Grammatical Inference by n-gram Modeling of Convex Groups: Representation of Visual Random Polytopes

Peter Michael Goebel, Markus Vincze, Bernard Favre-Bulle.

In this paper, a joint solution to the problem of finding appropriate abstract representations for visual polytopes is given. By using support from convex and stochastic geometry, collecting information of views from different viewpoints, perceptual grouping of 3D point-cloud image points into halfplanes with probabilistic robust fitting and the segmentation of edges and corners by intersecting halfplanes yields an aggregation of visual primitives into object prototypes by Bayes’ belief networks. In order to build object prototypes, a n-gram model is trained by edge and corner primitives, derived from Monte-Carlo simulations and processing of real 3D point-clouds. Finally, we use perplexity to find out the best performing network and define a Dirichlet distribution model of the n-grams.

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