Mobile AR applications benefit from fast initialization to display world-locked effects instantly. However, standard visual odometry or SLAM algorithms require motion parallax to initialize (see Figure 1) and, therefore, suffer from delayed initialization. In this paper, we present a 6-DoF monocular visual odometry that initializes instantly and without motion parallax. Our main contribution is a pose estimator that decouples estimating the 5-DoF relative rotation and translation direction from the 1-DoF translation magnitude. While scale is not observable in a monocular vision-only setting, it is still paramount to estimate a consistent scale over the whole trajectory (even if not physically accurate) to avoid AR effects moving erroneously along depth. In our approach, we leverage the fact that depth errors are not perceivable to the user during rotation-only motion. However, as the user starts translating the device, depth becomes perceivable and so does the capability to estimate consistent scale. Our proposed algorithm naturally transitions between these two modes. Our second contribution is a novel residual in the relative pose problem to further improve the results. The residual combines the Jacobians of the functional and the functional itself and is minimized using a Levenberg-Marquardt optimizer on the 5-DoF manifold. We perform extensive validations of our contributions with both a publicly available dataset and synthetic data. We show that the proposed pose estimator outperforms the classical approaches for 6-DoF pose estimation used in the literature in low-parallax configurations. Likewise, we show our relative pose estimator outperforms state-of-the-art approaches in an odometry pipeline configuration where we can leverage initial guesses. We release a dataset for the relative pose problem using real data to facilitate the comparison with future solutions for the relative pose problem. Our solution is either used as a full odometry or as a pre-SLAM component of any supported SLAM system (ARKit, ARCore) in world-locked AR effects on platforms such as Instagram and Facebook.

Finding the relative pose between two calibrated views ranks among the most fundamental geometric vision problems. It therefore appears as somewhat a surprise that a globally optimal solver that minimizes a properly defined energy over non-minimal correspondence sets and in the original space of relative transformations has yet to be discovered. This, notably, is the contribution of the present paper. We formulate the problem as a Quadratically Constrained Quadratic Program (QCQP), which can be converted into a Semidefinite Program (SDP) using Shor's convex relaxation. While a theoretical proof for the tightness of this relaxation remains open, we prove through exhaustive validation on both simulated and real experiments that our approach always finds and certifies (a-posteriori) the global optimum of the cost function.

The registration of 3D models by a Euclidean transformation is a fundamental task at the core of many application in computer vision. This problem is non-convex due to the presence of rotational constraints, making traditional local optimization methods prone to getting stuck in local minima. This paper addresses finding the globally optimal transformation in various 3D registration problems by a unified formulation that integrates common geometric registration modalities (namely point-to-point, point-to-line and point-to-plane). This formulation renders the optimization problem independent of both the number and nature of the correspondences. The main novelty of our proposal is the introduction of a strengthened Lagrangian dual relaxation for this problem, which surpasses previous similar approaches [32] in effectiveness. In fact, even though with no theoretical guarantees, exhaustive empirical evaluation in both synthetic and real experiments always resulted on a tight relaxation that allowed to recover a guaranteed globally optimal solution by exploiting duality theory. Thus, our approach allows for effectively solving the 3D registration with global optimality guarantees while running at a fraction of the time for the state-of-the-art alternative [34], based on a more computationally intensive Branch and Bound method.

Pose Graph Optimization (PGO) is the de facto choice to solve the trajectory of an agent in Simultaneous Localization and Mapping (SLAM). The Maximum Likelihood Estimation (MLE) for PGO is a non-convex problem for which no known technique is able to guarantee a globally optimal solution under general conditions. In recent years, Lagrangian duality has proved suitable to provide good, frequently tight relaxations of the hard PGO problem through convex Semidefinite Programming (SDP). In this work, we build from the state-of-the-art Lagrangian relaxation [1] and contribute a complete recovery procedure that, given the (tractable) optimal solution of the relaxation, provides either the optimal MLE solution if the relaxation is tight, or a remarkably good feasible guess if the relaxation is non-tight, which occurs in specially challenging PGO problems (very noisy observations, low graph connectivity, etc.). In the latter case, when used for initialization of local iterative methods, our approach outperforms other state-of-the-art approaches converging to better solutions. We support our claims with extensive experiments.

Graph-based SLAM has proved to be one of the most effective solutions to the Simultaneous Localization and Mapping problem. This approach relies on nonlinear iterative optimization methods that in practice perform both accurately and efficiently. However, due to the non-convexity of the problem, the obtained solutions come with no guarantee of global optimality and may get stuck in local minima. The application of SLAM to many real-world applications cannot be conceived without additional control tools that detect possible suboptimalities as soon as possible in order to take corrective action and avoid catastrophic failure of the entire system. This paper builds upon the state-of-the-art framework in verification for this problem and introduces a novel superior formulation that leads to a much higher efficiency. While retaining the same high effectiveness, the verification times of our proposal reduce up to >50x, paving the way for faster verification in critical real applications or in embedded low-power systems. We support our claims with extensive experiments with real and simulated data.

Most approaches to visual odometry estimates the camera motion based on point features, consequently, their performance deteriorates in low-textured scenes where it is difficult to find a reliable set of them. This paper extends a popular semi-direct approach to monocular visual odometry known as SVO [1] to work with line segments, hence obtaining a more robust system capable of dealing with both textured and structured environments. The proposed odometry system allows for the fast tracking of line segments since it eliminates the necessity of continuously extracting and matching features between subsequent frames. The method, of course, has a higher computational burden than the original SVO, but it still runs with frequencies of 60Hz on a personal computer while performing robustly in a wider variety of scenarios.

Robots are often equipped with 2D laser-rangefinders (LRFs) and cameras since they complement well to each other. In order to correctly combine measurements from both sensors, it is required to know their relative pose, that is, to solve their extrinsic calibration. In this paper we present a new approach to such problem which relies on the observations of orthogonal trihedrons which are profusely found as corners in human-made scenarios. Thus, the method does not require any specific pattern, which turns the calibration process fast and simpler to perform. The estimated relative pose has proven to be also very precise since it uses two different types of constraints, line-to-plane and point-to-plane, as a result of a richer configuration than previous proposals that relies on plane or V-shaped patterns. Our approach is validated with synthetic and real experiments, showing better performance than the state-of-art methods.

Robots are often equipped with 2D laser-rangefinders (LRFs) and cameras since they complement well to each other. In order to correctly combine the measurements from both sensors, it is required to know their relative pose, that is, to solve their extrinsic calibration. In this paper we present a simple, quick and effective minimal solution for the extrinsic calibration problem. Our approach does not require any onpurpose calibration pattern: it bases on the observation of an orthogonal trihedron, which is profusely found as corners in human-made scenarios. The proposal is validated with synthetic and real experiments, showing better performance than existing alternatives. An implementation of our approach is made available as open-source software.