We consider the problem of localizing a novel image in a large 3D model, given that the gravitational vector is known. In principle, this is just an instance of camera pose estimation, but the scale of the problem introduces some interesting challenges. Most importantly, it makes the correspondence problem very difficult so there will often be a significant number of outliers to handle. To tackle this problem, we use recent theoretical as well as technical advances. Many modern cameras and phones have gravitational sensors that allow us to reduce the search space. Further, there are new techniques to efficiently and reliably deal with extreme rates of outliers. We extend these methods to camera pose estimation by using accurate approximations and fast polynomial solvers. Experimental results are given demonstrating that it is possible to reliably estimate the camera pose despite cases with more than 99 percent outlier correspondences in city-scale models with several millions of 3D points.

It has long been recognized that one of the fundamental difficulties in the estimation of two-view epipolar geometry is the capability of handling outliers. In this paper, we develop a fast and tractable algorithm that maximizes the number of inlier under the assumption of a purely translating camera. Compared to classical random sampling methods, our approach is guaranteed to compute the optimal solution of a cost function based on reprojection errors and it has better time complexity. The performance is in fact independent of the inlier/outlier ratio of the data. This opens up for a more reliable approach to robust ego-motion estimation. Our basic translation estimator can be embedded into a system that computes the full camera rotation. We demonstrate the applicability in several difficult settings with large amounts of outliers. It turns out to be particularly well-suited for small rotations and rotations around a known axis (which is the case for cellular phones where the gravitation axis can be measured). Experimental results show that compared to standard RANSAC methods based on minimal solvers, our algorithm produces more accurate estimates in the presence of large outlier ratios.

We consider the problem of localizing a novel image in a large 3D model. In principle, this is just an instance of camera pose estimation, but the scale introduces some challenging problems. For one, it makes the correspondence problem very difficult and it is likely that there will be a significant rate of outliers to handle. In this paper we use recent theoretical as well as technical advances to tackle these problems. Many modern cameras and phones have gravitational sensors that allow us to reduce the search space. Further, there are new techniques to efficiently and reliably deal with extreme rates of outliers. We extend these methods to camera pose estimation by using accurate approximations and fast polynomial solvers. Experimental results are given demonstrating that it is possible to reliably estimate the camera pose despite more than 99% of outlier correspondences.

This paper is concerned with model fitting in the presence of noise and outliers. Previously it has been shown that the number of outliers can be minimized with polynomial complexity in the number of measurements. This paper improves on these results in two ways. First, it is shown that for a large class of problems, the statistically more desirable truncated L2-norm can be optimized with the same complexity. Then, with the same methodology, it is shown how to transform multi-model fitting into a purely combinatorial problem-with worst-case complexity that is polynomial in the number of measurements, though exponential in the number of models. We apply our framework to a series of hard registration and stitching problems demonstrating that the approach is not only of theoretical interest. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers for fitting problems with low-dimensional models.

Is the real problem in finding the relative orientation of two viewpoints the correspondence problem? We argue that this is only one difficulty. Even with known correspondences, popular methods like the eight point algorithm and minimal solvers may break down due to planar scenes or small relative motions. In this paper, we derive a simple, brute-force algorithm which is both robust to outliers and has no such algorithmic degeneracies. Several cost functions are explored including maximizing the consensus set and robust norms like truncated least-squares. Our method is based on parameter search in a four-dimensional space using a new epipolar parametrization. In principle, we do an exhaustive search of parameter space, but the computations are very simple and easily parallelizable, resulting in an efficient method. Further speed-ups can be obtained by restricting the domain of possible motions to, for example, planar motions or small rotations. Experimental results are given for a variety of scenarios including scenes with a large portion of outliers. Further, we apply our algorithm to 3D motion segmentation where we outperform state-of-the-art on the well-known Hopkins-155 benchmark database.

To improve traffic safety it is important to evaluate the safety of roads and intersections. Today this requires a large amount of manual labor so an automated system using cameras would be very beneficial. We focus on the geometric part of the problem, that is, how to get accurate three-dimensional data from images of a road or an intersection. This is essential in order to correctly identify different events and incidents, for example to estimate when two cars gets dangerously close to each other. The proposed method uses a standard tracker to find corresponding points between frames. Then a RANSAC-type algorithm detects points that are likely to belong to the same vehicle. To fully exploit the fact that vehicles rotate and translate only in the ground plane, the structure from motion is estimated using an optimization approach based on the L∞-norm. The same approach also allows for easy setup of the system by estimating the camera orientation relative to the ground plane. Promising results for real-world data are presented.

We study geometric reconstruction problems in one-dimensional retina vision. In such problems, the scene is modeled as a two-dimensional plane, and the camera sensor produces one-dimensional images of the scene. Our main contribution is an efficient method for computing the global optimum to the structure and motion problem with respect to the $L_{\infty}$ norm of the reprojection errors. One-dimensional cameras have proven useful in several applications, most prominently for autonomous vehicles, where they are used to provide inexpensive and reliable navigational systems. Previous results on one-dimensional vision are limited to the classification and solving of minimal cases, bundle adjustment for finding local optima, and linear algorithms for algebraic cost functions. In contrast, we present an approach for finding globally optimal solutions with respect to the $L_{\infty}$ norm of the angular reprojection errors. We show how to solve intersection and resection problems as well as the problem of simultaneous localization and mapping (SLAM). The algorithm is robust to use when there are missing data, which means that all points are not necessarily seen in all images. Our approach has been tested on a variety of different scenarios, both real and synthetic. The algorithm shows good performance for intersection and resection and for SLAM with up to five views. For more views the high dimension of the search space tends to give long running times. The experimental section also gives interesting examples showing that for one-dimensional cameras with limited field of view the SLAM problem is often inherently ill-conditioned.

We study the relative orientation problem for two calibrated cameras with outliers from the feature matching. In recent years there has been a growing interest in optimal algorithms for computer vision. Most people agree that to get accurate solutions to multiview geometry problems, an appropriate norm of the reprojection errors should be minimized. To this end local as well as global optimization methods have been employed. To handle outliers though, heuristic methods still dominate the field. In this paper we address the problem of estimating relative orientation from uncertain feature correspondences. We formulate this task as an optimization problem and propose a branchand-bound algorithm to find the optimal set of correspondences as well as the optimal relative orientation. The approach is based on geometric constraints for pairs of correspondences. The experimental results are promising, especially for omnidirectional cameras. An implementation of the algorithm is also made publicly available to facilitate further research.

Correspondence problems are of great importance in computer vision. They appear as subtasks in many applications such as object recognition, merging partial 3D reconstructions and image alignment. Automatically matching features from appearance only is difficult and errors are frequent. Thus, it is necessary to use geometric consistency to remove incorrect correspondences. Typically heuristic methods like RANSAC or EM-like algorithms are used, but they risk getting trapped in local optima and are in no way guaranteed to find the best solution. This paper illustrates how pairwise constraints in combination with graph methods can be used to efficiently find optimal correspondences. These ideas are implemented on two basic geometric problems, 3D-3D registration and 2D-3D registration. The developed scheme can handle large rates of outliers and cope with multiple hypotheses. Despite the combinatorial explosion, the resulting algorithm which has been extensively evaluated on real data, yields competitive running times compared to state of the art.

We present a framework for computing optimal transformations, aligning one point set to another, in the presence of outliers. Example applications include shape matching and registration (using, for example, similarity, affine or projective transformations) as well as multiview reconstruction problems (triangulation, camera pose etc.). While standard methods like RANSAC essentially use heuristics to cope with outliers, we seek to find the largest possible subset of consistent correspondences and the globally optimal transformation aligning the point sets. Based on theory from computational geometry, we show that this is indeed possible to accomplish in polynomial-time. We develop several algorithms which make efficient use of convex programming. The scheme has been tested and evaluated on both synthetic and real data for several applications.

The structure and motion problem of multiple one-dimensional projections of a two-dimensional environment is studied. One-dimensional cameras have proven useful in several different applications, most prominently for autonomous guided vehicles, but also in ordinary vision for analysing planar motion and the projection of lines. Previous results on one-dimensional vision are limited to classifying and solving minimal cases, bundle adjustment for finding local minima to the structure and motion problem and linear algorithms based on algebraic cost functions. In this paper, we present a method for finding the global minimum to the structure and motion problem using the max norm of reprojection errors. We show how the optimal solution can be computed efficiently using simple linear programming techniques. The algorithms have been tested on a variety of different scenarios, both real and synthetic, with good performance. In addition, we show how to solve the multiview triangulation problem, the camera pose problem and how to dualize the algorithm in the Carlsson duality sense, all within the same framework.