Although AFoVs allow us to generate the views that an object can produce efficiently, representing this information compactly would be critical. We have decided to use statistical learning techniques for this purpose. In particular, the views that an object can produce form a manifold in a lower-dimensional space. This manifold can be learned efficiently using Gaussian mixture models and the EM (Expectation Maximization) algorithm. The main advantage in our case is that we can generate a large number of sampled views using AFoVs, therefore, improving our chances to reveal and learn the true structure of the manifold.

Mixture models are a type of density model which comprises a number of component functions, usually Gaussian. These component functions are combined to provide a multimodal density. Once a model is generated, posterior probabilities can be computed according to the Bayes' rule. A mixture is defined as a weighted sum of K components where each component is a parametric density function

Figure1 shows the manifold obtained for a group of 8 points from an artificial object used in our experiments.

                 (a)

(b)

Figure 1 The mixture model obtained (shown in (a) for a group of 8 point features) from artificial object shown in (b).

Each hypothesis generated by the k-d tree search is ranked by computing its probability using the learned manifolds described above. Specifically, for each test view, we compute two probabilities, one from the x-coordinates of the view and the other from the y-coordinates of the view. The overall probability is then computed as follows:

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