Using Geometric Constraints for Camera Calibration and Positioning and 3d Scene Modelling

This work concerns the incorporation of geometric information in camera calibration and 3D modelling. Using geometric constraints enables stabler results and allows to perform tasks with fewer images. Our approach is interactive; the user defines geometric primitives and constraints between them. It is based on the observation that constraints such as coplanarity, parallelism or orthogonality, are easy to delineate by a user, and are well adapted to model the main structure of e.g. architectural scenes. We propose methods for camera calibration, camera position estimation and 3D scene reconstruction, all based on such geometric constraints. Various approaches exist for calibration and positioning from constraints, often based on vanishing points. We generalize this by considering composite primitives based on triplets of vanishing points. These are frequent in architectural scenes and considering composites of vanishing points makes computations more stable. They are defined by depicting in the images points belonging to parallelepipedic structures (e.g. appropriate points on two connected walls). Constraints on angles or length ratios on these structures can then be easily imposed. A method is proposed that “collects” all these data for all considered images, and computes simultaneously the calibration and pose of all cameras via matrix factorization. 3D scene reconstruction is then performed using many more geometric constraints, i.e. not only those encapsulated by parallelepipedic structures. A method is proposed that reconstructs the whole scene in iterations, solving a linear equation system at each iteration, and which includes an analysis of the parts of the scene that can/cannot be reconstructed at the current stage. The complete approach is validated by various experimental results, for cases where a single or several views are available.