点云数据配准算法研究
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摘要
随着计算机辅助设计技术的发展,通过实物模型产生数字模型的逆向工程技术由于它的独特魅力获得了越来越广泛的应用,与此同时,硬件设备的日趋完善也为数字模型操作提供了足够的技术支持。为了得到被测物体的完整数据模型,需要确定一个合适的坐标变换,将从各个视角得到的点集合并到一个统一的坐标系下,形成一个完整的数据点云,然后就可以方便的进行可视化等操作,这就是点云数据的配准。
点云配准有手动配准、依赖仪器的配准和自动配准。通常我们所说的点云配准技术即是指最后一种。点云自动配准技术是通过一定的算法或者统计学规律,利用计算机计算两片点云之间的错位,从而达到把两片点云自动配准的效果。其实质是把在不同的坐标系中测量得到的数据点云进行坐标变换,以得到整体的数据模型。问题的关键是如何求得坐标变换参数R(旋转矩阵)和T(平移向量),使得两视角下测得的三维数据经坐标变换后的距离最小。
目前,配准算法按照实现过程可以分为整体配准和局部配准,本文分别从速度和收敛性上论证了其优缺点并进行了一系列改进。
本文首先提出了基于迭代算法目标函数的改进,利用点到面的最小距离取代点到点的距离,得到了较好的收敛效果。但缺点是寻找点到面的最近点的过程增加了算法的时间复杂度。
接着,本文提出了一种基于法向特征的快速局部配准算法,通过人机交互的方法得到对应的配准点以后,通过在局部范围寻找精确对应点,将刚体变换矩阵的未知量减少为一个,即单方向绕法向的旋转,算法通过最小化局部最近点求解目标函数,整个算法过程简单快速,配准结果较为精确。
另外,本文提出了一种基于多尺度几何描述子搜索的局部选取配准算法,通过三种几何描述子来衡量点的几何特征,并通过引入多尺度的概念来衡量较大范围的几何特征,有效解决了算法所面临的二义性问题,使得对应点和局部范围的搜索更加精确,保证了配准算法的有效性。
最后,本文提出了一种基于等曲率点的逆向配准算法,首先对每个特征点的曲率利用哈希函数进行量化,然后利用曲率量化值反求三维点,通过对这些等曲率的点进行粗略的配准来完成预配准,然后再进行精确配准。实验表明,该算法比其它预配准更加有效。
由于目前配准算法的固有缺陷,本文所做的改进并未得到一个既精确又快速的算法,只能在速度和精确度上进行折中,事实上,目前对于精确度的要求要远高于配准速度,因此,如何更进一步的提高配准精度,并把配准时间限定在一个可接受的范围内,将是以后研究的重点。
With the development of computer-aided design technology, reverse engineering technology which can construct digital model via physical model is more and more widely used because of its unique charm, at the same time, hardware which is becoming more perfect has provided sufficient technical support for the operation of digital model. In order to complete the data model of the objects, we need to identify a suitable coordinate transformation, after which data points collected from various perspective directions can be measured in a uniform coordinate system and form a complete Point Cloud Data, then the visualization operation is convenient, this is called Point Cloud Data Registration. The related technology has a widely range of applications in reverse engineering, surface quality testing and virtual reality.
Point Cloud Registration includes manual registration, the registration rely on machines and automatic registration. Usually we are talking about refers the last one. The automatic registration technology is achieved through a certain algorithms or statistical regularity, computing the dislocation of two point clouds, so as to achieve an automatic registration result. In essence, it is to make a coordinate transformation between different data point clouds, in order to get the overall data model. The sticking point of the problem is how to confirm the transformation parameters R (rotation matrix) and T (translation vector), so that the distance between each group of 3D data measured in two perspective directions is minimum after transformation.
Registration algorithm can be divided into the overall registration and local registration based on registration process, the advantage and disadvantage are discussed from the speed and convergence, a series of improving is introduced.
First, the objective function based on ICP algorithm are improved, the point-to-point distance is replaced by point-to-surface distance. Thus a good convergence is gained. But the process of finding the nearest point on the surface increases the time complexity of the algorithm.
Then, this paper presents a local registration method based on normal characteristic, improvement of iterative algorithm, local registration based on the normal characteristics, the corresponding registration points are gained through HCI method, then the precise registration points are searched in a local area, thus the unknown parameter is reduced to 1, that is the rotation around the normal direction. The algorithm gains the minimum of the objective function, the entire algorithm is simple and fast, the result is accurate.
In addition, this paper proposes a local-selection registration algorithm based on multi-scale geometry describer, the geometric characteristics is measured through 3 kinds of geometry describer, and the multi-scale conception is introduced to measure the geometric characteristics in a larger area, thus the two-faced problem is solved effectively. The corresponding points and partial scope is more precise, the validity of the registration algorithm is guaranteed.
Finally, this paper proposes a reverse registration algorithm based on curvature, first using hash function to carve up and quantify the curvature of the points, and then using the curvature value to gain the points, the pre-registration is completed using these points, then the accurate registration is put up. Experiments shows that the algorithm is more effective.
Since the inherent defects of registration algorithm, the paper could not make an improvement that is rapid and accurate, compromise between speed and precision is needed, in fact, the requirements for accuracy is far higher than that speed, therefore, how to further improve the accuracy of registration, and make an acceptable time limit, will be the focus of our future study.
点云配准有手动配准、依赖仪器的配准和自动配准。通常我们所说的点云配准技术即是指最后一种。点云自动配准技术是通过一定的算法或者统计学规律,利用计算机计算两片点云之间的错位,从而达到把两片点云自动配准的效果。其实质是把在不同的坐标系中测量得到的数据点云进行坐标变换,以得到整体的数据模型。问题的关键是如何求得坐标变换参数R(旋转矩阵)和T(平移向量),使得两视角下测得的三维数据经坐标变换后的距离最小。
目前,配准算法按照实现过程可以分为整体配准和局部配准,本文分别从速度和收敛性上论证了其优缺点并进行了一系列改进。
本文首先提出了基于迭代算法目标函数的改进,利用点到面的最小距离取代点到点的距离,得到了较好的收敛效果。但缺点是寻找点到面的最近点的过程增加了算法的时间复杂度。
接着,本文提出了一种基于法向特征的快速局部配准算法,通过人机交互的方法得到对应的配准点以后,通过在局部范围寻找精确对应点,将刚体变换矩阵的未知量减少为一个,即单方向绕法向的旋转,算法通过最小化局部最近点求解目标函数,整个算法过程简单快速,配准结果较为精确。
另外,本文提出了一种基于多尺度几何描述子搜索的局部选取配准算法,通过三种几何描述子来衡量点的几何特征,并通过引入多尺度的概念来衡量较大范围的几何特征,有效解决了算法所面临的二义性问题,使得对应点和局部范围的搜索更加精确,保证了配准算法的有效性。
最后,本文提出了一种基于等曲率点的逆向配准算法,首先对每个特征点的曲率利用哈希函数进行量化,然后利用曲率量化值反求三维点,通过对这些等曲率的点进行粗略的配准来完成预配准,然后再进行精确配准。实验表明,该算法比其它预配准更加有效。
由于目前配准算法的固有缺陷,本文所做的改进并未得到一个既精确又快速的算法,只能在速度和精确度上进行折中,事实上,目前对于精确度的要求要远高于配准速度,因此,如何更进一步的提高配准精度,并把配准时间限定在一个可接受的范围内,将是以后研究的重点。
With the development of computer-aided design technology, reverse engineering technology which can construct digital model via physical model is more and more widely used because of its unique charm, at the same time, hardware which is becoming more perfect has provided sufficient technical support for the operation of digital model. In order to complete the data model of the objects, we need to identify a suitable coordinate transformation, after which data points collected from various perspective directions can be measured in a uniform coordinate system and form a complete Point Cloud Data, then the visualization operation is convenient, this is called Point Cloud Data Registration. The related technology has a widely range of applications in reverse engineering, surface quality testing and virtual reality.
Point Cloud Registration includes manual registration, the registration rely on machines and automatic registration. Usually we are talking about refers the last one. The automatic registration technology is achieved through a certain algorithms or statistical regularity, computing the dislocation of two point clouds, so as to achieve an automatic registration result. In essence, it is to make a coordinate transformation between different data point clouds, in order to get the overall data model. The sticking point of the problem is how to confirm the transformation parameters R (rotation matrix) and T (translation vector), so that the distance between each group of 3D data measured in two perspective directions is minimum after transformation.
Registration algorithm can be divided into the overall registration and local registration based on registration process, the advantage and disadvantage are discussed from the speed and convergence, a series of improving is introduced.
First, the objective function based on ICP algorithm are improved, the point-to-point distance is replaced by point-to-surface distance. Thus a good convergence is gained. But the process of finding the nearest point on the surface increases the time complexity of the algorithm.
Then, this paper presents a local registration method based on normal characteristic, improvement of iterative algorithm, local registration based on the normal characteristics, the corresponding registration points are gained through HCI method, then the precise registration points are searched in a local area, thus the unknown parameter is reduced to 1, that is the rotation around the normal direction. The algorithm gains the minimum of the objective function, the entire algorithm is simple and fast, the result is accurate.
In addition, this paper proposes a local-selection registration algorithm based on multi-scale geometry describer, the geometric characteristics is measured through 3 kinds of geometry describer, and the multi-scale conception is introduced to measure the geometric characteristics in a larger area, thus the two-faced problem is solved effectively. The corresponding points and partial scope is more precise, the validity of the registration algorithm is guaranteed.
Finally, this paper proposes a reverse registration algorithm based on curvature, first using hash function to carve up and quantify the curvature of the points, and then using the curvature value to gain the points, the pre-registration is completed using these points, then the accurate registration is put up. Experiments shows that the algorithm is more effective.
Since the inherent defects of registration algorithm, the paper could not make an improvement that is rapid and accurate, compromise between speed and precision is needed, in fact, the requirements for accuracy is far higher than that speed, therefore, how to further improve the accuracy of registration, and make an acceptable time limit, will be the focus of our future study.
引文
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[2]Gregory C,Sang W,and David K,ICP Registration using Invariant Features.IEEE Transactions on Pattern Analysis Machine Intelligence,2002,24(1);90-102.
[3]Liu Y H,Improving ICP with easy implementation for free-form surface matching[j].Pattern Recognition,2004,37(2);211-226.
[4]Chen Y,Medioni G·Object modeling by registration of multiple range images[J].Image and Vision Computing,1992,10(3):145-15.
[5]Z.Y.Zhang.Iterative point matching for registration of free-form curves and surfaces.International Journal of Computer Vision,13(2):119{152,October 1994.
[6]Niloy J.Mitra,Natasha Gelfand,Helmut Pottmann,and Leonidas Guibas,Registration of Point Cloud Data from a Geometric Optimization Perspective,Eurographics Symposium on Geometry Processing(2004).
[7]Chua C S,Jarvis R,Point signatures:a new representation for 3D object recognition[j],International Journal of computer Vision,1997,25(1):63-85.
[8]Yamany S M,Farag A,surface signature:an orientation independent free-form surface representation scheme for the purpose of objects registration and matching[j].IEEE Transactions on Pattern Analysis Machine Intelligence,2002,24(8):1105-1120.
[9]Johnson A,Hebert M.Surface registration by matching oriented points[C],Proceedings of International Conference on Recent,Advances in 3-D Digital Imaging and Modeling,Ottawa,1997:121-12.
[10]Ko K H,Maekawa T,Patrikalakis N M,An algorithm for optimal free-form object matching[j],Computer-Aided Design,2003,35(10):913-923.
[11]Ko K H,Maekawa T,Patrikalakis N M,et al.Shape intrinsic properties for free-form object matching[j],Journal of Computing and information Science in Engineering,2003,3(4):325-333.
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[13]BAREQUET G,SHARIR M Partial surface matching by using directed foot prints[J]Computational Geometry:Theory and Applications,1999,12(1-2):45-62.
[14]熊有伦,精密测量的数学方法[M].北京:中国计量出版社,1989.T.Lyche,K.Morken.The sensitivity of a spline function to perturbations of the knots.BIT,39:305-322.
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[18]张学昌,习俊通,严隽琪.基于点云数据的复杂型面数字化检测技术研究[J].计算机集成制造系统,2005,11(5):727-731.
[19]Evgeny Lomonosov,Dmitry Chetverikov,Pre-registration of arbitrarily oriented 3D surfaces using a genetic algorithm,Computer and Automation Research Institute Budapest,Kende u.13-17,H-1111.
[20]Garg,L.W.Clements,and R.L.Galloway,'A computational approach to pre-align point cloud data for surface registration in image guided liver surgery,Medical Imaging 2007:Visualization and Image-Guided Procedures:Proc.of the SPIE,2007.
[21]N.J.Mitra,S.Flory,M.Ovsjanikov,N.Gelfand,L.Guibas,H.Pottmann,Dynamic Geometry Registration,em＞Proc.Eurographics Symp.Geom.Processing,2007.
[22]P Payeurt,P.Htbertt,D.Laurendeaut,C.M.Gosselid,Probabilistic Octree Modeling of a 3-D Dynamic Environment,Proceedings of the 1997 IEEE International Conference on Robotics and Automation Albuquerque,New Mexico - April 1997.
[23]Kamgar-Parsi B,Kamgar-Parsi B·An open problem in matching sets of 3D lines[C],Proceedings of IEEE Conference Computer Vision and Pattern Recognition,Kauai,Hawaii,2001:651-656.
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[29]余正生,樊丰涛,王毅刚.点到隐式曲线曲面的最小距离.工程图学学报.2005年05期.
[30]张三元,隐式曲线、曲面的几何不变量及几何连续性.计算机学报.Vol.22,No.7,July 1999.
[31]Helmut Pottmann,Johannes Wallner,Qixing Huang,and Yong-Liang Yang,Integral Invariants for Robust Geometry Processing,Geometry Preprint 146,TU Wien,2005.
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[2]Gregory C,Sang W,and David K,ICP Registration using Invariant Features.IEEE Transactions on Pattern Analysis Machine Intelligence,2002,24(1);90-102.
[3]Liu Y H,Improving ICP with easy implementation for free-form surface matching[j].Pattern Recognition,2004,37(2);211-226.
[4]Chen Y,Medioni G·Object modeling by registration of multiple range images[J].Image and Vision Computing,1992,10(3):145-15.
[5]Z.Y.Zhang.Iterative point matching for registration of free-form curves and surfaces.International Journal of Computer Vision,13(2):119{152,October 1994.
[6]Niloy J.Mitra,Natasha Gelfand,Helmut Pottmann,and Leonidas Guibas,Registration of Point Cloud Data from a Geometric Optimization Perspective,Eurographics Symposium on Geometry Processing(2004).
[7]Chua C S,Jarvis R,Point signatures:a new representation for 3D object recognition[j],International Journal of computer Vision,1997,25(1):63-85.
[8]Yamany S M,Farag A,surface signature:an orientation independent free-form surface representation scheme for the purpose of objects registration and matching[j].IEEE Transactions on Pattern Analysis Machine Intelligence,2002,24(8):1105-1120.
[9]Johnson A,Hebert M.Surface registration by matching oriented points[C],Proceedings of International Conference on Recent,Advances in 3-D Digital Imaging and Modeling,Ottawa,1997:121-12.
[10]Ko K H,Maekawa T,Patrikalakis N M,An algorithm for optimal free-form object matching[j],Computer-Aided Design,2003,35(10):913-923.
[11]Ko K H,Maekawa T,Patrikalakis N M,et al.Shape intrinsic properties for free-form object matching[j],Journal of Computing and information Science in Engineering,2003,3(4):325-333.
[12]ALT H,BRASS P,GODAU M,ET AL.Computing the Hausdorff distance of geometric patterns and shapes[J].Discrete and Computational Geometry,Special Issue-The Goodman-Pollack -Festschrift,2003.65-76.
[13]BAREQUET G,SHARIR M Partial surface matching by using directed foot prints[J]Computational Geometry:Theory and Applications,1999,12(1-2):45-62.
[14]熊有伦,精密测量的数学方法[M].北京:中国计量出版社,1989.T.Lyche,K.Morken.The sensitivity of a spline function to perturbations of the knots.BIT,39:305-322.
[15]Rosen holm D,Torelegard K Three- dimensional absolute orientation of stereo models using digital elevation models.Photo-grammetric Engineering and Remote Sensing,1988,54(10):1385-1389.
[16]BlaisG,LevineM D.Registeringmultiview range data to create 3D computer graphics[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1995,17(8):820-824.
[17]Li Q,Griffiths J G.Iterative closest geometric objects registration[J].Computers and Mathematics with Applications,2000,40(10):1171-1188.
[18]张学昌,习俊通,严隽琪.基于点云数据的复杂型面数字化检测技术研究[J].计算机集成制造系统,2005,11(5):727-731.
[19]Evgeny Lomonosov,Dmitry Chetverikov,Pre-registration of arbitrarily oriented 3D surfaces using a genetic algorithm,Computer and Automation Research Institute Budapest,Kende u.13-17,H-1111.
[20]Garg,L.W.Clements,and R.L.Galloway,'A computational approach to pre-align point cloud data for surface registration in image guided liver surgery,Medical Imaging 2007:Visualization and Image-Guided Procedures:Proc.of the SPIE,2007.
[21]N.J.Mitra,S.Flory,M.Ovsjanikov,N.Gelfand,L.Guibas,H.Pottmann,Dynamic Geometry Registration,em＞Proc.Eurographics Symp.Geom.Processing,2007.
[22]P Payeurt,P.Htbertt,D.Laurendeaut,C.M.Gosselid,Probabilistic Octree Modeling of a 3-D Dynamic Environment,Proceedings of the 1997 IEEE International Conference on Robotics and Automation Albuquerque,New Mexico - April 1997.
[23]Kamgar-Parsi B,Kamgar-Parsi B·An open problem in matching sets of 3D lines[C],Proceedings of IEEE Conference Computer Vision and Pattern Recognition,Kauai,Hawaii,2001:651-656.
[24]Berthold K.P.Horn.Closed-form solution of absolute orientation using unit quaternions.Journal of the Optical Society of America A,4(4):629-642,April 1987.
[25]Nash,J.C."The Singular-Value Decomposition and Its Use to Solve Least-Squares Problems." Ch.3 in Compact Numerical Methods for Computers:Linear Algebra and Function Minimisation,2nd ed.Bristol,England:Adam Hilger,pp.30-48,1990.
[26]钟纲.曲线曲面重建方法研究.浙江大学博士学位论文.2002.5.
[27]徐翠薇,孙绳武.计算方法引论(第二版).高等教育出版社.2002.
[28]Lennerz C.Sch6merE.Efficient distance computation for quadratic curves and surfaces[A].In:2nl,Conference on Geometric Modeling and Processing[C].GMP'02,S.60 69.
[29]余正生,樊丰涛,王毅刚.点到隐式曲线曲面的最小距离.工程图学学报.2005年05期.
[30]张三元,隐式曲线、曲面的几何不变量及几何连续性.计算机学报.Vol.22,No.7,July 1999.
[31]Helmut Pottmann,Johannes Wallner,Qixing Huang,and Yong-Liang Yang,Integral Invariants for Robust Geometry Processing,Geometry Preprint 146,TU Wien,2005.
[32]张雄,胡炜,潘小飞,陆明万.加权最小二乘无网格法,力学学报,2003年04期.
[33]Carlos M.Fonseca,Peter J.Fleming,Genetic Algorithms for Multiobjective Optimization:Formulation,Discussion and Generalization(1993).
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