Gaussian Bayes Classifier for 2D Shapes in Kendall Space
We propose a 2D-shape Gaussian Bayes classifier based upon Kendall’s representations that help to quotient out the effects of non-altering shape geometric transformations. The Kendall space is a non linear space that coincides with the unit sphere modulo an isometry group. The proposed Riemannian metric is more apt in the case where shapes are different only in translation, scale and rotation. In addition to that, the manifold structure of this space renders the multivariate statistical analysis implementation unfeasible in practice. Consequently, tools such as learning and classification models are non trivial and not frequently available. To overcome these issues, we adapt the Gaussian Bayes classifier to this space. We computed the likelihood parameters through appropriate projections onto Kendall tangent space that provides a good linear approximation. In order to validate the robustness of our classifier, we proceeded to computer simulations using several benchmarks.
KeywordsKendall space Gaussian Bayes classifier Likelihood parameters
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