Exploiting Loops in the Graph of Trifocal Tensors for Calibrating a Network of Cameras

Abstract

A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is encoded by a 4-vector. The strength of this parameterization is that the homographies relating two adjacent trifocal tensors, as well as the projection matrices depend linearly on the parameters. A method for estimating these parameters in a global way benefiting from loops in the graph is developed. Experiments carried out on several real datasets demonstrate the efficiency of the proposed approach in distributing errors over the whole set of cameras.

Structure from motion for scenes with large duplicate structures

“…Subsequently, we simultaneously estimate rotation and translation using precomputed camera triplets and the extension described in Section 3.3. For computing relative pairwise pose and triplet reconstructions, we employ known techniques described in [14,17,13,18,19,2,9]. Finally, we use only the match pairs inferred as correct as input to a state of the art structure from motion pipeline with standard bundle adjustment [20] to compute the final reconstruction.…”

“…where p(x) is a pose prior (we place a prior only on one of the cameras, to fix it at the origin), and · C is the Mahalanobis distance with covariance matrix C. The term 2 Please see the supplementary material (http://www.cc.gatech.edu/~richard/cvpr11-supp/) for a derivation of these updates and brief explanation of Lie group notation.…”

“…The two largest disconnected sets are iteratively merged by computing a loop erased random walk [21] between triplets in these two sets. The random walk is performed on a trifocal graph [2], in which triplets form nodes and triplets that share edges (in the original match graph) are connected via edges. This random walk uses the same edge weights as the random spanning tree generator in Sec.…”

On Camera Calibration with Linear Programming and Loop Constraint Linearization

“…4 and the Appendix F, respectively. While the method described above in steps 1-5 appeared in our ECCV paper (Courchay et al 2010), this part is new and leads to improved results in terms of the achievability of loop constraints.…”

Computing similarity transformations from only image correspondences

“…The proposed algorithm is especially useful in applications like loop closure in visual odometry, SLAM, and SfM. Most strategies for loop closure involve computing the absolute orientation to align known scene landmarks, or they utilize PnP algorithms repeatedly to localize individual cameras [2,3,4,8,25,29]. Iterative Closest Point (ICP) [1,30] methods may also be used to align two 3D point clouds, though are often slow to converge and depend heavily on initialization.…”