Usual Structure-from-Motion (SfM) techniques require at least trifocal overlaps to calibrate cameras and reconstruct a scene. We consider here scenarios of reduced image sets with little overlap, possibly as low as two images at most seeing the same part of the scene. We propose a new method, based on line coplanarity hypotheses, for estimating the relative scale of two independent bifocal calibrations sharing a camera, without the need of any trifocal information or Manhattan-world assumption. We use it to compute SfM in a chain of up-to-scale relative motions. For accuracy, we however also make use of trifocal information for line and or point features, when present, relaxing usual trifocal constraints. For robustness to wrong assumptions and mismatches, we embed all constraints in a parameterless RANSAC-like approach. Experiments show that we can calibrate datasets that previously could not, and that this wider applicability does not come at the cost of inaccuracy.
Incremental SfM methods @cite_36 @cite_8 @cite_29 register a new image to a partial model already constructed, using 3D-2D correspondences. A number of Perspective-n-Points (PnP) algorithms @cite_25 @cite_39 have been proposed for solving this resection problem . , Whatever the method, at least 3 correspondences common to 3 images are required: three 3D points visible in the same 3 images, and up to minimum of 6 @cite_5 .
@cite_8 @cite_36 @cite_29 @cite_39 @cite_5 @cite_25
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We propose a novel algorithm to register multiple 3D point sets within a common reference frame using a manifold optimization approach. The point sets are obtained with multiple laser scanners or a mobile scanner. Unlike most prior algorithms, our approach performs an explicit optimization on the manifold of rotations, allowing us to formulate the registration problem as an unconstrained minimization on a constrained manifold. This approach exploits the Lie group structure of SO 3 and the simple representation of its associated Lie algebra so 3 in terms of R3. Our contributions are threefold. We present a new analytic method based on singular value decompositions that yields a closed-form solution for simultaneous multiview registration in the noise-free scenario. Secondly, we use this method to derive a good initial estimate of a solution in the noise-free case. This initialization step may be of use in any general iterative scheme. Finally, we present an iterative scheme based on Newton's method on SO 3 that has locally quadratic convergence. We demonstrate the efficacy of our scheme on scan data taken both from the Digital Michelangelo project and from scans extracted from models, and compare it to some of the other well known schemes for multiview registration. In all cases, our algorithm converges much faster than the other approaches, (in some cases orders of magnitude faster), and generates consistently higher quality registrations. Recent work in structure from motion (SfM) has successfully built 3D models from large unstructured collections of images downloaded from the Internet. Most approaches use incremental algorithms that solve progressively larger bundle adjustment problems. These incremental techniques scale poorly as the number of images grows, and can drift or fall into bad local minima. We present an alternative formulation for SfM based on finding a coarse initial solution using a hybrid discrete-continuous optimization, and then improving that solution using bundle adjustment. The initial optimization step uses a discrete Markov random field (MRF) formulation, coupled with a continuous Levenberg-Marquardt refinement. The formulation naturally incorporates various sources of information about both the cameras and the points, including noisy geotags and vanishing point estimates. We test our method on several large-scale photo collections, including one with measured camera positions, and show that it can produce models that are similar to or better than those produced with incremental bundle adjustment, but more robustly and in a fraction of the time. Structure from Motion (SfM) algorithms take as input multi-view stereo images (along with internal calibration information) and yield a 3D point cloud and camera orientations poses in a common 3D coordinate system. In the case of an incremental SfM pipeline, the process requires repeated model estimations based on detected feature points: homography, fundamental and essential matrices, as well as camera poses. These estimations have a crucial impact on the quality of 3D reconstruction. We propose to improve these estimations using the a contrario methodology. While SfM pipelines usually have globally-fixed thresholds for model estimation, the a contrario principle adapts thresholds to the input data and for each model estimation. Our experiments show that adaptive thresholds reach a significantly better precision. Additionally, the user is free from having to guess thresholds or to optimistically rely on default values. There are also cases where a globally-fixed threshold policy, whatever the threshold value is, cannot provide the best accuracy, contrary to an adaptive threshold policy. Abstract. In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it would be desirable to have an internal estimation of the accuracy of the estimated rotation and translation parameters of the camera pose. Thus, we propose a novel maximum likelihood solution to the PnP problem, that incorporates image observation uncertainties and remains real-time capable at the same time. Further, the presented method is general, as is works with 3D direction vectors instead of 2D image points and is thus able to cope with arbitrary central camera models. This is achieved by projecting (and thus reducing) the covariance matrices of the observations to the corresponding vector tangent space.