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 second recent improvement is the Robust PnL () algorithm of @cite_11 . Their method works with 4 or more lines and is more accurate and robust than the method of Mirzaei and Roumeliotis. An intermediate model coordinate system is used in the method of , which is aligned with a 3D line of longest projection. The lines are divided into triples, for each of which a P3L polynomial is formed. The optimal solution of the polynomial system is selected from the roots of its derivative in terms of a least squares residual.
@cite_11
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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). 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 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. 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. We propose a noniterative solution for the Perspective-n-Point ( P n P ) problem, which can robustly retrieve the optimum by solving a seventh order polynomial. The central idea consists of three steps: 1) to divide the reference points into 3-point subsets in order to achieve a series of fourth order polynomials, 2) to compute the sum of the square of the polynomials so as to form a cost function, and 3) to find the roots of the derivative of the cost function in order to determine the optimum. The advantages of the proposed method are as follows: First, it can stably deal with the planar case, ordinary 3D case, and quasi-singular case, and it is as accurate as the state-of-the-art iterative algorithms with much less computational time. Second, it is the first noniterative P n P solution that can achieve more accurate results than the iterative algorithms when no redundant reference points can be used (n 5). Third, large-size point sets can be handled efficiently because its computational complexity is O(n). The structural features in Manhattan world encode useful geometric information of parallelism, orthogonality and or coplanarity in the scene. By fully exploiting these structural features, we propose a novel monocular SLAM system which provides accurate estimation of camera poses and 3D map. The foremost contribution of the proposed system is a structural feature-based optimization module which contains three novel optimization strategies. First, a rotation optimization strategy using the parallelism and orthogonality of 3D lines is presented. We propose a global binding method to compute an accurate estimation of the absolute rotation of the camera. Then we propose an approach for calculating the relative rotation to further refine the absolute rotation. Second, a translation optimization strategy leveraging coplanarity is proposed. Coplanar features are effectively identified, and we leverage them by a unified model handling both points and lines to calculate the relative translation, and then the optimal absolute translation. Third, a 3D line optimization strategy utilizing parallelism, orthogonality and coplanarity simultaneously is proposed to obtain an accurate 3D map consisting of structural line segments with low computational complexity. Experiments in man-made environments have demonstrated that the proposed system outperforms existing state-of-the-art monocular SLAM systems in terms of accuracy and robustness. This paper proposes a novel closed-form solution to complete line-segment extraction. Given a voting angle in image space, the voting distribution is analyzed and two functional relationships are deduced. Regarding the corresponding column in Hough space, voting along the distance axis is considered as being a random variable, and voting values in cells are considered as forming a probability distribution. Statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve. Direction, length, and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves. The midpoint of a line segment is determined based on the fitted linear curve. The method is tested on simulated and real-world images; results show that the proposed closed-form solution is feasible in the presence of quantization errors or image noise. HighlightsWe proposed a method for obtaining the complete set of line-segment parameters.The direction, length and width of a line-segment are extracted simul- taneously in a closed form.We provided a complete theoretical derivation of voting variance with respect to voting angle.The midpoint of a line-segment is determined by the coefficients of the fitted linear curve.Parallel, crossing, and aligned line-segments are discussed by analysing events in image space and Hough space. We propose a minimal solution for the similarity registration (rigid pose and scale) between two sets of 3D lines, and also between a set of co-planar points and a set of 3D lines. The first problem is solved up to 8 discrete solutions with a minimum of 2 line-line correspondences, while the second is solved up to 4 discrete solutions using 4 point-line correspondences. We use these algorithms to perform the extrinsic calibration between a pose tracking sensor and a 2D 3D ultrasound (US) curvilinear probe using a tracked needle as calibration target. The needle is tracked as a 3D line, and is scanned by the ultrasound as either a 3D line (3D US) or as a 2D point (2D US). Since the scale factor that converts US scan units to metric coordinates is unknown, the calibration is formulated as a similarity registration problem. We present results with both synthetic and real data and show that the minimum solutions outperform the correspondent non-minimal linear formulations. We present a physics-based illumination estimation approach explicitly designed to handle natural images under ambient light. Existing physics-based color constancy methods are theoretically perfect but do not handle real-world images well because the majority of these methods assume a single illuminant. Therefore, specular pixels selected using existing methods produce estimated dichromatic lines that are thick or curvilinear in the presence of ambient light, thus generating significant errors. Based on the Phong reflection model, we show that a group of specular pixels on a uniformly colored object, although they are subject to intensity thresholding, produce a unique dichromatic line length depending on the geometry of each image path. Assuming that the longest dichromatic line is the most desirable when estimating the chromaticity of an illuminant, ambient-robust specular pixels are also found on the same path on which the longest dichromatic line segment is generated. Therefore, we propose a method to find the optimal image path in which the specular pixels produce the longest dichromatic line. Even though the number of collected specular pixels is reduced using the proposed method, they are proven to be more accurate when determining the illuminant chromaticity even in the existing methods. Experiments with an established benchmark data set and a self-produced image set find that the proposed method is better able to locate the illuminant chromaticity compared with the state-of-the-art color constancy methods. Three theorems are presented that establish polynomial straight-line complexity for certain operations on polynomials given by straight-line programs of unbounded input degree. The first theorem shows how to compute a higher order partial derivative in a single variable. The other two theorems impose the degree of the output polynomial as a parameter of the length of the output program. First it is shown that if a straight-line program computes an arbitrary power of a multivariate polynomial, that polynomial also admits a polynomial bounded straight-line computation. Second, any factor of a multivariate polynomial given by a division-free straight-line program with relatively prime co-factor also admits a straight-line computation of length polynomial in the input length and the degree of the factor. This result is based on a new Hensel lifting process, one where only one factor image is lifted back to the original factor. As an application we get that the greatest common divisor of polynomials given by a division-free straight-line program has polynomial straight-line complexity in terms of the input length and its own degree. In this paper, we develop a robust efficient visual SLAM system that utilizes heterogeneous point and line features. By leveraging ORB-SLAM [1], the proposed system consists of stereo matching, frame tracking, local mapping, loop detection, and bundle adjustment of both point and line features. In particular, as the main theoretical contributions of this paper, we, for the first time, employ the orthonormal representation as the minimal parameterization to model line features along with point features in visual SLAM and analytically derive the Jacobians of the re-projection errors with respect to the line parameters, which significantly improves the SLAM solution. The proposed SLAM has been extensively tested in both synthetic and real-world experiments whose results demonstrate that the proposed system outperforms the state-of-the-art methods in various scenarios. 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. In this work, we present a Direct Least-Squares (DLS) method for computing all solutions of the perspective-n-point camera pose determination (PnP) problem in the general case (n ≥ 3). Specifically, based on the camera measurement equations, we formulate a nonlinear least-squares cost function whose optimality conditions constitute a system of three third-order polynomials. Subsequently, we employ the multiplication matrix to determine all the roots of the system analytically, and hence all minima of the LS, without requiring iterations or an initial guess of the parameters. A key advantage of our method is scalability, since the order of the polynomial system that we solve is independent of the number of points. We compare the performance of our algorithm with the leading PnP approaches, both in simulation and experimentally, and demonstrate that DLS consistently achieves accuracy close to the Maximum-Likelihood Estimator (MLE). In this paper, we consider the problem of estimating the spatiotemporal alignment between N unsynchronized video sequences of the same dynamic 3D scene, captured from distinct viewpoints. Unlike most existing methods, which work for N = 2 and rely on a computationally intensive search in the space of temporal alignments, we present a novel approach that reduces the problem for general N to the robust estimation of a single line in RN. This line captures all temporal relations between the sequences and can be computed without any prior knowledge of these relations. Considering that the spatial alignment is captured by the parameters of fundamental matrices, an iterative algorithm is used to refine simultaneously the parameters representing the temporal and spatial relations between the sequences. Experimental results with real-world and synthetic sequences show that our method can accurately align the videos even when they have large misalignments (e.g., hundreds of frames), when the problem is seemingly ambiguous (e.g., scenes with roughly periodic motion), and when accurate manual alignment is difficult (e.g., due to slow-moving objects). The photorealistic modeling of large-scale objects, such as urban scenes, requires the combination of range sensing technology and digital photography. In this paper, we attack the key problem of camera pose estimation, in an automatic and efficient way. First, the camera orientation is recovered by matching vanishing points (extracted from 2D images) with 3D directions (derived from a 3D range model). Then, a hypothesis-and-test algorithm computes the camera positions with respect to the 3D range model by matching corresponding 2D and 3D linear features. The camera positions are further optimized by minimizing a line-to-line distance. The advantage of our method over earlier work has to do with the fact we do not need to rely on extracted planar facades, or other higher-order features; we are utilizing low- level linear features. That makes this method more general, robust, and efficient. Our method can also be enhanced by the incorporation of traditional structure-from-motion algorithms. We have also developed a user-interface for allowing users to accurately texture-map 2D images onto 3D range models at interactive rates. We have tested our system in a large variety of urban scenes. Consideration is given to a specific pose determination problem in which the sensory features are lines and the matched reference features are planes. The lines discussed are different from edge lines of an object in that they are not the intersection of boundary faces of the object. The author describes a polynomial method that, unlike previous methods, does not require prior knowledge about the location of the object. Closed-form solutions for orthogonal, coplanar, and parallel feature configurations of critical importance in real applications are derived. Basic findings concerning the necessary and sufficient conditions under which the pose determination problem can be solved are presented. > 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. Low cost CMOS cameras can have an acquisition mode called rolling shutter which sequentially exposes the scan-lines. When a single object moves with respect to the camera, this creates image distortions. Assuming 2D-3D correspondences known, previous work showed that the object pose and kinematics can be estimated from a single rolling shutter image. This was achieved using a suboptimal initialization followed by local iterative optimization. We propose a polynomial projection model for rolling shutter cameras and a constrained global optimization of its parameters. This is done by means of a semidefinite programming problem obtained from the generalized problem of moments method. Contrarily to previous work, our optimization does not require an initialization and ensures that the global minimum is achieved. This allows us to build automatically robust 2D-3D correspondences using a template to provide an initial set of correspondences. Experiments show that our method slightly improves previous work on both simulated and real data. This is due to local minima into which previous methods get trapped. We also successfully experimented building 2D-3D correspondences automatically with both simulated and real data. We present a novel method for recovering the 3D-line structure of a scene from multiple widely separated views. Traditional optimization-based approaches to line-based structure from motion minimize the error between measured line segments and the projections of corresponding 3D lines. In such a case, 3D lines can be optimized using a minimum of 4 parameters. We show that this number of parameters can be further reduced by introducing additional constraints on the orientations of lines in a 3D scene. In our approach, 2D-lines are automatically detected in images with the assistance of an EM-based vanishing point estimation method which assumes the existence of edges along mutally orthogonal vanishing directions. Each detected line is automatically labeled with the orientation (e.g. vertical, horizontal) of the 3D line which generated the measurement, and it is this additional knowledge that we use to reduce the number of degrees of freedom of 3D lines during optimization. We present 3D reconstruction results for urban scenes based on manually established feature correspondences across images. For multi-sensor integrated systems, such as the mobile mapping system (MMS), data fusion at sensor-level, i.e., the 2D-3D registration between an optical camera and LiDAR, is a prerequisite for higher level fusion and further applications. This paper proposes a line-based registration method for panoramic images and a LiDAR point cloud collected by a MMS. We first introduce the system configuration and specification, including the coordinate systems of the MMS, the 3D LiDAR scanners, and the two panoramic camera models. We then establish the line-based transformation model for the panoramic camera. Finally, the proposed registration method is evaluated for two types of camera models by visual inspection and quantitative comparison. The results demonstrate that the line-based registration method can significantly improve the alignment of the panoramic image and the LiDAR datasets under either the ideal spherical or the rigorous panoramic camera model, with the latter being more reliable.