In this paper we present a novel approach to global localization using an RGB-D camera in maps of visual features. For large maps, the performance of pure image matching techniques decays in terms of robustness and computational cost. Particularly, repeated occurrences of similar features due to repeating structure in the world (e.g., doorways, chairs, etc.) or missing associations between observations pose critical challenges to visual localization. We address these challenges using a two-step approach. We first estimate a candidate pose using few correspondences between features of the current camera frame and the feature map. The initial set of correspondences is established by proximity in feature space. The initial pose estimate is used in the second step to guide spatial matching of features in 3D, i.e., searching for associations where the image features are expected to be found in the map. A RANSAC algorithm is used to compute a fine estimation of the pose from the correspondences. Our approach clearly outperforms localization based on feature matching exclusively in feature space, both in terms of estimation accuracy and robustness to failure and allows for global localization in real time (30Hz).
Finding the transformation given by a set of point correspondences is a common problem in computer vision, e.g., for ego-motion estimation. A method to get a closed-form solution by means of a Least-Squares Estimation (LSE) is given in @cite_19 . However, when dealing with sets of point correspondences containing wrong associations, the result given by a LSE is distorted by the outliers. This is problem is commonly addressed by using a sample consensus method such as RANSAC @cite_26 .
@cite_19 @cite_26
2128019145 2085261163
A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate. Consider @math points in @math and @math local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the @math points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M=2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for @math . In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results fr... Outliers pose a problem in all real structure from motion systems. Due to the use of automatic matching methods one has to expect that a (sometimes very large) portion of the detected correspondences can be incorrect. In this paper we propose a method that estimates the relative translation between two cameras and simultaneously maximizes the number of inlier correspondences. Traditionally, outlier removal tasks have been addressed using RANSAC approaches. However, these are random in nature and offer no guarantees of finding a good solution. If the amount of mismatches is large, the approach becomes costly because of the need to evaluate a large number of random samples. In contrast, our approach is based on the branch and bound methodology which guarantees that an optimal solution will be found. While most optimal methods trade speed for optimality, the proposed algorithm has competitive running times on problem sizes well beyond what is common in practice. Experiments on both real and synthetic data show that the method outperforms state-of-the-art alternatives, including RANSAC, in terms of solution quality. In addition, the approach is shown to be faster than RANSAC in settings with a large amount of outliers. We introduce a new transformation estimation algorithm using the @math estimator and apply it to non-rigid registration for building robust sparse and dense correspondences. In the sparse point case, our method iteratively recovers the point correspondence and estimates the transformation between two point sets. Feature descriptors such as shape context are used to establish rough correspondence. We then estimate the transformation using our robust algorithm. This enables us to deal with the noise and outliers which arise in the correspondence step. The transformation is specified in a functional space, more specifically a reproducing kernel Hilbert space. In the dense point case for nonrigid image registration, our approach consists of matching both sparsely and densely sampled SIFT features, and it has particular advantages in handling significant scale changes and rotations. The experimental results show that our approach greatly outperforms state-of-the-art methods, particularly when the data contains severe outliers. In some statistical non-parametric models the mean of the random variable y has to satisfy specific constraints. We consider the case where the set defined by the constraints is a closed polyhedral cone K in Rk. For example, when the mean is required to be concave in x, the set of acceptable means is a closed convex cone defined by k-2 linear inequalities in Rk. The least squares estimate of the mean is then the projection of the data point y on the cone K. In this paper, we present an algorithm to find the least square estimate of the mean in a finite number of steps. Other algorithms to solve this problem have been given before. The successive approximations in such algorithms are usually points on the faces of K. The solution here is reached by following a fixed line joining an abitrary but suitably chosen initial point y0 to the data point y. The 1- dimensional subspace spanned by the generators of the cone K is divided into 2' regions which can be described as the set of points with non-negative coordinates in mixed primal-dual bases relative to the cone K. Any point y belongs to one and only one of these regions SJ with corresponding basis 3j. The projection of y on K is immediately obtained from the expression of y in Oj by dropping the dual component of y. In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90 ). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a two-stage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set. A popular approach to detect outliers in a data set is to find the largest consensus set, that is to say maximizing the number of inliers and estimating the underlying model. RANSAC is the most widely used method for this aim but is non-deterministic and does not guarantee to return the optimal solution. In this paper, we consider a rotation model and we present a new approach that performs consensus set maximization in a mathematically guaranteed globally optimal way. We solve the problem by a branch-and-bound framework associated with a rotation space search. Our mathematical formulation can be applied for various computer vision tasks such as panoramic image stitching, 3D registration with a rotating range sensor and line clustering and vanishing point estimation. Experimental results with synthetic and real data sets have successfully confirmed the validity of our approach. We propose a robust method for detecting local planar regions in a scene with an uncalibrated stereo. Our method is based on random sampling using distributions of feature point locations. For doing RANSAC, we use the distributions for each feature point defined by the distances between the point and the other points. We first choose a correspondence by using an uniform distribution and next choose candidate correspondences by using the distribution of the chosen point. Then, we compute a homography from the chosen correspondences and find the largest consensus set of the homography. We repeat this procedure until all regions are detected. We demonstrate that our method is robust to the outliers in a scene by simulations and real image examples. Real-time stereovision systems play an important role in automotive related applications. This paper concerns the problem of rigid motion estimation with a stereovision sensor. Given a set of corresponding 3D points in Euclidean space reconstructed from stereovision, efficient linear algorithms exist to solve for the rigid motion. However it has been well known that the noise in the Euclidean reconstruction from stereovision is heteroscedastic and anisotropic, therefore the linear algorithms are only sub-optimal. Recently a d-motion based algorithm has been developed to solve for the rigid motion directly in the disparity space, in which the noise can be approximated to be homogenous and isotropic. However this algorithm is nonlinear and requires iterative least-squares solution. By reformulating the problem, a closed-form linear solution is presented in this paper to solve for the rigid motion in disparity space. Synthetic experimental results show that this new algorithm outperforms the d-motion based algorithm in terms of both accuracy and computational cost. We believe that the closed-form linear solution is potentially very useful for applications making use of stereovision to estimate rigid motion. We introduce Coherent Point Drift (CPD), a novel probabilistic method for non-rigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the non-rigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex non-linear non-rigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points. We propose a real-time, robust to outliers and accurate solution to the Perspective-n-Point (PnP) problem. The main advantages of our solution are twofold: first, it in- tegrates the outlier rejection within the pose estimation pipeline with a negligible computational overhead, and sec- ond, its scalability to arbitrarily large number of correspon- dences. Given a set of 3D-to-2D matches, we formulate pose estimation problem as a low-rank homogeneous sys- tem where the solution lies on its 1D null space. Outlier correspondences are those rows of the linear system which perturb the null space and are progressively detected by projecting them on an iteratively estimated solution of the null space. Since our outlier removal process is based on an algebraic criterion which does not require computing the full-pose and reprojecting back all 3D points on the image plane at each step, we achieve speed gains of more than 100× compared to RANSAC strategies. An extensive exper- imental evaluation will show that our solution yields accu- rate results in situations with up to 50 of outliers, and can process more than 1000 correspondences in less than 5ms. The importance of precise homography estimation is often underestimated even though it plays a crucial role in various vision applications such as plane or planarity detection, scene degeneracy tests, camera motion classification, image stitching, and many more. Ignoring the radial distortion component in homography estimation—even for classical perspective cameras—may lead to significant errors or totally wrong estimates. In this paper, we fill the gap among the homography estimation methods by presenting two algorithms for estimating homography between two cameras with different radial distortions. Both algorithms can handle planar scenes as well as scenes where the relative motion between the cameras is a pure rotation. The first algorithm uses the minimal number of five image point correspondences and solves a nonlinear system of polynomial equations using Grobner basis method. The second algorithm uses a non-minimal number of six image point correspondences and leads to a simple system of two quadratic equations in two unknowns and one system of six linear equations. The proposed algorithms are fast, stable, and can be efficiently used inside a RANSAC loop. This paper presents a solution to panoramic image stitching of two images with coinciding optical centers, but unknown focal length and radial distortion. The algorithm operates with a minimal set of corresponding points (three) which means that it is well suited for use in any RANSAC style algorithm for simultaneous estimation of geometry and outlier rejection. Compared to a previous method for this problem, we are able to guarantee that the right solution is found in all cases. The solution is obtained by solving a small system of polynomial equations. The proposed algorithm has been integrated in a complete multi image stitching system and we evaluate its performance on real images with lens distortion. We demonstrate both quantitative and qualitative improvements compared to state of the art methods. This paper presents a way of using the Iteratively Reweighted Least Squares (IRLS) method to minimize several robust cost functions such as the Huber function, the Cauchy function and others. It is known that IRLS (otherwise known as Weiszfeld) techniques are generally more robust to outliers than the corresponding least squares methods, but the full range of robust M-estimators that are amenable to IRLS has not been investigated. In this paper we address this question and show that IRLS methods can be used to minimize most common robust M-estimators. An exact condition is given and proved for decrease of the cost, from which convergence follows. In addition to the advantage of increased robustness, the proposed algorithm is far simpler than the standard L1 Weiszfeld algorithm. We show the applicability of the proposed algorithm to the rotation averaging, triangulation and point cloud alignment problems. A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing This paper proposes an efficient mixture model for establishing robust point correspondences between two sets of points under multi-layer motion. Our algorithm starts by creating a set of putative correspondences which can contain a number of false correspondences, or outliers, in addition to the true correspondences (inliers). Next we solve for correspondence by interpolating a set of spatial transformations on the putative correspondence set based on a mixture model, which involves estimating a consensus of inlier points whose matching follows a non-parametric geometrical constraint. We formulate this as a maximum a posteriori (MAP) estimation of a Bayesian model with hidden latent variables indicating whether matches in the putative set are outliers or inliers. We impose non-parametric geometrical constraints on the correspondence, as a prior distribution, in a reproducing kernel Hilbert space (RKHS). MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We further provide a fast implementation based on sparse approximation which can achieve a significant speed-up without much performance degradation. We illustrate the proposed method on 2D and 3D real images for sparse feature correspondence, as well as a public available dataset for shape matching. The quantitative results demonstrate that our method is robust to non-rigid deformation and multi-layer large discontinuous motion. Finding the largest consensus set is one of the key ideas used by the original RANSAC for removing outliers in robust-estimation. However, because of its random and non-deterministic nature, RANSAC does not fulfill the goal of consensus set maximization exactly and optimally. Based on global optimization, this paper presents a new algorithm that solves the problem exactly. We reformulate the problem as a mixed integer programming (MIP), and solve it via a tailored branch-and-bound method, where the bounds are computed from the MIP's convex under-estimators. By exploiting the special structure of linear robust-estimation, the new algorithm is also made efficient from a computational point of view. This paper studies segmentation of multiple rigid-body motions in a 3-D dynamic scene under perspective camera projection. We consider dynamic scenes that contain both 3-D rigid-body structures and 2-D planar structures. Based on the well-known epipolar and homography constraints between two views, we propose a hybrid perspective constraint (HPC) to unify the representation of rigid-body and planar motions. Given a mixture of K hybrid perspective constraints, we propose an algebraic process to partition image correspondences to the individual 3-D motions, called Robust Algebraic Segmentation (RAS). Particularly, we prove that the joint distribution of image correspondences is uniquely determined by a set of (2K)-th degree polynomials, a global signature for the union of K motions of possibly mixed type. The first and second derivatives of these polynomials provide a means to recover the association of the individual image samples to their respective motions. Finally, using robust statistics, we show that the polynomials can be robustly estimated in the presence of moderate image noise and outliers. We conduct extensive simulations and real experiments to validate the performance of the new algorithm. The results demonstrate that RAS achieves notably higher accuracy than most existing robust motion-segmentation methods, including random sample consensus (RANSAC) and its variations. The implementation of the algorithm is also two to three times faster than the existing methods. The implementation of the algorithm and the benchmark scripts are available at http: perception.csl.illinois.edu ras . This paper deals with the problem of registering a known structured 3D scene and its metric Structure-from-Motion (SfM) counterpart. The proposed work relies on a prior plane segmentation of the 3D scene and aligns the data obtained from both modalities by solving the point-to-plane assignment problem. An inliers-maximization approach within a Branch-and-Bound (BnB) search scheme is adopted. For the first time in this paper, a Sum-of-Squares optimization theory framework is employed for identifying point-to-plane mismatches (i.e. outliers) with certainty. This allows us to iteratively build potential inliers sets and converge to the solution satisfied by the largest number of point-to-plane assignments. Furthermore, our approach is boosted by new plane visibility conditions which are also introduced in this paper. Using this framework, we solve the registration problem in two cases: (i) a set of putative point-to-plane correspondences (with possibly overwhelmingly many outliers) is given as input and (ii) no initial correspondences are given. In both cases, our approach yields outstanding results in terms of robustness and optimality. The problem of dense point set registration, given a sparse set of prior correspondences, often arises in computer vision tasks. Unlike in the rigid case, integrating prior knowledge into a registration algorithm is especially demanding in the non-rigid case due to the high variability of motion and deformation. In this paper we present the Extended Coherent Point Drift registration algorithm. It enables, on the one hand, to couple correspondence priors into the dense registration procedure in a closed form and, on the other hand, to process large point sets in reasonable time through adopting an optimal coarse-to-fine strategy. Combined with a suitable keypoint extractor during the preprocessing step, our method allows for non-rigid registrations with increased accuracy for point sets with structured outliers. We demonstrate advantages of our approach against other non-rigid point set registration methods in synthetic and real-world scenarios.