Rotation Invariant Kernels and Their Application to Shape Analysis
| Autor: | Onur C. Hamsici, Aleix M. Martinez |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Rotation
Feature vector Bingham distribution Geometry Sensitivity and Specificity Pattern Recognition Automated Imaging Three-Dimensional Artificial Intelligence Image Interpretation Computer-Assisted Mathematics business.industry Applied Mathematics Reproducibility of Results Invariant (physics) Hypersphere Scale invariance Image Enhancement Computational Theory and Mathematics Kernel (statistics) Norm (mathematics) Computer Vision and Pattern Recognition Artificial intelligence business Algorithm Algorithms Software Shape analysis (digital geometry) |
| Zdroj: | IEEE Transactions on Pattern Analysis and Machine Intelligence. 31:1985-1999 |
| ISSN: | 0162-8828 |
| DOI: | 10.1109/tpami.2008.234 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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