基于未标定图像的三维重建算法

提出一种基于多幅未标定图像的三维重建算法。在标记点匹配的基础上进行射影重建,通过施加度量约束将射影重建升级为欧氏重建,即利用未标定的透视图像恢复相机的内、外部参数以及标记点的三维空间坐标,实现场景的三维重建。标记点易于进行点对精确匹配,较手动拾取匹配提高了效率。实验结果表明,利用该算法能够大幅减小再投影误差。     

一种无需基础矩阵的鲁棒性极线校正算法

立体视觉校正也称为极线校正,它的目的是使得立体图像的对应极线平行于水平方向,消除垂直方向上的视差,从而使得在立体匹配过程中可以更为快速准确地寻找对应点.在传统的投影校正算法的基础上提出了一种鲁棒性校正算法,直接通过原始匹配点计算投影变换矩阵,利用遗传算法良好的全局搜索能力和Levenberg-Marquardt算法稳定快速的局部搜索功能进行分步优化计算,同时本算法采用了随机抽样一致算法（RANSAC）鲁棒估计思想,避免了由于对应点噪声引起的误差.此外,还针对两个平行放置的摄像机之间具有较小运动的情况,提出了一种鲁棒的优化函数.实验结果说明,该算法是一种有效的极线校正方法.     

基于未标定彩色图像三维重建的立体匹配算法

提出了一种用于三维重建的未标定彩色图像立体匹配算法。针对Harris角点的聚簇现象,引入了限制因子来消除,通过采用精度较高的邻域彩色相关法进行匹配。针对相机平移旋转较小的情况,提出了利用抖率一致性剔除明显的误匹配,然后运用随机抽样算法估计基础矩阵,同时进一步剔除误匹配点对,最后用基础矩阵引导未匹配特征点进行匹配。实验表明,该算法用于三维重建,能够较好地恢复物体的结构,是一种有效的匹配算法。     

一种非定标图像高精度三维重建算法

由非定标图像重建三维场景有着广泛的应用。给出了一种非定标多视图像三维重建算法。该算法主要基于因子分解和光束法平差技术。首先用因子分解方法得到射影空间下相机投影矩阵和物点坐标,以旋转矩阵的正交性以及对偶绝对二次曲面秩为3为约束,将射影空间升级到欧式空间,最后用光束法平差进行优化。该方法可同时获得相机的内外参数、畸变系数和场景的三维坐标。仿真实验表明,在1000 mm×1000 mm×400mm的范围内,当像点检测误差在0-1pixel和0-2pixel内,所重建三维点的误差分别为0.1530 mm和0.6712 mm。在500 mm×500 m×200 mm下,真实实验重构三维点的误差在0.3 mm以内。所提出的算法稳定可靠,可对实际工程进行指导。     

基于自适应迭代松弛的立体点对匹配鲁棒算法

图像匹配是立体视觉的重要部分,也是双目立体测量系统必须解决和最难解决的问题。为了对图像进行鲁棒性匹配,提出了一种基于自适应迭代松弛的立体点对匹配方法。该方法首先利用视差梯度约束来构造匹配支持度函数;然后通过松弛方法优化该函数来完成立体点对的匹配。由于利用了动态更新松弛匹配过程参数的方法,因此有效地降低了误匹配率和误剔除率。在此基础上还提出了对松弛过程结束后的匹配结果,再次使用视差梯度约束来进行进一步检验的策略,该策略能够以一定幅度的误剔除率提升为代价,大幅度降低了误匹配率,从而可满足许多要求严格限制误匹配率的应用。实验结果证明,该新算法是有效的,并已经用于一个双目立体测量原型系统当中。     

Stabilizing the Focal Length Computation for 3-D Reconstruction from Two Uncalibrated Views

In order to reconstruct 3-D shape from two uncalibrated views, one needs to resolve two problems: (i) the computed focal lengths can be imaginary; (ii) the computation fails for fixated images. We present a practical remedy for these by subsampling feature points and fixing the focal length. We first summarize theoretical backgrounds and then do simulations, which reveal a rather surprising fact that when the focal length is actually fixed, not using that knowledge yields better results for non-fixated images. We give an explanation to this seeming paradox and derive a hybrid method switching the computation by judging whether or not the images are fixated. Doing simulations and real image experiments, we demonstrate the effectiveness of our method.     

Projective Rectification with Reduced Geometric Distortion for Stereo Vision and Stereoscopic Video

Projective geometry has been proved to be a useful tool for solving the rectification problem without camera calibration. However, if the matrices used for projective rectification (homographies) are not constrained properly, the rectification process can cause great geometric distortion. For visual application, e.g., tele-operation for remotely controlled robot arm, rectification with minimum geometry distortion should be pursued. In this paper, we propose an improved algorithm to minimize the distortion by combining a newly developed projective transform with a properly chosen shearing transform. Experimental data show that our proposed method works quite well for all the image pairs under test. Comparison with other available methods based on visual inspection and numerical data demonstrates the superiority of the new approach.     

基于立体视觉的水下三维测量系统研究

随着我国海洋战略的提出,对于海洋观测技术和装备的需求日趋迫切。针对现有水下成像系统无法实现精确三维测量这一难题,该文提出了一种基于双目立体视觉原理的水下三维测量系统研究方法,并对其可行性进行了验证。针对水下成像过程存在的水体界面折射问题,该文提出了相应的相机成像模型及系统参数标定方法,建立了防水深度达 30 m 的双目水下测量及照明装置,并在水池、近海条件下进行了实地测试。实验结果显示,在水体条件较好的情况下,系统观测距离可达 8 m 以上,有效测量距离为 0.5～4.5 m,在 0.5 m 和 4.5 m 距离处的测量误差分别为 2 mm 和 20 mm。实验验证了 水下双目成像模型、立体标定、测量模型等方法的有效性和精确性,可为水下检修作业等海洋工程行业提供一种有效的三维测量技术手段。     

基础矩阵估计的加权归一化线性算法

基础矩阵是对来自同一景物的两幅未定标图像进行分析的基本工具.对其进行估计的常用线性算法有八点算法和改进的八点算法,其最大的优点是运算简单、易于实现,但对噪声和错误数据较敏感,因此实用性差.通过引入与余差有关的代价函数,给出了一种新的鲁棒性线性算法——加权归一化算法.首先将原始输入数据加权归一化处理,然后再用八点算法求F阵的8个参数,实现了F阵的估计.大量的模拟数据和真实图像的实验结果表明,此算法不仅具有良好的鲁棒性,而且可提高基础矩阵的估计精度.     

Multiple View Geometry of General Algebraic Curves

We introduce a number of new results in the context of multi-view geometry from general algebraic curves. We start with the recovery of camera geometry from matching curves. We first show how one can compute, without any knowledge on the camera, the homography induced by a single planar curve. Then we continue with the derivation of the extended Kruppa's equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve. As part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus.We then establish new results on the reconstruction of general algebraic curves from multiple views. We address three different representations of curves: (i) the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions, one of degree d and the other of degree d(d – 1). Moreover using this representation, we address the problem of homography recovery for planar curves, (ii) dual space representation (tangents) for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus, and (iii) a new representation (to computer vision) based on the set of lines meeting the curve which does not require any curve fitting in image space, for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone.     

视图合成中基础矩阵的鲁棒性估计算法

在未定标系统中，对基础矩阵进行稳定估计是视图合成的关键环节。本文考虑到各匹配点由于误差不同而对基础矩阵造成的不同影响，通过在最优目标函数中引入与余差有关的权重因子提出了一种新的迭代加权线性算法。实验表明，此方法进一步提高了基础矩阵的估计精度，具有较好的稳定性且运算速度快，易于实现。     

一种高精度估计的基础矩阵的线性算法

通过引入与余差有关的代价函数,给出了一种高精度估计基础矩阵的线性算法--加权平移算法.首先将原始输入数据加权,计算加权后数据的重心坐标,将坐标原点平移到该重心坐标,再作归一化处理.然后用8点算法求出基础矩阵F阵的8个参数,实现了F阵的高精度估计.实验结果表明,此算法具有良好的鲁棒性,且余差和对极距离都小于其他线性算法,提高了基础矩阵的精度.     

A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation

In this paper, we present an analytic solution to the problem of estimating an unknown number of 2-D and 3-D motion models from two-view point correspondences or optical flow. The key to our approach is to view the estimation of multiple motion models as the estimation of a single multibody motion model. This is possible thanks to two important algebraic facts. First, we show that all the image measurements, regardless of their associated motion model, can be fit with a single real or complex polynomial. Second, we show that the parameters of the individual motion model associated with an image measurement can be obtained from the derivatives of the polynomial at that measurement. This leads to an algebraic motion segmentation and estimation algorithm that applies to most of the two-view motion models that have been adopted in computer vision. Our experiments show that the proposed algorithm out-performs existing algebraic and factorization-based methods in terms of efficiency and robustness, and provides a good initialization for iterative techniques, such as Expectation Maximization, whose performance strongly depends on good initialization. This paper is an extended version of [34]. The authors thank Sampreet Niyogi for his help with the experimental section of the paper. This work was partially supported by Hopkins WSE startup funds, UIUC ECE startup funds, and by grants NSF CAREER IIS-0347456, NSF CAREER IIS-0447739, NSF CRS-EHS-0509151, NSF-EHS-0509101, NSF CCF-TF-0514955, ONR YIP N00014-05-1-0633 and ONR N00014-05-1-0836. René Vidal received his B.S. degree in Electrical Engineering (highest honors) from the Universidad Católica de Chile in 1997 and his M.S. and Ph.D. degrees in Electrical Engineering and Computer Sciences from the University of California at Berkeley in 2000 and 2003, respectively. In 2004, he joined The Johns Hopkins University as an Assistant Professor in the Department of Biomedical Engineering and the Center for Imaging Science. He has co-authored more than 70 articles in biomedical imaging, computer vision, machine learning, hybrid systems, robotics, and vision-based control. Dr. Vidal is recipient of the 2005 NFS CAREER Award, the 2004 Best Paper Award Honorable Mention at the European Conference on Computer Vision, the 2004 Sakrison Memorial Prize, the 2003 Eli Jury Award, and the 1997 Award of the School of Engineering of the Universidad Católica de Chile to the best graduating student of the school. Yi Ma received his two bachelors' degree in Automation and Applied Mathematics from Tsinghua University, Beijing, China in 1995. He received an M.S. degree in Electrical Engineering and Computer Science (EECS) in 1997, an M.A. degree in Mathematics in 2000, and a PhD degree in EECS in 2000 all from the University of California at Berkeley. Since August 2000, he has been on the faculty of the Electrical and Computer Engineering Department of the University of Illinois at Urbana-Champaign, where he is now an associate professor. In fall 2006, he is a visiting faculty at the Microsoft Research in Asia, Beijing, China. He has written more than 40 technical papers and is the first author of a book, entitled “An Invitation to 3-D Vision: From Images to Geometric Models,” published by Springer in 2003. Yi Ma was the recipient of the David Marr Best Paper Prize at the International Conference on Computer Vision in 1999 and Honorable Mention for the Longuet-Higgins Best Paper Award at the European Conference on Computer Vision in 2004. He received the CAREER Award from the National Science Foundation in 2004 and the Young Investigator Program Award from the Office of Naval Research in 2005.     

一种基于基本矩阵的相机畸变差自动校正方法

在计算机视觉的应用领域中,为了提高图像量测和3维重建的精度,必须对相机的畸变误差进行修正。为此提出了一种基于基本矩阵的相机径向畸变的自动校正方法,该方法不需要预先获得场景的结构信息和相机的内部参数,仅利用两张影像同名点集之间的内在几何关系,即可求取相机的径向畸变系数,进而可对这两幅图像的畸变误差进行自动校正。试验结果表明,该方法是一种有效的畸变图像校正算法,能够获得到满意的校正结果。     

基于镜面成像技术的三维立体视觉测量与重构综述

利用镜面成像技术获取被测物体或场景的三维信息得到研究者越来越多的关注。光线与平面镜或曲面镜交互时产生镜面成像。平面镜的反射属性可以改善视觉效果,基于光路射线展开过程可应用于不同的平面镜成像系统,采用光路展开替代镜面交互应用于三维场景,得到虚拟三维空间,平面镜成像使得复杂的射线交互可以用一种虚拟的方式可视化,且坐标系统的变化容易跟踪。曲面镜成像通常不具有透视投影属性,根据曲面的曲率来改变空间显示。曲面镜常常导致折反射,故针对不同的三维立体视觉测量及重构需设计相应的几何恢复算法。从计算机图形学和计算机视觉的角度,分析了镜面成像的基本原理,对近年来较典型的基于镜面成像技术的三维测量与重构方法及最新研究进展进行综述。     

应用神经网络隐式视觉模型进行立体视觉的三维重建

针对传统的基于精确数学模型的立体视觉方法过程繁琐的不足，提出一种应用BP神经网络隐式视觉模型进行三维重建的算法。该算法将多个标定平面放置在有效视场内，用神经网络模拟立体视觉由两个二维图像重建三维几何的过程，经过网络训练建模后，无须摄像机标定即可进行三维重建。仿真实验结果证明，该算法比较简单，且能保持较高的精度。     

基本矩阵的鲁棒贪心估计算法

分析了基于随机抽样检验思想的现有鲁棒算法在基本矩阵的求解问题中存在的不足,提出一种获得基本矩阵最优解的算法.利用各种鲁棒技术获得内点集,以点到极线的距离作为最优量度标准,采用贪心策略在内点集中寻找最优子集,并利用最优子集来计算基本矩阵.合成数据与真实图像的实验结果表明,该算法在基本矩阵的求解精度、抗噪声能力、对极点的稳定性等方面优于现有的鲁棒方法.     

基于控制点排列组合的立体视觉定标算法

针对传统的DLT算法对控制点检测精度的过度依赖问题,提出了一种基于控制点排列组合的立体视觉定标算法。该算法通过对参与计算DLT参数的控制点进行排列组合,获取经过筛选的稳定的控制点子集合,剔除发生畸变或严重偏离实际数据的控制点,从而具有较好的精度与壮健性。     

基于双目被动立体视觉的三维人脸重构与识别

提出一种基于双目被动视觉的三维人脸识别方法, 该方法采用非接触式的人脸信息采集技术, 利用图像中弱特征检测方法实现双目视觉中的人脸检测与初步视差估计, 运用基于复小波的相位相关技术对人脸表面进行亚像素级小区域匹配, 重建人脸三维点云信息. 通过可调训练次数的神经网络技术实现多层次人脸曲面重建, 并结合人脸2D图像对重构曲面进行仿射归一, 继而迭代地进行特征提取与识别过程. 实验结果表明, 双目视觉方法使人脸信息采集过程友好隐蔽; 在对应点匹配中, 运用复小波的相位相关算法可获得密集的亚像素精度配准点对, 用神经网络方法可正确重建人脸曲面. 识别过程对环境以及人脸位姿表情等鲁棒性强. 该系统成本十分低廉, 适合在许多领域推广应用.     

基于改进Census变换的自由曲面立体匹配方法

针对基于网格投影的自由曲面三维重建方法中,特征点集中分布于投影网格线条之上,而投影网格线条未能覆盖的部分即投影网格线条间的自由曲面区域无特征点,导致重建精度较低的问题,提出一种基于自适应窗口的改进Census变换立体匹配方法,对投影网格线条间的自由曲面进行三维重建;将特征匹配算法与区域匹配算法相结合,以图像中目标物体上的投影网格指导Census变换;利用可变视差范围计算Hamming距离作为匹配代价;通过筛选获得精度较高的匹配点对。实验结果表明,该算法应用于双目视觉图像三维重建,可有效提高投影网格线条间自由曲面的重建精度。