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.
Recently, @cite_10 developed a DLT method, which acts on 3D lines directly. The lines are parameterized using Plücker coordinates, hence the name of the method is . The method yields more accurate estimates of camera orientation than DLT-Lines at the cost of a bit larger reprojection error and slightly lower computational efficiency. Also, the minimum number of lines required is 9.
@cite_10
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In this paper we approach the problem of in- situ camera calibration using an auxiliary mobile color-depth camera. The calibration is based on image lines and the Direct Linear Transformation (DLT). Calibration includes intrinsic and extrinsic parameters, and radial distortion. Traditionally, camera calibration methods based on DLT combine 2D and 3D points. Using 2D image lines allows adding simple image processing methods for fine tuning the calibration data (lines). Experimental comparison of points and lines based calibration shows that the automatic fine tuning of the lines is beneficial for the calibration process in noisy conditions. Experiments on both synthetic and real setups show that despite the low computational complexity of the DLT, the proposed calibration methodology yields promising accurate results. I. I NTRODUCTION 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. 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). 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. We address the problem of camera motion and 3D structure reconstruction from line correspondences across multiple views, from initialization to final bundle adjustment. One of the main difficulties when dealing with line features is their algebraic representation. First, we consider the triangulation problem. Based on Plucker coordinates to represent the 3D lines, we propose a maximum likelihood algorithm, relying on linearizing the Plucker constraint and on a Plucker correction procedure, computing the closest Plucker coordinates to a given 6-vector. Second, we consider the bundle adjustment problem, which is essentially a nonlinear optimization process on camera motion and 3D line parameters. Previous overparameterizations of 3D lines induce gauge freedoms and or internal consistency constraints. We propose the orthonormal representation, which allows handy nonlinear optimization of 3D lines using the minimum four parameters with an unconstrained optimization engine. We compare our algorithms to existing ones on simulated and real data. Results show that our triangulation algorithm outperforms standard linear and bias-corrected quasi-linear algorithms, and that bundle adjustment using our orthonormal representation yields results similar to the standard maximum likelihood trifocal tensor algorithm, while being usable for any number of views. 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. 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. Lighting variation and uneven feature distribution are main challenges for indoor RGB-D visual odometry where color information is often combined with depth information. To meet the challenges, we fuse point and line features to form a robust odometry algorithm. Line features are abundant indoors and less sensitive to lighting change than points. We extract 3D points and lines from RGB-D data, analyze their measurement uncertainties, and compute camera motion using maximum likelihood estimation. We prove that fusing points and lines produces smaller motion estimate uncertainty than using either feature type alone. In experiments we compare our method with state-of-the-art methods including a keypoint-based approach and a dense visual odometry algorithm. Our method outperforms the counterparts under both constant and varying lighting conditions. Specifically, our method achieves an average translational error that is 34.9 smaller than the counterparts, when tested using public datasets. A method for the determination of camera location from two-dimensional (2-D) to three-dimensional (3-D) straight line or point correspondences is presented. With this method, the computations of the rotation matrix and the translation vector of the camera are separable. First, the rotation matrix is found by a linear algorithm using eight or more line correspondences, or by a nonlinear algorithm using three or more line correspondences, where the line correspondences are either given or derived from point correspondences. Then, the translation vector is obtained by solving a set of linear equations based on three or more line correspondences, or two or more point correspondences. Eight 2-D to 3-D line correspondences or six 2-D to 3-D point correspondences are needed for the linear approach; three 2-D to 3-D line or point correspondences for the nonlinear approach. Good results can be obtained in the presence of noise if more than the minimum required number of correspondences are used. > We present a new shape-from-distortion framework for recovering specular (reflective refractive) surfaces. While most existing approaches rely on accurate correspondences between 2D pixels and 3D points, we focus on analyzing the curved images of 3D lines which we call curved line images or CLIs. Our approach models CLIs of local reflections or refractions using the recently proposed general linear cameras (GLCs). We first characterize all possible CLIs in a GLC. We show that a 3D line will appear as a conic in any GLC. For a fixed GLC, the conic type is invariant to the position and orientation of the line and is determined by the GLC parameters. Furthermore, CLIs under single reflection refraction can only be lines or hyperbolas. Based on our new theory, we develop efficient algorithms to use multiple CLIs to recover the GLC camera parameters. We then apply the curvature-GLC theory to derive the Gaussian and mean curvatures from the GLC intrinsics. This leads to a complete distortion-based reconstruction framework. Unlike conventional correspondence-based approaches that are sensitive to image distortions, our approach benefits from the CLI distortions. Finally, we demonstrate applying our framework for recovering curvature fields on both synthetic and real specular surfaces. This paper presents a new document image dewarping method that removes geometric distortions in camera-captured document images. The proposed method does not directly use the text-line which has been the most widely used feature for the document dewarping. Instead, we use the discrete representation of text-lines and text-blocks which are the sets of connected components. Also, we model the geometric distortions caused by page curl and perspective view as the generalized cylindrical surfaces and camera rotation respectively. With these distortion models and the discrete representation of the features, we design a cost function whose minimization yields the parameters of the distortion model. In the cost function, we encode the properties of the pages such as text-block alignment, line-spacing, and the straightness of text-lines. By describing the text features using the sets of discrete points, the cost function can be easily defined and efficiently solved by Levenberg-Marquadt algorithm. Experiments show that the proposed method works well for the various layouts and curved surfaces, and compares favorably with the conventional methods on the standard dataset. HighlightsDocument dewarping is an important problem in camera-based OCR.We formulate the dewarping as an optimization problem.The proposed method performs dewarping in a fully automatic manner.The proposed method can handle various layouts of documents.Our method yields the improved OCR performances compared with other methods. We present a novel on-line approach for extrinsic robot-camera calibration, a process often referred to as hand-eye calibration, that uses object pose estimates from a real-time model-based tracking approach. While off-line calibration has seen much progress recently due to the incorporation of bundle adjustment techniques, on-line calibration still remains a largely open problem. Since we update the calibration in each frame, the improvements can be incorporated immediately in the pose estimation itself to facilitate object tracking. Our method does not require the camera to observe the robot or to have markers at certain fixed locations on the robot. To comply with a limited computational budget, it maintains a fixed size configuration set of samples. This set is updated each frame in order to maximize an observability criterion. We show that a set of size 20 is sufficient in real-world scenarios with static and actuated cameras. With this set size, only 100 microseconds are required to update the calibration in each frame, and we typically achieve accurate robot-camera calibration in 10 to 20 seconds. Together, these characteristics enable the incorporation of calibration in normal task execution. Archaeological line drawing is an essential component of an archaeological report. In this paper, we propose a multi-scale approach to generating 3D line drawing on a triangular mesh model for archaeological illustration. The discrete multi-scale representation of a given model is first constructed based on random walks. Then, we propose a probabilistic method for local scale selection based on the minimum description length (MDL) principle. Finally, the ridges or valleys are detected with the selected scales. Experimental results show that the multi-scale 3D line drawings can well depict the shapes of cultural heritage objects. Compared with the traditional manual method, our method is more accurate and convenient. Furthermore, the time cost of archaeological mapping is decreased to a large extent and the detected lines can be rendered with specific scales and view directions. The computer-generated line drawing can be used to assist the archaeologists to draw archaeological line drawing. 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. We present a low-drift visual odometry algorithm that separately estimates rotational and translational motion from lines, planes, and points found in RGB-D images. Previous methods estimate drift-free rotational motion from structural regularities to reduce drift in the rotation estimate, which is the primary source of positioning inaccuracy in visual odometry. However, multiple orthogonal planes are required to be visible throughout the entire motion estimation process; otherwise, these VO approaches fail. We propose a new approach to estimate drift-free rotational motion jointly from both lines and planes by exploiting environmental regularities. We track the spatial regularities with an efficient SO(3)-manifold constrained mean shift algorithm. Once the drift-free rotation is found, we recover the translational motion from all tracked points with and without depth by minimizing the de-rotated reprojection error. We compare the proposed algorithm to other state-of-the-art visual odometry methods on a variety of RGB-D datasets (including especially challenging pure rotations) and demonstrate improved accuracy and lower drift error. 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. 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. 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. Line segment detection in images is already a well-investigated topic, although it has received considerably less attention in 3D point clouds. Benefiting from current LiDAR devices, large-scale point clouds are becoming increasingly common. Most human-made objects have flat surfaces. Line segments that occur where pairs of planes intersect give important information regarding the geometric content of point clouds, which is especially useful for automatic building reconstruction and segmentation. This paper proposes a novel method that is capable of accurately extracting plane intersection line segments from large-scale raw scan points. The 3D line-support region, namely, a point set near a straight linear structure, is extracted simultaneously. The 3D line-support region is fitted by our Line-Segment-Half-Planes (LSHP) structure, which provides a geometric constraint for a line segment, making the line segment more reliable and accurate. We demonstrate our method on the point clouds of large-scale, complex, real-world scenes acquired by LiDAR devices. We also demonstrate the application of 3D line-support regions and their LSHP structures on urban scene abstraction. Abstract The Hough transform (HT) is commonly used in machine vision applications for detecting discontinuous patterns in noisy images. The process of using the HT to detect lines in an image involves the computation of the HT for the entire image, accumulating votes in an accumulator array and searching the array for peaks which hold information of potential lines present in the input image. The peaks provide only the length of the normal to the line and the angle that the normal makes with the x -axis. They do not provide any information regarding the length, position or end points of the line segments. However, the butterfly shaped [1] spread of votes in the accumulator array, generated by the process of peak formation, holds vital information like the length and position of the input line segment. Some authors [2] have used this property to develop an algorithm to determine the coordinates of the end points, the length, and the normal parameters of straight lines. A limitation of this method, making it unsuitable for application to a real machine vision problem, is that it would yield erroneous results if applied to an image consisting of anything more than a single line segment. Moreover, the precision of this algorithm is dependent on the sharpness of the peak. In this paper, new techniques which address the above mentioned shortcomings have been described. This paper details the method developed to provide complete line segment description for an image consisting of multiple line segments. In addition, the developed techniques are more robust and accurate than the previously proposed methods as they do not depend upon the sharpness of the peak.