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I would like to have a model for that represents the likelihood of a certain configuration of the relative angles between streets at an intersection. Since the angles sum up to 360 degrees, the angles effectively live on a n-1 simplex, where n is the number of ends in a street. Also, the distribution may be multi-modal. [Geiger] solved this by using using a "common trick in the statistics community " where he projects the angles to R^n and models them with an infinite mixture of gaussians. These can then be projected back into the simplex, having something more or less similar to a mixture of dirichlets. (one mixture of dirichlets for each value of n) I was wondering if there might be a simpler solution to this problem. Maybe exploiting that permutations should give the same probability p(phi1,phi2,phi3)=p(phi3,phi1,phi2)=p(phi2,phi3,phi1). see an image here Any idea of how such a distribution could be modeled easily? [Geiger]A Generative Model for 3D Urban Scene Understanding from Movable Platforms |
