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Chapter 2: Literature Review 17objects of different genus which makes it impossible for most of the 2D similarityassessment methods extendable to 3D. The challenge in 3D computer vision is morethan just the lack of information as in the 2D case and needs to address thecomputational effort and descriptive representation. The 3D data usually are representedas meshes or assemblies of simple primitives. The representation scheme is suitable forvisualization but not for recognition and computer vision tasks. The process of shapeassessment hence becomes a two step process: (1) the shape signature extraction and (2)the comparison of shape signatures with distance functions. Based on how the shape isextracted from the 3D model representation techniques can be classified as shown inFigure 2.3.2.3.2 Feature ExtractionFeature extraction techniques usually attempt to represent the shape of the 3D objectby a combination of one-dimensional feature vectors. A common approach forsimilarity models is based on the paradigm of feature vectors. A feature transformmaps a complex object onto a feature vector in a multidimensional space. Thesimilarity of two objects is then defined as the vicinity of their feature vectors in thefeature space. Geometric parameters and ratios such as the surface area, volume ratio,compactness, Euler numbers and crinkliness have been used with limiteddiscrimination capabilities.3D ShapeFeature ExtractionDescriptiveRepresentationShape HistogramsTopologyDescriptionShape ContextShock GraphsAlpha ShapesAspect GraphSpin ImagesHarmonic Shape ImagesCOSMOSGeometry ImagesShape DistributionsSpider modelLocal Feature HistogramReeb graphSkeletal graphsModel SignaturesFigure 2.3: Classification of methods on 3D data.
Chapter 2: Literature Review 18Kortgen et al. [Kortgen et al., 2003] achieves shape matching by extending the 2Dshape contexts [Belongie, 2003] to 3D. They use the shape context at a point on thesurface as the summary of the global shape characteristics invariant to rotation,translation and scaling. Vranic and Saupe [Vranic and Saupe, 2001] propose a newmethod for shape similarity search on polygonal meshes. They characterize spatialproperties of 3D objects such that similar objects are mapped as close points in thefeature space. They then perform a coarse voxelization of the object in the canonicalcoordinate frame and compute the absolute value of the 3D Fourier coefficients as thefeature vector. Vranic improves it further in [Vranic, 2003]. Ohbuchi et al. [Obhuchi etal., 2003] describe a multi-resolution analysis technique for the task of shapesimilarity comparison. They use 3D alpha shapes to generate a multi-resolutionhierarchy of shapes of a given query object. They then follow that by applying asimple shape descriptor such as the D 2 shape function introduced by [Osada et al.,2002] on each of the multi-resolution representations and call it the multi-resolutionshape descriptor.Automated feature recognition has also been attempted by extracting instances ofmanufactured features from engineering designs. Henderson [Henderson et al., 1993]is an extensive survey of such methods that make use of a library of machiningfeatures for description. With the assumption of primitives, procedural methodsproposed by Elinson et al. [Elinson et al., 1997] and Mukai et al. [Mukai et al., 2002]have applied constructive solid geometry (CSG’s) to classify CAD models ofmechanical parts. Their methods however cannot be extended to a more general classof shapes represented as point sets and meshes. Biermann et al. in [Biermann et al.,2001] propose Boolean operations of primitives for shape description. However, directassessment of similarity between 3D models using Boolean operations iscomputationally slow due to the difficulty in aligning the models before performingthe operation. With a large database, it is not a pragmatic solution. Zhang and Chen[Zhang and Chen, 2001] discuss efficient global feature extraction methods from themesh representation.Duda and Hart [Duda and Hart, 1973] have been extended by Khotanzad et al.[Khotanzad et al., 1980] to a subset of 3D moments that are invariant to rotation,translation and scaling that can be used as feature vectors for shapes as shown inEquation 2.6.∞∞∞ m = x y z ρ (x, y,z) dxdydzpqr−∞ −∞ -∞pqrwhere ρ (x, y, z) represents the point cloud of the model. (2.6)Cybenko et al. [Cybenko et al., 1997] use second-order moments, spherical kernelmoment invariants, bounding-box dimensions, object centroid and surface area alongwith a correlation metric for shape-similarity measurement. Elad et al. [Elad et al.,
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Page 3 and 4: Acknowledgementsii“Experience is
Page 5 and 6: Contents1 INTRODUCTION.............
Page 7 and 8: List of TablesviTable 2.1:Qualitati
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Chapter 6: Conclusions 82complexity
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Bibliography 84BIBLIOGRAPHY
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Bibliography 86[Biermann, 2001][Bel
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Bibliography 88[Cyr and Kimia, 2001
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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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