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Issue No.11 - November (2009 vol.31)
pp: 1985-1999
Onur C. Hamsici , The Ohio State University, Columbus
Aleix M. Martinez , The Ohio State University, Columbus
ABSTRACT
Shape analysis requires invariance under translation, scale, and rotation. Translation and scale invariance can be realized by normalizing shape vectors with respect to their mean and norm. This maps the shape feature vectors onto the surface of a hypersphere. After normalization, the shape vectors can be made rotational invariant by modeling the resulting data using complex scalar-rotation invariant distributions defined on the complex hypersphere, e.g., using the complex Bingham distribution. However, the use of these distributions is hampered by the difficulty in estimating their parameters and the nonlinear nature of their formulation. In the present paper, we show how a set of kernel functions that we refer to as rotation invariant kernels can be used to convert the original nonlinear problem into a linear one. As their name implies, these kernels are defined to provide the much needed rotation invariance property allowing one to bypass the difficulty of working with complex spherical distributions. The resulting approach provides an easy, fast mechanism for 2D & 3D shape analysis. Extensive validation using a variety of shape modeling and classification problems demonstrates the accuracy of this proposed approach.
INDEX TERMS
Shape analysis, kernel functions, rotation invariance, spherical-homoscedastic distributions, face recognition, object recognition, handshape, LB1.
CITATION
Onur C. Hamsici, Aleix M. Martinez, "Rotation Invariant Kernels and Their Application to Shape Analysis", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 11, pp. 1985-1999, November 2009, doi:10.1109/TPAMI.2008.234
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