三维重构中关键算法研究
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摘要
计算机视觉的研究目标是从二维图像获取三维景物的结构信息,其过程是一个复杂的逆问题,需要借助各种优化技术和射影几何理论来解决,而且对噪声或离散化引起的误差极其敏感。图像匹配和摄像机标定是实现三维重构的基础,但二者的求解是病态问题,所以对其研究具有一定的理论意义和实用价值。本文认为,改进算法的着眼点应该是优化方法的寻求和约束条件的确定。在上述思路指导下,本文给出了基于图谱理论基础上的图像特征匹配、基于图割优化算法下的图像密集匹配、基于射影几何理论的摄像机自标定等算法。
本论文针对三维场景重构中关键步骤:图像匹配和摄像机标定展开研究,给出了如下匹配和标定算法:
1.基于图的Laplace谱的特征点匹配算法。根据两幅图像的特征点分别定义其Laplace矩阵,分析该矩阵的特征值及特征向量,构造特征点匹配矩阵。根据匹配矩阵元素的大小和位置信息,实现特征点匹配。并从理论上证明本算法在对图像作等距变换或相似变换下能获得精确匹配。真实实验表明该算法匹配精度可以达到80%以上。
2.基于图割优化的图像密集匹配算法。通过建立能量函数,把匹配问题转化为能量函数最小化问题;并构造网络,建立能量与网络割的容量之间的联系;最后利用图的网络流理论给出能量最小化解,从而获得图像匹配的视差数据。与目前已有的基于图割匹配算法比较,本算法将标号从1维向量推广到2维向量,适用于更一般情形下的视觉匹配,并且在全局上获得能量函数最小。真实实验表明该算法可以达到75%以上的准确率。
3.基于埸景平面结构信息的摄像机自标定算法。给出了场景中的平面与像平面的单应关系、绝对二次曲线及其图像,以及虚圆点对摄像机内参数的约束等显式形式。应用上述形式,给出了基于矩形、梯形和等边三角形等三种不同场景平面结构信息的摄像机自标定方法。实验结果表明,所给出的方法都具有
The object of computer vision is to make the computer have the ability of understanding 3D environmental information from 2D images, which is a complicated inverse problem since it recurs to the combinatorial optimization techniques and projective geometry theory and is very sensitive to errors caused by noises and discretization. Image matching and camera calibration are the foundations for realizing 3D reconstruction, which are both abnormal on problems solving. Hence research on image matching and camera calibration has both theoretical significance and practical values. We think that the focus of improving the above two kinds of algorithms should be searching optimization methods and determining the constraint conditions. Under above idea, the thesis presents algorithms of feature matching of images based on spectral graph theory, dense matching of images based on graph cut optimization, and camera calibration based on projective geometry theory.The thesis focuses on the key algorithms of 3D reconstruction: image matching and camera calibration, and acquires the main achievements as follows:1. The algorithm of feature points matching based on Laplacian spectral theorey. Given feature points of two images, we define Laplacian matrices respectively, analysis the eigenvalues and eigenvectors of the matrices, and construct a feature points matching matrix. By information of magnitude and position of entries in the matching matrix, we realize the feature points matching. Furthermore, we theoretically prove that our algorithm can acquire an exact matching under an equilong transformation or equiform transformation on images. Real experiments show that the matching rate may attain 80% upwards.2. The algorithm of dense matching of images based on graph cuts optimization. Firstly, the energy function is established and the problem of matching can be transformed into that of energy function minimization. A network is constructed such that the energies can be related to the capacities of the cuts of the network. Finally,
the minimization of the energy function is obtained by the theory of network-flows, and hence the disparity data are obtained. Comparing with some known algorithms based on graph cuts, the algorithm in this paper extends the label from ID vector to ID vector, and adapts visual matching of more general cases; furthermore the algorithm can obtain the minimization in global. Real experiments show that the matching rate can achieve 75% upwards.3. The algorithm of camera self-calibration based on planar structural information of scenes. We give explicit forms of the homography between a plane in the scene and that of an image, the absolute conic and its images, and the constraints of circular points to the camera intrinsic parameters. Applying above forms, we give methods of camera self-calibration based on three kinds of planar structural information of scene which are rectangles, isosceles trapezoids, equilateral triangles. Experimental results show that all methods have high accuracy.4. The algorithm of camera self-calibration with moving ID objects using a bi-cameras setting. First, we give the images of circular points in the plane which the ID object translates on, and the constraints of them to the camera intrinsic parameters, and also give a numerical solving method of the constraints equations (and hence obtain the camera intrinsic parameters). By recovering the coordinates of 3D points under camera coordinates system, we can resolve the poses between two cameras (i.e. the camera external parameters). For a general rigid motion of ID objects, we give a method which transforms it into translations. Experimental results of both simulated data and real-world data show that this method has a high accuracy and practical values.
本论文针对三维场景重构中关键步骤:图像匹配和摄像机标定展开研究,给出了如下匹配和标定算法:
1.基于图的Laplace谱的特征点匹配算法。根据两幅图像的特征点分别定义其Laplace矩阵,分析该矩阵的特征值及特征向量,构造特征点匹配矩阵。根据匹配矩阵元素的大小和位置信息,实现特征点匹配。并从理论上证明本算法在对图像作等距变换或相似变换下能获得精确匹配。真实实验表明该算法匹配精度可以达到80%以上。
2.基于图割优化的图像密集匹配算法。通过建立能量函数,把匹配问题转化为能量函数最小化问题;并构造网络,建立能量与网络割的容量之间的联系;最后利用图的网络流理论给出能量最小化解,从而获得图像匹配的视差数据。与目前已有的基于图割匹配算法比较,本算法将标号从1维向量推广到2维向量,适用于更一般情形下的视觉匹配,并且在全局上获得能量函数最小。真实实验表明该算法可以达到75%以上的准确率。
3.基于埸景平面结构信息的摄像机自标定算法。给出了场景中的平面与像平面的单应关系、绝对二次曲线及其图像,以及虚圆点对摄像机内参数的约束等显式形式。应用上述形式,给出了基于矩形、梯形和等边三角形等三种不同场景平面结构信息的摄像机自标定方法。实验结果表明,所给出的方法都具有
The object of computer vision is to make the computer have the ability of understanding 3D environmental information from 2D images, which is a complicated inverse problem since it recurs to the combinatorial optimization techniques and projective geometry theory and is very sensitive to errors caused by noises and discretization. Image matching and camera calibration are the foundations for realizing 3D reconstruction, which are both abnormal on problems solving. Hence research on image matching and camera calibration has both theoretical significance and practical values. We think that the focus of improving the above two kinds of algorithms should be searching optimization methods and determining the constraint conditions. Under above idea, the thesis presents algorithms of feature matching of images based on spectral graph theory, dense matching of images based on graph cut optimization, and camera calibration based on projective geometry theory.The thesis focuses on the key algorithms of 3D reconstruction: image matching and camera calibration, and acquires the main achievements as follows:1. The algorithm of feature points matching based on Laplacian spectral theorey. Given feature points of two images, we define Laplacian matrices respectively, analysis the eigenvalues and eigenvectors of the matrices, and construct a feature points matching matrix. By information of magnitude and position of entries in the matching matrix, we realize the feature points matching. Furthermore, we theoretically prove that our algorithm can acquire an exact matching under an equilong transformation or equiform transformation on images. Real experiments show that the matching rate may attain 80% upwards.2. The algorithm of dense matching of images based on graph cuts optimization. Firstly, the energy function is established and the problem of matching can be transformed into that of energy function minimization. A network is constructed such that the energies can be related to the capacities of the cuts of the network. Finally,
the minimization of the energy function is obtained by the theory of network-flows, and hence the disparity data are obtained. Comparing with some known algorithms based on graph cuts, the algorithm in this paper extends the label from ID vector to ID vector, and adapts visual matching of more general cases; furthermore the algorithm can obtain the minimization in global. Real experiments show that the matching rate can achieve 75% upwards.3. The algorithm of camera self-calibration based on planar structural information of scenes. We give explicit forms of the homography between a plane in the scene and that of an image, the absolute conic and its images, and the constraints of circular points to the camera intrinsic parameters. Applying above forms, we give methods of camera self-calibration based on three kinds of planar structural information of scene which are rectangles, isosceles trapezoids, equilateral triangles. Experimental results show that all methods have high accuracy.4. The algorithm of camera self-calibration with moving ID objects using a bi-cameras setting. First, we give the images of circular points in the plane which the ID object translates on, and the constraints of them to the camera intrinsic parameters, and also give a numerical solving method of the constraints equations (and hence obtain the camera intrinsic parameters). By recovering the coordinates of 3D points under camera coordinates system, we can resolve the poses between two cameras (i.e. the camera external parameters). For a general rigid motion of ID objects, we give a method which transforms it into translations. Experimental results of both simulated data and real-world data show that this method has a high accuracy and practical values.
引文
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