We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth.
We present a linear method for global camera pose registration from pair wise relative poses encoded in essential matrices. Our method minimizes an approximate geometric error to enforce the triangular relationship in camera triplets. This formulation does not suffer from the typical unbalanced scale' problem in linear methods relying on pair wise translation direction constraints, i.e. an algebraic error, nor the system degeneracy from collinear motion. In the case of three cameras, our method provides a good linear approximation of the trifocal tensor. It can be directly scaled up to register multiple cameras. The results obtained are accurate for point triangulation and can serve as a good initialization for final bundle adjustment. We evaluate the algorithm performance with different types of data and demonstrate its effectiveness. Our system produces good accuracy, robustness, and outperforms some well-known systems on efficiency.  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. 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. We consider the problem of distributed estimation of the poses of N cameras in a camera sensor network using image measurements only. The relative rotation and translation (up to a scale factor) between pairs of neighboring cameras can be estimated using standard computer vision techniques. However, due to noise in the image measurements, these estimates may not be globally consistent. We address this problem by minimizing a cost function on SE(3)N in a distributed fashion using a generalization of the classical consensus algorithm for averaging Euclidean data. We also derive a condition for convergence, which relates the step-size of the consensus algorithm and the degree of the camera network graph. While our methods are designed with the camera sensor network application in mind, our results are applicable to other localization problems in a more general setting. We also provide synthetic simulations to test the validity of our approach. 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. Multiview structure recovery from a collection of images requires the recovery of the positions and orientations of the cameras relative to a global coordinate system. Our approach recovers camera motion as a sequence of two global optimizations. First, pair wise Essential Matrices are used to recover the global rotations by applying robust optimization using either spectral or semi definite programming relaxations. Then, we directly employ feature correspondences across images to recover the global translation vectors using a linear algorithm based on a novel decomposition of the Essential Matrix. Our method is efficient and, as demonstrated in our experiments, achieves highly accurate results on collections of real images for which ground truth measurements are available. While motion estimation has been extensively studied in the computer vision literature, the inherent information redundancy in an image sequence has not been well utilised. In particular as many as N(N-1) 2 pairwise relative motions can be estimated efficiently from a sequence of N images. This highly redundant set of observations can be efficiently averaged resulting in fast motion estimation algorithms that are globally consistent. In this paper we demonstrate this using the underlying Lie-group structure of motion representations. The Lie-algebras of the Special Orthogonal and Special Euclidean groups are used to define averages on the Lie-group which in turn gives statistically meaningful, efficient and accurate algorithms for fusing motion information. Using multiple constraints also controls the drift in the solution due to accumulating error. The performance of the method in estimating camera motion is demonstrated on image sequences. Extrinsic calibration of large-scale ad hoc networks of cameras is posed as the following problem: Calculate the locations of N mobile, rotationally aligned cameras distributed over an urban region, subsets of which view some common environmental features. We show that this leads to a novel class of graph embedding problems that admit closed-form solutions in linear time via partial spectral decomposition of a quadratic form. The minimum squared error (mse) solution determines locations of cameras and or features in any number of dimensions. The spectrum also indicates insufficiently constrained problems, which can be decomposed into well-constrained rigid subproblems and analyzed to determine useful new views for missing constraints. We demonstrate the method with large networks of mobile cameras distributed over an urban environment, using directional constraints that have been extracted automatically from commonly viewed features. Spectral solutions yield layouts that are consistent in some cases to a fraction of a millimeter, substantially improving the state of the art. Global layout of large camera networks can be computed in a fraction of a second.  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. Recently, there has been interest in formulating various geometric problems in Computer Vision as L optimization problems. The advantage of this approach is that under L norm, such problems typically have a single minimum, and may be efficiently solved using Second-Order Cone Programming (SOCP). This paper shows that such techniques may be used effectively on the problem of determining the track of a camera given observations of features in the environment. The approach to this problem involves two steps: determination of the orientation of the camera by estimation of relative orientation between pairs of views, followed by determination of the translation of the camera. This paper focusses on the second step, that of determining the motion of the camera. It is shown that it may be solved effectively by using SOCP to reconcile translation estimates obtained for pairs or triples of views. In addition, it is observed that the individual translation estimates are not known with equal certainty in all directions. To account for this anisotropy in uncertainty, we introduce the use of covariances into the L optimization framework. This paper presents a new framework for solving geometric structure and motion problems based on the Linfin-norm. Instead of using the common sum-of-squares cost function, that is, the L2-norm, the model-fitting errors are measured using the Linfin-norm. Unlike traditional methods based on L2, our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using second-order cone programming (SOCP), which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance. In this paper we describe two methods for estimating the motion parameters of an image sequence. For a sequence of N images, the global motion can be described by N-1 independent motion models. On the other hand, in a sequence there exist as many as sub 2 sup N(N-1) pairwise relative motion constraints that can be solve for efficiently. In this paper we show how to linearly solve for consistent global motion models using this highly redundant set of constraints. In the first case, our method involves estimating all available pairwise relative motions and linearly fining a global motion model to these estimates. In the second instance, we exploit the fact that algebraic (i.e. epipolar) constraints between various image pairs are all related to each other by the global motion model. This results in an estimation method that directly computes the motion of the sequence by using all possible algebraic constraints. Unlike using reprojection error, our optimisation method does not solve for the structure of points resulting in a reduction of the dimensionality of the search space. Our algorithms are used for both 3D camera motion estimation and camera calibration. We provide real examples of both applications.