasize in these results on howshape information behaves with symmetry and how important the assumption on sizeand resolution turns out to be. We would also like to note that the shape informationfrom the Shannon’s measure cannot be compared if the two images are not at the sameresolution and comparable size. Hence for the real data we have normalized thesegmented region of interest for size and resolution and then computed the curvaturebasedmeasure on the normalized boundary contour. We would like to recall fromChapter 2 and note that our method falls under the boundary-based descriptionmethods. In Figure 5.8(b) we show an example with an X-ray image of a baggage. Thebag contains a few objects that we have segmented manually. We take each of thesegmented objects and then compute the shape information on each of these contours.Our measure categorizes complex objects and simple ones with satisfactory ease.Next, we show some results on range images in Figure 5.8(c).We believe that we willbe able to distinguish between the man-made structures that have flat and nice edgeslike the building in Figure 5.8 (c) and natural vegetation that has rugged boundaries.5.3.2 Surface RuggednessIn terms of resolution we would like to present some results on synthetic DEMs(Digital Elevation Maps) of the same resolution. The Shannon’s entropy of curvaturegives a consistent ruggedness measure of the surface. But we still face inconsistencywith resolution. We formulate our algorithm on the heuristic that the variation in theshape characteristics of surfaces is mathematically the variation of curvature. Wedefine shape information as the entropy of the curvature density of the surface underconsideration.
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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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