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This paper concerns the incorporation of geometric information in camera calibration and 3D modeling. Using geometric constraints enables more stable results and allows us to perform tasks with fewer images. Our approach is motivated and developed within a framework of semi-automatic 3D modeling, where the user defines geometric primitives and constraints between them. It is based on the observation that constraints, such as coplanarity, parallelism, or orthogonality, are often embedded intuitively in parallelepipeds. Moreover, parallelepipeds are easy to delineate by a user and are well adapted to model the main structure of, e.g., architectural scenes. In this paper, first a duality that exists between the shape parameters of a parallelepiped and the intrinsic parameters of a camera is described. Then, a factorization-based algorithm exploiting this relation is developed. Using images of parallelepipeds, it allows us to simultaneously calibrate cameras, recover shapes of parallelepipeds, and estimate the relative pose of all entities. Besides geometric constraints expressed via parallelepipeds, our approach simultaneously takes into account the usual self-calibration constraints on cameras. The proposed algorithm is completed by a study of the singular cases of the calibration method. A complete method for the reconstruction of scene primitives that are not modeled by parallelepipeds is also briefly described. The proposed methods are validated by various experiments with real and simulated data, for single-view as well as multiview cases.
3D modeling, calibration, geometric constraints.

P. Sturm, M. Wilczkowiak and E. Boyer, "Using Geometric Constraints through Parallelepipeds for Calibration and 3D Modeling," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 27, no. , pp. 194-207, 2005.
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