We introduce the distributed camera model, a novel model for Structure-from-Motion (SfM). This model describes image observations in terms of light rays with ray origins and directions rather than pixels. As such, the proposed model is capable of describing a single camera or multiple cameras simultaneously as the collection of all light rays observed. We show how the distributed camera model is a generalization of the standard camera model and describe a general formulation and solution to the absolute camera pose problem that works for standard or distributed cameras. The proposed method computes a solution that is up to 8 times more efficient and robust to rotation singularities in comparison with gDLS. Finally, this method is used in an novel large-scale incremental SfM pipeline where distributed cameras are accurately and robustly merged together. This pipeline is a direct generalization of traditional incremental SfM; however, instead of incrementally adding one camera at a time to grow the reconstruction the reconstruction is grown by adding a distributed camera. Our pipeline produces highly accurate reconstructions efficiently by avoiding the need for many bundle adjustment iterations and is capable of computing a 3D model of Rome from over 15,000 images in just 22 minutes.
To additionally recover scale transformations in multi-camera rigs, Ventura al @cite_10 presented the first minimal solution to the generalized pose-and-scale problem. They use the generalized camera model and employ Gr "obner basis computations to efficiently solve for scale, rotation, and translation using 4 2D-3D correspondences. Sweeney al @cite_25 presented the first nonminimal solver, gDLS, for the generalized pose and scale problem. By extending the Direct Least Squares (DLS) P @math P algorithm of Hesch and Roumeliotis @cite_14 , rotation, translation, and scale can be solved for in a fixed size polynomial system. While this method is very scalable the large elimination template of the gDLS method makes it very inefficient and the Cayley rotation parameterization results in singularities. In this paper, we extend the gDLS solution method to a non-singular representation and show that using the Gr "obner basis technique achieves an 8 @math speedup.
@cite_14 @cite_10 @cite_25
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In this work, we present a scalable least-squares solution for computing a seven degree-of-freedom similarity transform. Our method utilizes the generalized camera model to compute relative rotation, translation, and scale from four or more 2D-3D correspondences. In particular, structure and motion estimations from monocular cameras lack scale without specific calibration. As such, our methods have applications in loop closure in visual odometry and registering multiple structure from motion reconstructions where scale must be recovered. We formulate the generalized pose and scale problem as a minimization of a least squares cost function and solve this minimization without iterations or initialization. Additionally, we obtain all minima of the cost function. The order of the polynomial system that we solve is independent of the number of points, allowing our overall approach to scale favorably. We evaluate our method experimentally on synthetic and real datasets and demonstrate that our methods produce higher accuracy similarity transform solutions than existing methods. We propose a novel solution to the generalized camera pose problem which includes the internal scale of the generalized camera as an unknown parameter. This further generalization of the well-known absolute camera pose problem has applications in multi-frame loop closure. While a well-calibrated camera rig has a fixed and known scale, camera trajectories produced by monocular motion estimation necessarily lack a scale estimate. Thus, when performing loop closure in monocular visual odometry, or registering separate structure-from-motion reconstructions, we must estimate a seven degree-of-freedom similarity transform from corresponding observations. Existing approaches solve this problem, in specialized configurations, by aligning 3D triangulated points or individual camera pose estimates. Our approach handles general configurations of rays and points and directly estimates the full similarity transformation from the 2D-3D correspondences. Four correspondences are needed in the minimal case, which has eight possible solutions. The minimal solver can be used in a hypothesize-and-test architecture for robust transformation estimation. Our solver also produces a least-squares estimate in the overdetermined case. The approach is evaluated experimentally on synthetic and real datasets, and is shown to produce higher accuracy solutions to multi-frame loop closure than existing approaches. We propose a novel solution for computing the relative pose between two generalized cameras that includes reconciling the internal scale of the generalized cameras. This approach can be used to compute a similarity transformation between two coordinate systems, making it useful for loop closure in visual odometry and registering multiple structure from motion reconstructions together. In contrast to alternative similarity transformation methods, our approach uses 2D-2D image correspondences thus is not subject to the depth uncertainty that often arises with 3D points. We utilize a known vertical direction (which may be easily obtained from IMU data or vertical vanishing point detection) of the generalized cameras to solve the generalized relative pose and scale problem as an efficient Quadratic Eigenvalue Problem. To our knowledge, this is the first method for computing similarity transformations that does not require any 3D information. Our experiments on synthetic and real data demonstrate that this leads to improved performance compared to methods that use 3D-3D or 2D-3D correspondences, especially as the depth of the scene increases. 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.