海面透视图像的度量矫正方法

在海洋测绘中,通过图像矫正的方法估算出测量仪器的位置具有非常重要的意义。针对海面目标位置估算中的图像透视矫正问题,提出一种基于平面虚圆点图像的海面图像度量矫正方法。利用不同角度下照片中圆形特征物的图像计算出绝对二次曲线的图像;根据绝对二次曲线以及图像中的海平线辨认海平面虚圆点的图像;通过对与海平面虚圆点对偶的二次曲线的图像进行奇异值分解,获得海平面图像的度量矫正矩阵。在图像实验中,平面上的角度矫正误差小于1.3°,表明这种方法具有较好的矫正精度,能够满足多种海洋测绘作业的要求。     

Self-Calibration of Turntable Sequences from Silhouettes

This paper addresses the problem of recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes of an object in a turntable sequence. Previous silhouette-based approaches have exploited correspondences induced by epipolar tangents to estimate the image invariants under turntable motion and achieved a weak calibration of the cameras. It is known that the fundamental matrix relating any two views in a turntable sequence can be expressed explicitly in terms of the image invariants, the rotation angle, and a fixed scalar. It will be shown that the imaged circular points for the turntable plane can also be formulated in terms of the same image invariants and fixed scalar. This allows the imaged circular points to be recovered directly from the estimated image invariants, and provide constraints for the estimation of the imaged absolute conic. The camera calibration matrix can thus be recovered. A robust method for estimating the fixed scalar from image triplets is introduced, and a method for recovering the rotation angles using the estimated imaged circular points and epipoles is presented. Using the estimated camera intrinsics and extrinsics, a Euclidean reconstruction can be obtained. Experimental results on real data sequences are presented, which demonstrate the high precision achieved by the proposed method.     

一种基于平面模板的摄像机自定标方法

给出仿射坐标系下场景中平面与像平面的单应关系、绝对二次曲线及其图像的表示．通过对场景中一个平面模板获取3幅图像(该模板是由含内切圆的等边三角形构成)，利用上述单应关系并结合圆环点对摄像机内参数的约束，获得一组线性方程，进而确定摄像机的内参数．实验结果表明，所给出的方法切实可行，且具有较高的求解精度．     

基于扩展摄像机成像模型的自标定方法

提出了一种基于扩展摄像机成像模型的自标定方法,将采用不同视点成像的观念转换为不同方向透视投影下分析,得到在一幅图像中同时建立三对不同方向的空间面与图像面的单应关系,进而建立不同面的圆环点绝对二次方程,实现单幅图像标定。采用长方体进行实验,模拟实验和真实图像实验均验证了这种思维方法的可行性和正确性。     

基于单像视觉的平面透视影像度量纠正方法

该文针对基于单幅影像的建筑物三维重建,提出一种对平面的透视影像进行度量纠正的方法。利用建筑物立面上的平行线作为约束条件,计算相应平面的透视影像上的灭点、灭线、投影中心及其他特征点线,以二维直接线性变换表达平面的透视影像与其平行影像间的变换关系,对建筑物立面影像进行纠正,通过纠正生成具有度量特性的平行影像。文章重点阐述了生成平行影像的原理和算法,同时也介绍了获取平行影像的长度比例的方法,并进行了算法的实现和实验,最后根据实验结果进行了误差分析。     

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。     

A Linear Algorithm for Computing the Homography from Conics in Correspondence

This paper presents a study, based on conic correspondences, on the relationship between two perspective images acquired by an uncalibrated camera. We show that for a pair of corresponding conics, the parameters representing the conics satisfy a linear constraint. To be more specific, the parameters that represent a conic in one image are transformed by a five-dimensional projective transformation to the parameters that represent the corresponding conic in another image. We also show that this transformation is expressed as the symmetric component of the tensor product of the transformation based on point/line correspondences and itself. In addition, we present a linear algorithm for uniquely determining the corresponding point-based transformation from a given conic-based transformation up to a scale factor. Accordingly, conic correspondences enable us to easily handle both points and lines in uncalibrated images of a planar object.     

A random sampling strategy for piecewise planar scene segmentation

We investigate the problem of automatically creating 3D models of man-made environments that we represent as collections of textured planes. A typical approach is to automatically reconstruct a sparse 3D model made of points, and to manually indicate their plane membership, as well as the delineation of the planes: this is the piecewise planar segmentation phase. Texture images are then extracted by merging perspectively corrected input images. We propose an automatic approach to the piecewise planar segmentation phase, that detects the number of planes to approximate the scene surface to some extent, and the parameters of these planes, from a sparse 3D model made of points. Our segmentation method is inspired from the robust estimator ransac. It generates and scores plane hypotheses by random sampling of the 3D points. Our plane scoring function and our plane comparison function, required to prevent detecting the same plane twice, are designed to detect planes with large or small support. The plane scoring function recovers the plane delineation and quantifies the saliency of the plane hypothesis based on approximate photoconsistency. We finally refine all the 3D model parameters, i.e., the planes and the points on these planes, as well as camera pose, by minimizing the reprojection error with respect to the measured image points, using bundle adjustment. The approach is validated on simulated and real data.     

Planar rectification by solving the intersection of two circles under 2D homography

In this paper, we show that planar rectification can be achieved by simply solving the intersection of two circles on a plane. The resulting closed form solution gives the images of the ‘circular points’ on the image plane and eliminates the troublesome step of vanishing line detection that presents in many previous solutions to the planar rectification problem. Specifically, we formulate the problem as solving a set of quadratic equations with two variables and propose an efficient algorithm to convert them into a standard real coefficient quartic equation for which a closed form solution is obtained. The experimental results confirm the advantages of the method.     

Geometric rectification of camera-captured document images

Compared to typical scanners, handheld cameras offer convenient, flexible, portable, and non-contact image capture, which enables many new applications and breathes new life into existing ones. However, camera-captured documents may suffer from distortions caused by non-planar document shape and perspective projection, which lead to failure of current OCR technologies. We present a geometric rectification framework for restoring the frontal-flat view of a document from a single camera-captured image. Our approach estimates 3D document shape from texture flow information obtained directly from the image without requiring additional 3D/metric data or prior camera calibration. Our framework provides a unified solution for both planar and curved documents and can be applied in many, especially mobile, camera-based document analysis applications. Experiments show that our method produces results that are significantly more OCR compatible than the original images.     

Detecting image forgeries using metrology

Image forgery technology has become popular for tampering with digital photography. This paper presents a framework for detecting fake regions using single view metrology and enforcing geometric constraints from shadows. In particular, we describe how to (1) estimate the region of interest’s 3D measurements from a single perspective view of a scene given only minimal geometric information determined from the image, (2) determine the fake region by exploring the imaged shadow relations that are modeled by the planar homology. We also show that image forgery on the vertical plane or arbitrary plane can be detected through the measurement on such plane. Our approach efficiently extracts geometric constraints from a single image and makes use of them for the digital forgery detection. Experimental results on both the synthetic data against noise and visually plausible images demonstrate the performance of the proposed method.     

Identical Projective Geometric Properties of Central Catadioptric Line Images and Sphere Images with Applications to Calibration

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. Lines and spheres in space are all projected into conics in the central catadioptric image planes, and such conics are called line images and sphere images, respectively. We discovered that there exists an imaginary conic in the central catadioptric image planes, defined as the modified image of the absolute conic (MIAC), and by utilizing the MIAC, the novel identical projective geometric properties of line images and sphere images may be exploited: Each line image or each sphere image is double-contact with the MIAC, which is an analogy of the discovery in pinhole camera that the image of the absolute conic (IAC) is double-contact with sphere images. Note that the IAC also exists in the central catadioptric image plane, but it does not have the double-contact properties with line images or sphere images. This is the main reason to propose the MIAC. From these geometric properties with the MIAC, two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework. Note that there are many linear approaches to central catadioptric camera calibration using line images. It seems that to use the properties that line images are tangent to the MIAC only leads to an alternative geometric construction for calibration. However, for sphere images, there are only some nonlinear calibration methods in literature. Therefore, to propose linear methods for sphere images may be the main contribution of this paper. Our new algorithms have been tested in extensive experiments with respect to noise sensitivity.     

An Approach to the Vanishing Line Identification Based on Normalized Barycentric Coordinates

The vanishing line is useful information for recovering affine properties of the plane in computer vision. This paper describes how to determine analytically the vanishing line from a single perspective view of a plane containing the four points of known normalized barycentric coordinates in a general position, and further how to compute the vanishing line via the eigenvector representation. We also propose that the projectivity may be expressed directly and analytically from the vanishing line and three 3D–2D point correspondences. It is shown that plane affine properties may be computed and the metric may be recovered from known metric information, which includes an angle, two equal but unknown angles, and a length ratio of two non-parallel line segments, without using the image of the circular points as an intermediate step. The correctness and performance of the novel results are demonstrated by thorough testing on both synthetic and real data.     

Quantitative planar region detection

This paper presents a means of segmenting planar regions from two views of a scene using point correspondences. The initial selection of groups of coplanar points is performed on the basis of conservation of two five point projective invariants (groups for which this invariant is conserved are assumed to be coplanar). The five point correspondences are used to estimate a projectivity which is used to predict the change in position of other points assuming they lie on the same plane as the original four. The variance in any points new position is then used to define a distance threshold between actual and predicted position which is used as a coplanarity test to find extended planar regions. If two distinct planar regions can be found then a novel motion direction estimator suggests itself. The projection of the line of intersection of two planes in an image may also be recovered. An analytical error model is derived which relates image uncertainty in a corner's position to genuine perpendicular height of a point above a given plane in the world. The model may be used for example to predict the performance of given stereo ground plane prediction system or a monocular drivable region detection system on and AGV. The model may also be used in reverse to determine the camera resolution required if a vehicle in motion is to resolve obstacles of a given height a given distance from it.     

1D camera geometry and its application to the self-calibration of circular motion sequences

This paper proposes a novel method for robustly recovering the camera geometry of an uncalibrated image sequence taken under circular motion. Under circular motion, all the camera centers lie on a circle and the mapping from the plane containing this circle to the horizon line observed in the image can be modelled as a 1D projection. A 2x2 homography is introduced in this paper to relate the projections of the camera centers in two 1D views. It is shown that the two imaged circular points of the motion plane and the rotation angle between the two views can be derived directly from such a homography. This way of recovering the imaged circular points and rotation angles is intrinsically a multiple view approach, as all the sequence geometry embedded in the epipoles is exploited in the estimation of the homography for each view pair. This results in a more robust method compared to those computing the rotation angles using adjacent views only. The proposed method has been applied to self-calibrate turntable sequences using either point features or silhouettes, and highly accurate results have been achieved.     

The Absolute Line Quadric and Camera Autocalibration

We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques. This work has been partly supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT) of the Spanish Government.     

平面非规则曲线的一种快速识别与匹配算法

平面非规则曲线的识别与匹配主要用于图像识别、物体匹配等领域。文章在综合研究比较国内外的研究成果后,提出了一种新的快速提取特征进行筛选而后进行细节比对进行匹配的方法。该方法首先通过提取构成平面非规则曲线的一系列离散点的关键特征进行快速筛选,而后逐步比对细节特征,分析其变化趋势,对平面非规则曲线的匹配有着较为满意的匹配效果。该方法相比现有的匹配方法,具有识别与匹配速度快,准确率高,适应性强等优点。     

Quasi-Euclidean epipolar rectification of uncalibrated images

This paper deals with the problem of epipolar rectification in the uncalibrated case. First the calibrated (Euclidean) case is recognized as the ideal one, then we observe that in that case images are transformed with a collineation induced by the plane at infinity, which has a special structure. Hence, that structure is imposed to the sought transformation while minimizing a rectification error. Experiments show that this method yields images that are close to the ones produced by Euclidean rectification.     

Detecting the motion of a planar surface by line and surface integrals

A mathematical formulation is presented for detecting the 3D motion of a planar surface from the motion of its perspective image without knowing correspondence of points. The motion is determined explicitly by numerical computation of certain line or surface integrals on the image. The same principle is also used to know the position and orientation of a planar surface fixed in the space by moving the camera or using several appropriately positioned cameras, and no correspondence of points is involved. Some numerical examples are also given.     

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.