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.
Among the earliest efforts in this field are those of @cite_9 and @cite_17 . Both methods solve the minimal problem of pose estimation from 3 line correspondences in a closed form. Solutions of the P3L problem are multiple: up to 8 solutions may exist . Unfortunately, neither method is able to exploit more measurements to remove the ambiguity, and both methods are sensitive to presence of image noise.
@cite_9 @cite_17
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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. 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. 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. 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. 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. 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. 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. We address the problem of estimating human pose in a single image using a part based approach. Pose accuracy is directly affected by the accuracy of the part detectors but more accurate detectors are likely to be also more computationally expensive. We propose to use multiple, heterogeneous part detectors with varying accuracy and computation requirements, ordered in a hierarchy, to achieve more accurate and efficient pose estimation. For inference, we propose an algorithm to localize articulated objects by exploiting an ordered hierarchy of detectors with increasing accuracy. The inference uses branch and bound method to search for each part and use kinematics from neighboring parts to guide the branching behavior and compute bounds on the best part estimate. We demonstrate our approach on a publicly available People dataset and outperform the state-of-art methods. Our inference is 3 times faster than one based on using a single, highly accurate detector. The problem of pose estimation arises in many areas of computer vision, including object recognition, object tracking, site inspection and updating, and autonomous navigation when scene models are available. We present a new algorithm, called SoftPOSIT, for determining the pose of a 3D object from a single 2D image when correspondences between object points and image points are not known. The algorithm combines the iterative softassign algorithm (Gold and Rangarajan, 1996; , 1998) for computing correspondences and the iterative POSIT algorithm (DeMenthon and Davis, 1995) for computing object pose under a full-perspective camera model. Our algorithm, unlike most previous algorithms for pose determination, does not have to hypothesize small sets of matches and then verify the remaining image points. Instead, all possible matches are treated identically throughout the search for an optimal pose. The performance of the algorithm is extensively evaluated in Monte Carlo simulations on synthetic data under a variety of levels of clutter, occlusion, and image noise. These tests show that the algorithm performs well in a variety of difficult scenarios, and empirical evidence suggests that the algorithm has an asymptotic run-time complexity that is better than previous methods by a factor of the number of image points. The algorithm is being applied to a number of practical autonomous vehicle navigation problems including the registration of 3D architectural models of a city to images, and the docking of small robots onto larger robots. 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 propose a powerful pipeline for determining the pose of a query image relative to a point cloud reconstruction of a large scene consisting of more than one million 3D points. The key component of our approach is an efficient and effective search method to establish matches between image features and scene points needed for pose estimation. Our main contribution is a framework for actively searching for additional matches, based on both 2D-to-3D and 3D-to-2D search. A unified formulation of search in both directions allows us to exploit the distinct advantages of both strategies, while avoiding their weaknesses. Due to active search, the resulting pipeline is able to close the gap in registration performance observed between efficient search methods and approaches that are allowed to run for multiple seconds, without sacrificing run-time efficiency. Our method achieves the best registration performance published so far on three standard benchmark datasets, with run-times comparable or superior to the fastest state-of-the-art methods. Abstract This paper mathematically analyzes and proposes new solutions for the problem of estimating the camera 3D location and orientation ( pose determination ) from a matched set of 3D model and 2D image landmark features. Least-squares techniques for line tokens, which minimize both rotation and translation simultaneously, are developed and shown to be far superior to the earlier techniques which solved for rotation first and then translation. However, least-squares techniques fail catastrophically when outliers (or gross errors) are present in the match data. Outliers arise frequently due to incorrect correspondences or gross errors in the 3D model. Robust techniques for pose determination are developed to handle data contaminated by fewer than 50.0 outliers. Finally, the sensitivity of pose determination to incorrect estimates of camera parameters is analyzed. It is shown that for small field of view systems, offsets in the image center do not significantly affect the location of the camera in a world coordinate system. Errors in the focal length significantly affect only the component of translation along the optical axis in the pose computation. 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. We propose an end-to-end architecture for joint 2D and 3D human pose estimation in natural images. Key to our approach is the generation and scoring of a number of pose proposals per image, which allows us to predict 2D and 3D poses of multiple people simultaneously. Hence, our approach does not require an approximate localization of the humans for initialization. Our Localization-Classification-Regression architecture, named LCR-Net, contains 3 main components: 1) the pose proposal generator that suggests candidate poses at different locations in the image; 2) a classifier that scores the different pose proposals; and 3) a regressor that refines pose proposals both in 2D and 3D. All three stages share the convolutional feature layers and are trained jointly. The final pose estimation is obtained by integrating over neighboring pose hypotheses, which is shown to improve over a standard non maximum suppression algorithm. Our method recovers full-body 2D and 3D poses, hallucinating plausible body parts when the persons are partially occluded or truncated by the image boundary. Our approach significantly outperforms the state of the art in 3D pose estimation on Human3.6M, a controlled environment. Moreover, it shows promising results on real images for both single and multi-person subsets of the MPII 2D pose benchmark. 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. 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). 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. 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. In this paper we provide new simple closed-form solutions to two minimal absolute pose problems for the case of known vertical direction. In the first problem we estimate absolute pose of a calibrated camera from two 2D-3D correspondences and a given vertical direction. In the second problem we assume camera with unknown focal length and radial distortion and estimate its pose together with the focal length and the radial distortion from three 2D-3D correspondences and a given vertical direction. The vertical direction can be obtained either by direct physical measurement by, e.g., gyroscopes and inertial measurement units or from vanishing points constructed in images. Both our problems result in solving one polynomial equation of degree two in one variable and one, respectively two, systems of linear equations and can be efficiently solved in a closed-form. By evaluating our algorithms on synthetic and real data we demonstrate that both our solutions are fast, efficient and numerically stabled. An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences.