Abstract This work is concerned with camera pose estimation from correspondences of 3D 2D lines, i. e. with the Perspective-n-Line (PnL) problem. We focus on large line sets, which can be efficiently solved by methods using linear formulation of PnL. We propose a novel method “DLT-Combined-Lines” based on the Direct Linear Transformation (DLT) algorithm, which benefits from a new combination of two existing DLT methods for pose estimation. The method represents 2D structure by lines, and 3D structure by both points and lines. The redundant 3D information reduces the minimum required line correspondences to 5. A cornerstone of the method is a combined projection matrix estimated by the DLT algorithm. It contains multiple estimates of camera rotation and translation, which can be recovered after enforcing constraints of the matrix. Multiplicity of the estimates is exploited to improve the accuracy of the proposed method. For large line sets (10 and more), the method is comparable to the state-of-the-art in accuracy of orientation estimation. It achieves state-of-the-art accuracy in estimation of camera position and it yields the smallest reprojection error under strong image noise. The method achieves top-3 results on real world data. The proposed method is also highly computationally effective, estimating the pose of 1000 lines in 12 ms on a desktop computer.
The task of camera pose estimation from line correspondences has been receiving attention for more than a quarter of century. Some of the earliest works are those by @cite_9 and @cite_7 . They introduce two different ways to deal with the PnL problem -- algebraic and iterative approaches -- both of which have different properties and thus also different uses. A specific subset of algebraic approaches are the methods based on linear formulation of the PnL problem.
@cite_9 @cite_7
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In this paper we deal with the camera pose estimation problem from a set of 2D 3D line correspondences, which is also known as PnL (Perspective-n-Line) problem. We carry out our study by comparing PnL with the well-studied PnP (Perspective-n-Point) problem, and our contributions are three-fold: (1) We provide a complete 3D configuration analysis for P3L, which includes the well-known P3P problem as well as several existing analyses as special cases. (2) By exploring the similarity between PnL and PnP, we propose a new subset-based PnL approach as well as a series of linear-formulation-based PnL approaches inspired by their PnP counterparts. (3) The proposed linear-formulation-based methods can be easily extended to deal with the line and point features simultaneously. We propose a non-iterative solution for the Perspective-n-Line (PnL) problem, which can efficiently and accurately estimate the camera pose for both small number and large number of line correspondences. By selecting a rotation axis in the camera framework, the reference lines are divided into triplets to form a sixteenth order cost function, and then the optimum is retrieved from the roots of the derivative of the cost function by evaluating the orthogonal errors and the reprojected errors of the local minima. The final pose estimation is normalized by a 3D alignment approach. The advantages of the proposed method are as follows: (1) it stably retrieves the optimum of the solution with very little computational complexity and high accuracy; (2) small line sets can be robustly handled to achieve highly accurate results and; (3) large line sets can be efficiently handled because it is O(n). Estimation of camera pose from an image of n points or lines with known correspondence is a thoroughly studied problem in computer vision. Most solutions are iterative and depend on nonlinear optimization of some geometric constraint, either on the world coordinates or on the projections to the image plane. For real-time applications, we are interested in linear or closed-form solutions free of initialization. We present a general framework which allows for a novel set of linear solutions to the pose estimation problem for both n points and n lines. We then analyze the sensitivity of our solutions to image noise and show that the sensitivity analysis can be used as a conservative predictor of error for our algorithms. We present a number of simulations which compare our results to two other recent linear algorithms, as well as to iterative approaches. We conclude with tests on real imagery in an augmented reality setup. The determination of camera position and orientation from known correspondences of 3D reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry. It is well-known that from three corresponding points there are at most four algebraic solutions. Less appears to be known about the cases of four and five corresponding points. We propose a family of linear methods that yield a unique solution to 4- and 5-point pose determination for generic reference points. We first review the 3-point algebraic method. Then we present our two-step, 4-point and one-step, 5-point linear algorithms. The 5-point method can also be extended to handle more than five points. Finally, we demonstrate our methods on both simulated and real images. We show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice. We present a new method for solving the problem of camera pose and calibration from a limited number of correspondences between noisy 2D and 3D features. We show that the probabilistic estimation problem can be expressed as a partially linear problem, where point and line correspondences are mixed using a common formulation. Our Sampling-Solving algorithm enables to robustly estimate the parameters and evaluate the probability distribution of the estimated parameters. It solves the problem of pose estimation with unknown focal length using a minimum of only four correspondences (five if the principal point is also unknown). To our knowledge, this is the first calibration method using so few correspondences of both points and lines. Experimental results on minimal data sets show that the algorithm is very robust to Gaussian noise. Experimental comparisons show that our method is much more stable than existing camera calibration methods for small data sets. Finally, some tests show the potential of global uncertainty estimates on real data sets. We propose a real-time and accurate solution to the Perspective-n-Point (PnP) problem –estimating the pose of a calibrated camera from n 3D-to-2D point correspondences– that exploits the fact that in practice the 2D position of not all 2D features is estimated with the same accuracy. Assuming a model of such feature uncertainties is known in advance, we reformulate the PnP problem as a maximum likelihood minimization approximated by an unconstrained Sampson error function, which naturally penalizes the most noisy correspondences. The advantages of this approach are thoroughly demonstrated in synthetic experiments where feature uncertainties are exactly known. Pre-estimating the features uncertainties in real experiments is, though, not easy. In this paper we model feature uncertainty as 2D Gaussian distributions representing the sensitivity of the 2D feature detectors to different camera viewpoints. When using these noise models with our PnP formulation we still obtain promising pose estimation results that outperform the most recent approaches. We address the model-to-image registration problem with line features in the following two ways. (a) We present a robust solution to simultaneously recover the camera pose and the three-dimensional-to-two-dimensional line correspondences. With weak pose priors, our approach progressively verifies the pose guesses with a Kalman filter by using a subset of recursively found match hypotheses. Experiments show our method is robust to occlusions and clutter. (b) We propose a new line feature based pose estimation algorithm, which iteratively optimizes the objective function in the object space. Experiments show that the algorithm has strong robustness to noise and outliers and that it can attain very accurate results efficiently. This paper identifies and fills the probably last two missing items in minimal pose estimation algorithms using points and lines. Pose estimation refers to the problem of recovering the pose of a calibrated camera given known features (points or lines) in the world and their projections on the image. There are four minimal configurations using point and line features: 3 points, 2 points and 1 line, 1 point and 2 lines, 3 lines. The first and the last scenarios that depend solely on either points or lines have been studied a few decades earlier. However the mixed scenarios, which are more common in practice, have not been solved yet. In this paper we show that it is indeed possible to develop a general technique that can solve all four scenarios using the same approach and that the solutions involve computing the roots of either a 4th degree or an 8th degree equation. The centerpiece of our method is a simple and generic method that uses collinearity and coplanarity constraints for solving the pose. In addition to validating the performance of these algorithms in simulations, we also show a compelling application for geo-localization using image sequences and coarse (plane-based) 3D models of GPS-challenged urban canyons. We propose a non-iterative solution to the PnP problem--the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences--whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n 5) or even O(n 8), without being more accurate. Our method is applicable for all n?4 and handles properly both planar and non-planar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12×12 matrix and solving a small constant number of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closed-form solution can be used to initialize a Gauss-Newton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and real-data. We address the problem of estimating the pose of a cam- era relative to a known 3D scene from a single RGB-D frame. We formulate this problem as inversion of the generative rendering procedure, i.e., we want to find the camera pose corresponding to a rendering of the 3D scene model that is most similar with the observed input. This is a non-convex optimization problem with many local optima. We propose a hybrid discriminative-generative learning architecture that consists of: (i) a set of M predictors which generate M camera pose hypotheses, and (ii) a 'selector' or 'aggregator' that infers the best pose from the multiple pose hypotheses based on a similarity function. We are interested in predictors that not only produce good hypotheses but also hypotheses that are different from each other. Thus, we propose and study methods for learning 'marginally relevant' predictors, and compare their performance when used with different selection procedures. We evaluate our method on a recently released 3D reconstruction dataset with challenging camera poses, and scene variability. Experiments show that our method learns to make multiple predictions that are marginally relevant and can effectively select an accurate prediction. Furthermore, our method outperforms the state-of-the-art discriminative approach for camera relocalization. We consider the machine vision task of pose estimation from static images, specifically for the case of articulated objects. This problem is hard because of the large number of degrees of freedom to be estimated. Following a established line of research, pose estimation is framed as inference in a probabilistic model. In our experience however, the success of many approaches often lie in the power of the features. Our primary contribution is a novel casting of visual inference as an iterative parsing process, where one sequentially learns better and better features tuned to a particular image. We show quantitative results for human pose estimation on a database of over 300 images that suggest our algorithm is competitive with or surpasses the state-of-the-art. Since our procedure is quite general (it does not rely on face or skin detection), we also use it to estimate the poses of horses in the Weizmann database. Image-based localization approaches aim to determine the camera pose from which an image was taken. Finding correct 2D-3D correspondences between query image features and 3D points in the scene model becomes harder as the size of the model increases. Current state-of-the-art methods therefore combine elaborate matching schemes with camera pose estimation techniques that are able to handle large fractions of wrong matches. In this work we study the benefits and limitations of spatial verification compared to appearance-based filtering. We propose a voting-based pose estimation strategy that exhibits O(n) complexity in the number of matches and thus facilitates to consider much more matches than previous approaches - whose complexity grows at least quadratically. This new outlier rejection formulation enables us to evaluate pose estimation for 1-to-many matches and to surpass the state-of-the-art. At the same time, we show that using more matches does not automatically lead to a better performance. Correspondences between 3D lines and their 2D images captured by a camera are often used to determine position and orientation of the camera in space. In this work, we propose a novel algebraic algorithm to estimate the camera pose. We parameterize 3D lines using Plucker coordinates that allow linear projection of the lines into the image. A line projection matrix is estimated using Linear Least Squares and the camera pose is then extracted from the matrix. An algebraic approach to handle mismatched line correspondences is also included. The proposed algorithm is an order of magnitude faster yet comparably accurate and robust to the state-of-the-art, it does not require initialization, and it yields only one solution. The described method requires at least 9 lines and is particularly suitable for scenarios with 25 and more lines, as also shown in the results. In this study, the authors have proposed a new solution for the problem of pose estimation from a set of matched 3D model and 2D image lines. Traditional line-based pose estimation methods utilising the finite information of the observations are based on the assumption that the noises for the two endpoints of the image line segment are statistically independent. However, in this study, the authors prove that these two noises are negatively correlative when the image line segment is fitted by the least-squares technique from the noisy edge points. Moreover, the authors derive the noise model describing the probabilistic relationship between the 3D model line and their finite image observations. Based on the proposed noise model, the maximum-likelihood approach is exploited to estimate the pose parameters. The authors have carried out synthetic experiments to compare the proposed method to other pose optimisation methods in the literature. The experimental results show that the proposed methods yield a clear higher precision than the traditional methods. The authors also use real image sequences to demonstrate the performance of the proposed method. Correspondences between 2D lines in an image and 3D lines in the surrounding environment can be exploited to determine the camera's position and attitude (pose). In this paper, we introduce a novel approach to estimate the camera's pose by directly solving the corresponding least-squares problem algebraically. Specifically, the optimality conditions of the least-squares problem form a system of polynomial equations, which we efficiently solve through the eigendecomposition of a so-called multiplication matrix. Contrary to existing methods, the proposed algorithm (i) is guaranteed to find the globally optimal estimate in the least-squares sense, (ii) does not require initialization, and (iii) has computational cost only linear in the number of measurements. The superior performance of the proposed algorithm compared to previous approaches is demonstrated through extensive simulations and experiments. This paper considers the task of articulated human pose estimation of multiple people in real world images. We propose an approach that jointly solves the tasks of detection and pose estimation: it infers the number of persons in a scene, identifies occluded body parts, and disambiguates body parts between people in close proximity of each other. This joint formulation is in contrast to previous strategies, that address the problem by first detecting people and subsequently estimating their body pose. We propose a partitioning and labeling formulation of a set of body-part hypotheses generated with CNN-based part detectors. Our formulation, an instance of an integer linear program, implicitly performs non-maximum suppression on the set of part candidates and groups them to form configurations of body parts respecting geometric and appearance constraints. Experiments on four different datasets demonstrate state-of-the-art results for both single person and multi person pose estimation. Models and code available at this http URL. This paper considers the task of articulated human pose estimation of multiple people in real world images. We propose an approach that jointly solves the tasks of detection and pose estimation: it infers the number of persons in a scene, identifies occluded body parts, and disambiguates body parts between people in close proximity of each other. This joint formulation is in contrast to previous strategies, that address the problem by first detecting people and subsequently estimating their body pose. We propose a partitioning and labeling formulation of a set of body-part hypotheses generated with CNN-based part detectors. Our formulation, an instance of an integer linear program, implicitly performs non-maximum suppression on the set of part candidates and groups them to form configurations of body parts respecting geometric and appearance constraints. Experiments on four different datasets demonstrate state-of-the-art results for both single person and multi person pose estimation1. Estimating a camera pose given a set of 3D-object and 2D-image feature points is a well understood problem when correspondences are given. However, when such correspondences cannot be established a priori, one must simultaneously compute them along with the pose. Most current approaches to solving this problem are too computationally intensive to be practical. An interesting exception is the SoftPosit algorithm, that looks for the solution as the minimum of a suitable objective function. It is arguably one of the best algorithms but its iterative nature means it can fail in the presence of clutter, occlusions, or repetitive patterns. In this paper, we propose an approach that overcomes this limitation by taking advantage of the fact that, in practice, some prior on the camera pose is often available. We model it as a Gaussian Mixture Model that we progressively refine by hypothesizing new correspondences. This rapidly reduces the number of potential matches for each 3D point and lets us explore the pose space more thoroughly than SoftPosit at a similar computational cost. We will demonstrate the superior performance of our approach on both synthetic and real data. Traditionally, the camera pose recovery problem has been formulated as one of estimating the optimal camera pose given a set of point correspondences. This critically depends on the accuracy of the point correspondences and would have problems in dealing with ambiguous features such as edge contours and high visual clutter. Joint estimation of camera pose and correspondence attempts to improve performance by explicitly acknowledging the chicken and egg nature of the pose and correspondence problem. However, such joint approaches for the two-view problem are still few and even then, they face problems when scenes contain largely edge cues with few corners, due to the fact that epipolar geometry only provides a "soft" point to line constraint. Viewed from the perspective of point set registration, the point matching process can be regarded as the registration of points while preserving their relative positions (i.e. preserving scene coherence). By demanding that the point set should be transformed coherently across views, this framework leverages on higher level perceptual information such as the shape of the contour. While thus potentially allowing registration of non-unique edge points, the registration framework in its traditional form is subject to substantial point localization error and is thus not suitable for estimating camera pose. In this paper, we introduce an algorithm which jointly estimates camera pose and correspondence within a point set registration framework based on motion coherence, with the camera pose helping to localize the edge registration, while the "ambiguous" edge information helps to guide camera pose computation. The algorithm can compute camera pose over large displacements and by utilizing the non-unique edge points can recover camera pose from what were previously regarded as feature-impoverished SfM scenes. Our algorithm is also sufficiently flexible to incorporate high dimensional feature descriptors and works well on traditional SfM scenes with adequate numbers of unique corners. We propose a novel solution to the generalized camera pose problem which includes the internal scale of the generalized camera as an unknown parameter. This further generalization of the well-known absolute camera pose problem has applications in multi-frame loop closure. While a well-calibrated camera rig has a fixed and known scale, camera trajectories produced by monocular motion estimation necessarily lack a scale estimate. Thus, when performing loop closure in monocular visual odometry, or registering separate structure-from-motion reconstructions, we must estimate a seven degree-of-freedom similarity transform from corresponding observations. Existing approaches solve this problem, in specialized configurations, by aligning 3D triangulated points or individual camera pose estimates. Our approach handles general configurations of rays and points and directly estimates the full similarity transformation from the 2D-3D correspondences. Four correspondences are needed in the minimal case, which has eight possible solutions. The minimal solver can be used in a hypothesize-and-test architecture for robust transformation estimation. Our solver also produces a least-squares estimate in the overdetermined case. The approach is evaluated experimentally on synthetic and real datasets, and is shown to produce higher accuracy solutions to multi-frame loop closure than existing approaches.