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.     

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.     

基于单幅透视图像确定相机参数的几何方法

提出一种求解相机内、外参数的几何方法．在不考虑相机镜头变形的前提下，首先根据空间平面上的单个矩形，从该矩形的两灭点透视图中，根据灭点间的几何关系，补出另外一个灭点的坐标；然后根据透视投影的灭点理论，计算出相机的相对位置；若已知矩形边的实际长度，可以恢复出相机在三维空间中的实际位置和矩形顶点的空间坐标；最后根据透视投影关系计算出相机的有效焦距．大量的模拟和真实实验表明，该方法简单、易于操作，具有标定精度高、鲁棒性强的优点．     

Camera calibration and light source orientation from solar shadows

In this paper, we describe a method for recovering camera parameters from perspective views of daylight shadows in a scene, given only minimal geometric information determined from the images. This minimal information consists of two 3D stationary points and their cast shadows on the ground plane. We show that this information captured in two views is sufficient to determine the focal length, the aspect ratio, and the principal point of a pinhole camera with fixed intrinsic parameters. In addition, we are also able to compute the orientation of the light source. Our method is based on exploiting novel inter-image constraints on the image of the absolute conic and the physical properties of solar shadows. Compared to the traditional methods that require images of some precisely machined calibration patterns, our method uses cast shadows by the sun, which are common in natural environments, and requires no measurements of any distance or angle in the 3D world. To demonstrate the accuracy of the proposed algorithm and its utility, we present the results on both synthetic and real images, and apply the method to an image-based rendering problem.     

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.     

Creating Architectural Models from Images

We present methods for creating 3D graphical models of scenes from a limited numbers of images, i.e. one or two, in situations where no scene co-ordinate measurements are available. The methods employ constraints available from geometric relationships that are common in architectural scenes – such as parallelism and orthogonality – together with constraints available from the camera. In particular, by using the circular points of a plane simple, linear algorithms are given for computing plane rectification, plane orientation and camera calibration from a single image. Examples of image based 3D modelling are given for both single images and image pairs.     

交互的极线几何建模方法

讨论了一种基于图像的交互式几何建模方法，该方法利用手动方式标定模型的平行线、特征点，得到照相机参数，进而计算出模型的几何信息，并从图像中提取纹理，提出一种最优纹理选取算法，以确保拼接纹理的合理性，该算法主要应用于构造形状规则的模型，不需要知识照相机的内外参数，简便实用，实验结果表明，该方法在一定的场合下可以满足重建要求，重建出的三维模型具有照片真实感，并且能够实时漫游。     

Tour Into the Picture using a Vanishing Line and its Extension to Panoramic Images

Tour into the picture (TIP) proposed by Horry et al. ¹³ is a method for generating a sequence of walk-through images from a single reference picture (or image). By navigating a 3D scene model constructed from the picture, TIP produces convincing 3D effects. Assuming that the picture has one vanishing point, they proposed the scene modeling scheme called spidery mesh. However, this scheme has to go through major modification when the picture contains multiple vanishing points or does not have any well-defined vanishing point. Moreover, the spidery mesh is hard to generalize for other types of images such as panoramic images. In this paper, we propose a new scheme for TIP which is based on a single vanishing line instead of a vanishing point. Based on projective geometry, our scheme is simple and yet general enough to address the problems faced with the previous method. We also show that our scheme can be naturally extended to a panoramic image.     

一种快速的人工场景图像消失点检测方法

人工场景中包含了大量的空间平行线以及垂直边,这些空间平行线映射到图像中相交产生的交点即消失点。消失点检测对摄像机标定、三维场景重建等都有着重要的意义。传统的消失点检测算法往往基于二维霍夫参数空间,复杂度高、效率低。因此,提出一种新的方法,先检测图像中较长的边界线,并将检测到的线段进行筛选、分组;然后利用消失点与焦距之间的制约关系,确定三向消失点的位置以及焦距的大小。该方法将传统的二维霍夫参数空间转换为二级一维霍夫参数空间。实验表明,这种方法运算复杂度低、运行时间短。在室外场景图像中,鲁棒性好,且保持较高的准确率。     

Computing camera parameters using vanishing-line information from a rectangular parallelepiped

A new approach to camera calibration using vanishing line information for three-dimensional computer vision is proposed. Calibrated parameters include the orientation, the position, the focal length, and the image plane center of a camera. A rectangular parallelepiped is employed as the calibration target to generate three principal vanishing points and then three vanishing lines from the projected image of the parallelepiped. Only a monocular image is required for solving these camera parameters. It is shown that the image plane center is the orthocenter of a triangle formed by the three vanishing lines. From the slopes of the vanishing lines the camera orientation parameters can be determined. The focal length can be computed by the area of the triangle. The camera position parameters can then be calibrated by using related geometric projective relationships. The derived results show the geometric meanings of these camera parameters. The calibration formulas are analytic and simple to compute. Experimental results show the feasibility of the proposed approach for a practical application—autonomous land vehicle guidance.This work was supported by National Science Council, Republic of China under Grant NSC-77-0404-E-009-31.