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.
As for global SfM methods, their main objective is merging relative motions between two cameras into a consistent graph of all cameras. Besides robustness concerns, to get rid of outlier edges, and various approaches to average rotations, one of the main issues is that the relative translations are only given up to an unknown scale factor; only their directions are known. Most methods to infer global translations rely on information redundancy assuming a densely-connected graph @cite_0 @cite_42 , or on additional information from trifocal tensors @cite_19 @cite_46 (hence requiring 4 tracked points across 3 views). A number of other methods @cite_6 @cite_43 @cite_26 compute the global translations, possibly along with the 3D points, by solving equations relating points visible in two images; however, they implicitly assume that enough points are visible in at least 3 images to cancel the degrees of freedom of the relative scale factors. Besides, they do not all address point match outliers.
@cite_26 @cite_42 @cite_6 @cite_0 @cite_19 @cite_43 @cite_46
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Global structure-from-motion (SfM) methods solve all cameras simultaneously from all available relative motions. It has better potential in both reconstruction accuracy and computation efficiency than incremental methods. However, global SfM is challenging, mainly because of two reasons. Firstly, translation averaging is difficult, since an essential matrix only tells the direction of relative translation. Secondly, it is also hard to filter out bad essential matrices due to feature matching failures. We propose to compute a sparse depth image at each camera to solve both problems. Depth images help to upgrade an essential matrix to a similarity transformation, which can determine the scale of relative translation. Thus, camera registration is formulated as a well-posed similarity averaging problem. Depth images also make the filtering of essential matrices simple and effective. In this way, translation averaging can be solved robustly in two convex L1 optimization problems, which reach the global optimum rapidly. We demonstrate this method in various examples including sequential data, Internet data, and ambiguous data with repetitive scene structures. We present a new structure from motion (Sfm) technique based on point and vanishing point (VP) matches in images. First, all global camera rotations are computed from VP matches as well as relative rotation estimates obtained from pairwise image matches. A new multi-staged linear technique is then used to estimate all camera translations and 3D points simultaneously. The proposed method involves first performing pairwise reconstructions, then robustly aligning these in pairs, and finally aligning all of them globally by simultaneously estimating their unknown relative scales and translations. In doing so, measurements inconsistent in three views are efficiently removed. Unlike sequential Sfm, the proposed method treats all images equally, is easy to parallelize and does not require intermediate bundle adjustments. There is also a reduction of drift and significant speedups up to two order of magnitude over sequential Sfm. We compare our method with a standard Sfm pipeline [1] and demonstrate that our linear estimates are accurate on a variety of datasets, and can serve as good initializations for final bundle adjustment. Because we exploit VPs when available, our approach is particularly well-suited to the reconstruction of man-made scenes. Multi-view structure from motion (SfM) estimates the position and orientation of pictures in a common 3D coordinate frame. When views are treated incrementally, this external calibration can be subject to drift, contrary to global methods that distribute residual errors evenly. We propose a new global calibration approach based on the fusion of relative motions between image pairs. We improve an existing method for robustly computing global rotations. We present an efficient a contrario trifocal tensor estimation method, from which stable and precise translation directions can be extracted. We also define an efficient translation registration method that recovers accurate camera positions. These components are combined into an original SfM pipeline. Our experiments show that, on most datasets, it outperforms in accuracy other existing incremental and global pipelines. It also achieves strikingly good running times: it is about 20 times faster than the other global method we could compare to, and as fast as the best incremental method. More importantly, it features better scalability properties. It is known that the problem of multiview reconstruction can be solved in two steps: first estimate camera rotations and then translations using them. This paper presents new robust techniques for both of these steps, (i) Given pair-wise relative rotations, global camera rotations are estimated linearly in least squares, (ii) Camera translations are estimated using a standard technique based on Second Order Cone Programming. Robustness is achieved by using only a subset of points according to a new criterion that diminishes the risk of choosing a mismatch. It is shown that only four points chosen in a special way are sufficient to represent a pairwise reconstruction almost equally as all points. This leads to a significant speedup. In image sets with repetitive or similar structures, non-existent epipolar geometries may be found. Due to them, some rotations and consequently translations may be estimated incorrectly. It is shown that iterative removal of pairwise reconstructions with the largest residual and reregistration removes most non-existent epipolar geometries. The performance of the proposed method is demonstrated on difficult wide base-line image sets.