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

More documents

Recommendations

Info

Chapter 5: Analysis and Results 67Fan Disk Model CurvednessShape Index Gaussian Curvature2 2κ1+ κ1 12−1κ1+ κ2 κ = κΚ =η = − tan1κ 222 π κ1− κ2(a) (b) (c) (d)Figure 5.5: Curvature-based descriptors.We would like to make the following conclusions from Figure 5.5. Curvedness provesto be a good descriptor that detects abrupt change in curvature. Curvedness is consistentat low resolutions but with bad triangulation it produces erroneous results. We attributethis result however to the curvature estimation method that assumes good and uniformtriangulation. While on the other hand, we see how shape index is colorful indicatingsurface variation along the flat surface facing us in the diagram. The definition of shapeindex assumes uniform topology of meshes as in range images. That is why the shapeindex of a spherical cap and a spherical cup which look the same visually possessdifferent shape indices. We see in Figure 5.5(d) that the Gaussian curvature clearlyshows variation in curvature in each of the surface patches and no or very little variationin the flat surfaces.We have also implemented a recent method for shape classification and descriptioncalled Shape Distributions [Osada, 2002]. The approach represents shapes ashistograms. Randomly sampled points on the surface of a triangle mesh is used toextract several features such as the centroidal profile, distance between two points, anglebetween three random points. These features are binned into a histogram. Thishistogram is used for object detection and classification. Results show similar shapeshaving similar feature histograms. This algorithm was implemented for shape searchingand retrieval on the web. We have tested this algorithm with our automotive parts andhave come to realize that several 1D features cannot represent completely the 3Dinformation in an object. We show our implementation of Shape Distributions in Figure5.6 and our experience in representing automotive components in Figure 5.7. Wedemonstrate the lack of uniqueness in description with the fan disk, disc brake andmuffler models. These models have the same bounding box but we see that the discbrake and the fan disk though extremely different in shape have a similar histogram,while mufflers though similar in shape have noticeable amount of variation.
Chapter 5: Analysis and Results 68Adapted from [Osada, 2002](a) (b) (c)Adapted from [Osada, 2002](d) (e) (f)Figure 5.6: Implementation of Shape Distributions. (a) Wire frame model of acube. (b) Shape Distribution result from the paper [Osada,2002] for a cube. (c) Resultof our implementation on the cube. (d) Wire frame model of a sphere. (e) ShapeDistribution result from the paper [Osada, 2002] for a sphere. (f) Result of ourimplementation on the sphere.
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
Page 19 and 20:
Chapter 2: Literature Review 102.2.
Page 21 and 22:
Chapter 2: Literature Review 12Bimb
Page 23 and 24:
Chapter 2: Literature Review 14is f
Page 25 and 26: Chapter 2: Literature Review 16foun
Page 27 and 28: Chapter 2: Literature Review 18Kort
Page 29 and 30: Chapter 2: Literature Review 20boun
Page 31 and 32: Chapter 2: Literature Review 22Gots
Page 33 and 34: Chapter 2: Literature Review 24Tabl
Page 35 and 36: Chapter 3: Data Collection and Mode
Page 49 and 50: Chapter 4: Algorithm Overview 404.1
Page 51 and 52: Chapter 4: Algorithm Overview 42Tri
Page 53 and 54: Chapter 4: Algorithm Overview 44whe
Page 55 and 56: Chapter 4: Algorithm Overview 46The
Page 57 and 58: Chapter 4: Algorithm Overview 48of
Page 59 and 60: Chapter 4: Algorithm Overview 50∞
Page 61 and 62: Chapter 4: Algorithm Overview 52The
Page 63 and 64: Chapter 4: Algorithm Overview 54smo
Page 65 and 66: Chapter 4: Algorithm Overview 564.2
Page 67 and 68: Chapter 4: Algorithm Overview 58Wit
Page 69 and 70: Chapter 5: Analysis and Results 60W
Page 71 and 72: Chapter 5: Analysis and Results 62S
Page 73 and 74: Chapter 5: Analysis and Results 64F
Page 75: Chapter 5: Analysis and Results 66t
Page 79 and 80: Chapter 5: Analysis and Results 705
Page 81 and 82: Chapter 5: Analysis and Results 72S
Page 83 and 84: Chapter 5: Analysis and Results 74W
Page 85 and 86: Chapter 5: Analysis and Results 76C
Page 87 and 88: Chapter 5: Analysis and Results 78T
Page 89 and 90: Chapter 5: Analysis and Results 80(
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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?