We present algorithms for plane-based calibration of general radially distorted cameras. By this, we understand cameras that have a distortion center and an optical axis such that the projection rays of pixels lying on a circle centered on the distortion center form a right viewing cone centered on the optical axis. The camera is said to have a single viewpoint (SVP) if all such viewing cones have the same apex (the optical center); otherwise, we speak of NSVP cases. This model encompasses the classical radial distortion model [5], fisheyes, and most central or noncentral catadioptric cameras. Calibration consists in the estimation of the distortion center, the opening angles of all viewing cones, and their optical centers. We present two approaches of computing a full calibration from dense correspondences of a single or multiple planes with known euclidean structure. The first one is based on a geometric constraint linking viewing cones and their intersections with the calibration plane (conic sections). The second approach is a homography-based method. Experiments using simulated and a broad variety of real cameras show great stability. Furthermore, we provide a comparison with Hartley-Kang's algorithm [12], which, however, cannot handle such a broad variety of camera configurations, showing similar performance.

Matrix factorization is a key component for solving several computer vision problems. It is particularly challenging in the presence of missing or erroneous data, which often arise in structure-from-motion. We propose batch algorithms for matrix factorization. They are based on closure and basis constraints, that are used either on the cameras or the structure, leading to four possible algorithms. The constraints are robustly computed from complete measurement sub-matrices with e.g. random data sampling. The cameras and 3D structure are then recovered through linear least squares. Prior information about the scene such as identical camera positions or orientations, smooth camera trajectory, known 3D points and coplanarity of some 3D points can be directly incorporated. We demonstrate our algorithms on challenging image sequences with tracking error and more than 95% missing data.

This paper presents a novel algorithm that improves the localization of disparity discontinuities of disparity maps obtained by multi-baseline stereo. Rather than associating a disparity label to every pixel of a disparity map, it associates a position to every disparity discontinuity. This formulation allows us to find an approximate solution to a 2D labeling problem with robust smoothing term by minimizing multiple 1D problems, thus making possible the use of dynamic programming. Dynamic programming allows the efficient computation of the visibility of most of the cameras during the minimization. Whilst the proposed minimization strategy is particularly suitable for stereo with occlusion, it may be used with other labeling problems.

This paper presents a new model to overcome the occlusion problems coming from wide baseline multiple camera stereo. Rather than explicitly modeling occlusions in the matching cost function, it detects occlusions in the depth map obtained from regular efficient stereo matching algorithms. Occlusions are detected as inconsistencies of the depth map by computing the visibility of the map as it is reprojected into each camera. Our approach has the particularity of not discriminating between occluders and occludees. The matching cost function is modified according to the detected occlusions by removing the offending cameras from the computation of the matching cost. The algorithm gradually modifies the matching cost function according to the history of inconsistencies in the depth map, until convergence. While two graph-theoretic stereo algorithms are used in our experiments, our framework is general enough to be applied to many others. The validity of our framework is demonstrated using real imagery with different baselines.