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

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.,