3D Reconstruction from a Single Image
MINNESOTA UNIV MINNEAPOLIS INST FOR MATHEMATICS AND ITS APPLICATIONS
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A probabilistic framework for 3D object reconstruction from a single image is introduced in this work. First, a probabilistic generative model to represent the distribution of mass of a class of objects in 3D space, namely a 3D shape prior, is presented. Next, following the Beer-Lambert law in optics, a framework to translate these 3D probabilities into the corresponding 2D probabilities in the camera plane is developed. Exploiting this framework to encode prior knowledge about the class and to project it to 2D, the problem of 3D reconstruction from a single image is casted as a statistical inference problem in graphical models, where actual observations in the single image are naturally integrated with 3D prior knowledge of the class. The reconstruction is obtained by running modified belief propagation in this graphical model, and in some cases, optimal solutions are guaranteed. The proposed modification allows the exact computation of the messages to pass in quasi-linear time, a significant improvement over the exponential time complexity of general implementations. The presentation of the proposed framework is complemented with evaluation of the experimental results obtained for the important class of walking people, demonstrating the accuracy of the approach for 3D reconstruction, localization and volume estimation.