未标定单幅结构场景图像的三维重构

提出了一种单视三维重构方法，该方法是利用用户提供图像点及其对应的三维点之间几何信息。由于结构场景是由大量平面构成的，存在大量的平行性、正交性约束，因此该方法主要应用于结构场景的三维重构。首先，相机定标和计算每个平面的度量信息，即先基于3组互相垂直方向的影灭点，对方形像素相机标定，再利用影灭线和圆环点像，对每个平面度量校正；然后考虑每个校正平面的尺度因子和非正交平面间的相对面向，从而将所有校正后的平面缝合起来。采用真实图像进行实验，实验结果表明，该方法简单易用。     

Single View Metrology

We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to the plane. It is shown that affine scene structure may then be determined from the image, without knowledge of the camera's internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose).In particular, we show how to (i) compute the distance between planes parallel to the reference plane (up to a common scale factor); (ii) compute area and length ratios on any plane parallel to the reference plane; (iii) determine the camera's location. Simple geometric derivations are given for these results. We also develop an algebraic representation which unifies the three types of measurement and, amongst other advantages, permits a first order error propagation analysis to be performed, associating an uncertainty with each measurement.We demonstrate the technique for a variety of applications, including height measurements in forensic images and 3D graphical modelling from single images.     

基于仿射点对应的分层重构

提出了一种基于仿射点对应的分层重构方法,所谓仿射点对应是指相差一个仿射变换的两个空间点集的图像对应．该方法主要分为以下三个步骤：首先,从点对应计算准仿射重构;然后,由仿射点对应的准仿射重构建立一个三维射影变换,并利用这个射影变换的特征向量来确定无穷远平面,从而得到仿射重构;最后,从仿射重构所获得的无穷远平面单应矩阵标定摄像机内参数,进而得到度量重构．在上述三个步骤中,第二个步骤是最关键的,即如何确定对应于无穷远平面的特征向量,这也是该文的新思想和主要贡献所在．仿真和真实图像实验均表明,该文的方法是有效的,并且有很好的鲁棒性．     

A study on the dual vanishing point property

Vanishing points and vanishing lines are useful information in computer vision. In this study, an interesting dual property of vanishing point is first introduced. Next, we point out that there also exists a dual property of vanishing line. With the dual vanishing point and vanishing line properties, some 3D intersection inference can be made based on their image lines. Two applications are given to illustrate the usage of the new results. The first one is to derive the 3D pose determination of a circle using two parallel image lines. The second one uses six specially designed 3D lines to adjust the cameras with respect to a fixture in a binocular vision system such that the resultant camera coordinate axes become parallel.     

Depth computations from polyhedral images

A method is developed for the computation of depth maps, modulo scale, from one single image of a polyhedral scene. Only affine shape properties of the scene and image are used, no metric information. Results from simple experiments show good performance, both concerning exactness and robustness. It is also shown how the underlying theory may be used to single out and characterize certain singular situations that may occur in machine interpretation of line drawings.     

An error analysis for surface orientation from vanishing points

Given two parallel lines in a plane, their images formed by central projection onto the viewing plane intersect at a vanishing point, which provides a constraint on the orientation of the plane. Two such independent constraints define a vanishing line and thereby determine the orientation of the plane uniquely. In order to effectively use this information, an estimate of its accuracy must be incorporated. In the approach suggested, line directions and surface normal vectors are represented as points on a Gaussian sphere, and the error bounds are computed as regions on the sphere. Information from multiple vanishing points and surfaces is combined by intersecting the corresponding regions. In addition, constraints based on real-world knowledge can be introduced to improve the accuracy. Some experimental results on natural images re presented to illustrate this method     

Hypercatadioptric line images for 3D orientation and image rectification

In central catadioptric systems 3D lines are projected into conics. In this paper we present a new approach to extract conics in the raw catadioptric image, which correspond to projected straight lines in the scene. Using the internal calibration and two image points we are able to compute analytically these conics which we name hypercatadioptric line images. We obtain the error propagation from the image points to the 3D line projection in function of the calibration parameters. We also perform an exhaustive analysis on the elements that can affect the conic extraction accuracy. Besides that, we exploit the presence of parallel lines in man-made environments to compute the dominant vanishing points (VPs) in the omnidirectional image. In order to obtain the intersection of two of these conics we analyze the self-polar triangle common to this pair. With the information contained in the vanishing points we are able to obtain the 3D orientation of the catadioptric system. This method can be used either in a vertical stabilization system required by autonomous navigation or to rectify images required in applications where the vertical orientation of the catadioptric system is assumed. We use synthetic and real images to test the proposed method. We evaluate the 3D orientation accuracy with a ground truth given by a goniometer and with an inertial measurement unit (IMU). We also test our approach performing vertical and full rectifications in sequences of real images.     

Plane-Based Resection for Metric Affine Cameras

We study the problem of resecting the metric affine camera models from at least three non-colinear point correspondences. A direct application is plane pose estimation. We consider the three most popular metric affine cameras, namely the paraperspective, weak-perspective and orthographic cameras. For each model, we give an algebraic procedure which finds the optimal solution, where by optimal we mean the global minimizer of the reprojection error under the Euclidean norm. Our algebraic procedures cover both the minimal case of three points and the redundant cases of more than three points. They always return two solutions, as the problem has a two-way ambiguity on the rotation and translation for the three cameras in the general case. The scale of the paraperspective and weak-perspective cameras is, however, recovered uniquely. The orthographic case is the most involved and has not been solved analytically in the literature. We characterize its intrinsic complexity by showing that it reduces to finding the roots of an irreducible and non-solvable by radicals sextic polynomial. The previous algorithms for the paraperspective and weak-perspective cases have singularities, while, in contrast, our algebraic procedures do not.     

Projection matrix by orthogonal vanishing points

Calculation of camera projection matrix, also called camera calibration, is an essential task in many computer vision and 3D data processing applications. Calculation of projection matrix using vanishing points and vanishing lines is well suited in the literature; where the intersection of parallel lines (in 3D Euclidean space) when projected on the camera image plane (by a perspective transformation) is called vanishing point and the intersection of two vanishing points (in the image plane) is called vanishing line. The aim of this paper is to propose a new formulation for easily computing the projection matrix based on three orthogonal vanishing points. It can also be used to calculate the intrinsic and extrinsic camera parameters. The proposed method reaches to a closed-form solution by considering only two feasible constraints of zero-skewness in the internal camera matrix and having two corresponding points between the world and the image. A nonlinear optimization procedure is proposed to enhance the computed camera parameters, especially when the measurement error of input parameters or the skew factor are not negligible. The proposed method has been run on real and synthetic data for more precise evaluations. The provided experimental results demonstrate the superiority of the proposed method.     

On the complexity of labeling perspective projections of polyhedral scenes

This paper investigates the computational time complexity of the labeling problem for line drawings of trihedral scenes. It is shown that the class of problems having polynomial complexity is larger than the simple case of line drawings of Legoland scenes (Kirousis and Papadimitriou, 1988). Once the location of the vanishing points in the image plane is known, the labeling problem can be solved in time O(Nn) where N is the number of segments and n is the number of vanishing points. The vanishing points can be given a priori, otherwise can, in many cases, be detected by standard techniques from the line drawing itself. The NP-completeness of the labeling problem for line drawings of trihedral scenes (Kirousis and Papadimitriou, 1988) is then due to the lack of knowledge about the vanishing points. which is equivalent to the knowledge of the possible directions for the edges. These results help draw a more accurate boundary between the problems in the interpretation of line drawings that are polynomially solvable and those that are NP-complete.     

基于2个灭点和局部尺度的三维空间尺度估计

三维空间尺度估计是三维重建中的一个重要工作,现实世界中也存在一些基于单幅图像进行三维空间尺度估计的需求。通常情况下,尺度估计需先对相机进行标定。根据单目图像符合透视原理的特性,提出了一种基于2个灭点和局部尺度信息的方法对相机进行标定,从而得到单目图像物体中三维空间尺度信息的估计。首先,从单目图像中选择2组互相正交的平行线组,得到对应2个灭点的坐标;然后,利用灭点坐标和焦距信息得到世界坐标系和相机坐标系之间的旋转矩阵,再利用灭点的性质和已知局部尺度信息得到平移向量,完成单目相机的标定;最后,还原二维图像中像素点对应的三维世界坐标值,计算出图像中2个像素点在三维空间的尺度信息。实验结果表明,该方法能有效地对单幅图像中的建筑物体进行尺度估计。     

Efficient extraction of metric measurements for planar scene under 2D homography with the help of planar circles

Extraction of metric properties from perspective view is a challenging task in many machine vision applications. Most conventional approaches typically first recover the perspective transformation parameters up to a similarity transform and make measurements in the resulting rectified image. In this paper, a new approach is proposed to allow quick and reliable Euclidean measures to be made directly from a perspective view without explicitly recovering the world plane. Unlike previous planar rectification strategies, our approach makes use of planar circles to help identify the image of the absolute conic, which makes it capable of performing effective rectification under many difficult cases that are unable to be treated with other rectification approaches. This is made possible by solving the images of the circular points in closed-form from the vanishing line and the image of one arbitrary planar circle and by exploiting the invariant relationship between the circular points and the absolute conic under projective transformation. Subsequently, planar Euclidean measures can be made directly from the image plane. The practical advantages and the efficiency of this method are demonstrated by experiments on both synthetic and real scenes.     

一种优化的消失点估计方法及误差分析

空间一组平行直线在图像平面上所成的像的交点称为消失点. 消失点可以提供大量的场景三维结构信息. 本文提出一种新的优化的消失点估计方法. 该方法基于随机采样一致算法(Random sample consensus, RANSAC)对图像空间中的线段进行聚类, 通过最小化Sampson误差获得消失点的极大似然估计(Maximum likelihood estimation, MLE). 该方法不需要预知摄像机参数及直线的三维位置信息. 为了对该算法进行定量评估, 构造了基于反向传播的消失点误差传递模型. 实验结果验证了本文提出算法的有效性.     

Using points at infinity for parameter decoupling in camera calibration

The majority of camera calibration methods, including the gold standard algorithm, use point-based information and simultaneously estimate all calibration parameters. In contrast, we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages. We formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points. Unlike previous vanishing point methods, parallel line pairs are not required. Additionally, the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters. We compare this method with vanishing point methods and the gold standard algorithm and demonstrate that it has comparable performance.     

The 3D Line Motion Matrix and Alignment of Line Reconstructions

We study the problem of aligning two 3D line reconstructions in projective, affine, metric or Euclidean space.We introduce the 6 × 6 3D line motion matrix that acts on Plücker coordinates. We characterize its algebraic properties and its relation to the usual 4 × 4 point motion matrix, and propose various methods for estimating 3D motion from line correspondences, based on cost functions defined in images or 3D space. We assess the quality of the different estimation methods using simulated data and real images.     

Using vanishing points for camera calibration and coarse 3D reconstruction from a single image

In this paper, we show how to calibrate a camera and to recover the geometry and the photometry (textures) of objects from a single image. The aim of this work is to make it possible walkthrough and augment reality in a 3D model reconstructed from a single image. The calibration step does not need any calibration target and makes only four assumptions: (1) the single image contains at least two vanishing points, (2) the length (in 3D space) of one line segment (for determining the translation vector) in the image is known, (3) the principle point is the center of the image, and (4) the aspect ratio is fixed by the user. Each vanishing point is determined from a set of parallel lines. These vanishing points help determine a 3D world coordinate system R _o. After having computed the focal length, the rotation matrix and the translation vector are evaluated in turn for describing the rigid motion between R _o and the camera coordinate system R _c. Next, the reconstruction step consists in placing, rotating, scaling, and translating a rectangular 3D box that must fit at best with the potential objects within the scene as seen through the single image. With each face of a rectangular box, a texture that may contain holes due to invisible parts of certain objects is assigned. We show how the textures are extracted and how these holes are located and filled. Our method has been applied to various real images (pictures scanned from books, photographs) and synthetic images.     

The complexity of understanding line drawings of origami scenes

This paper deals with the interpretation of line drawings of Origami scenes (Kanade, 1980), that is scenes obtained by assembling planar panels of negligible thickness, and it addresses the computational complexity of the problem of consistently assigning suitable labels to the segments describing 3D properties as convexity, concavity and occlusion (labeling problem). The main results of the paper are the following: (a) the labeling problem for line drawings of Origami scenes is NP, as for the case of trihedral scenes; (b) the problem remains NP even if the location of the vanishing points in the image plane is given, whereas for trihedral scenes the problem was polynomially solvable; (c) in case the vanishing points are known the labeling problem can be subdivided into two subproblems, the paneling problem and the labeling-a-paneled-line-drawing problem which are both polynomially solvable (there may be, however, exponentially many legal panelings to check against labelability).The approach provides geometrical constraints which help select natural interpretations even in the presence of occlusions and in the absence of apparent 3D-symmetries, and which may help highlight the role of geometrical regularities in the design of biologically plausible algorithms for the interpretation of line drawings.     

Camera calibration by vanishing lines for 3-D computer vision

A novel approach to camera calibration by vanishing lines is proposed. Calibrated parameters include the orientation, position, and focal length of a camera. A hexagon is used as the calibration target to generate a vanishing line of the ground plane from its projected image. It is shown that the vanishing line includes useful geometric hints about the camera orientation parameters and the focal length, from which the orientation parameters can be solved easily and analytically. And the camera position parameters can be calibrated by the use of related geometric projective relationships. The simplicity of the target eliminates the complexity of the environment setup and simplifies the feature extraction in relevant image processing. The calibration formulas are also simple to compute. Experimental results show the feasibility of the proposed approach     

利用交比不变性的摄像机内参数标定方法

提出一种完全线性的针孔摄像机标定方法。在已知一个消隐点的情况下,利用交比不变性及消隐点的知识对摄像机进行标定。该方法简单易用,不涉及图像的匹配问题,也无须知道任何物理度量,整个定标过程可以自动进行。实验表明,该方法精确度较高,鲁棒性较强,有一定的实用性。