面向光栅投影的点云预处理与曲面重构技术研究
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摘要
面向光栅投影的点云预处理与曲面重构是以光栅扫描作为测量手段,以实物、样件等作为研究对象,对三维数据采集、点云数据预处理、曲面重构、快速制造等内容进行研究。该研究是实现产品快速开发和制造的重要技术之一,在汽车、摩托车、飞机、家电、模具、工艺品、服装与医学领域的原型与创新设计方面具有广阔的应用前景。
研究了光栅投影位相测量的相关理论。分析了光栅投影三维测量的相位调制原理,建立了物体高度与光栅相位之间的对应关系。比较了一维傅里叶变换和二维傅里叶变换相位解调效果,结果表明二维傅里叶变换能更精确反映物体表面任何方向上的变化。分析了相移法相位解调的原理,采用四步相移法求解光栅相位,并建立了变形光栅相位的求解公式。研究了包裹相位产生的原因以及对三维面型测量的影响,采用最小差分算法进行相位去包裹处理,实现了真实相值相位连续。
研究了点云数据预处理中的点云配准与精简技术。在点云手动拼接中,提出了继承与优化算法,经过迭代25次可获取配准所需的旋转矩阵和平移向量,实现了无序点云拼接,拼接误差为0.10mm,相比最邻近点迭代算法,具有拼接偏差小和迭代次数少等优点。在点云数据自动拼接中,通过Gauss-Markoff模型减小曲面间的欧氏距离平方和,采用最小二乘原理对重叠区域进行匹配,实现了无需标志点的点云自动拼接。在点云精简技术中,根据物体形貌及点云曲率采用不同的网格尺寸,并通过中值滤波删减冗余点云数据,既能继承均匀网格法速度快且有效的优点,又能保留物体细节信息。
研究了无序点云三角剖分、四边域剖分和NURBS曲面重建。采用基于法矢量夹角最小原则的三角形生长法对空间离散点直接剖分,它首先根据阈值范围规定扩展边的点集,然后寻找构成三角形逆时针排列的第三点,最后用局部优化准则三角网格进行优化。根据三角形质量计算四边形变形因子进行最大权匹配,实现了四边域的划分。通过对物体三维点云进行三角剖分、曲率检测、构造轮廓线、四边域剖分、建立UV参数线和曲面拟合,最终生成NURBS曲面。
研究了曲面-点云误差和曲面光顺特性及其影响因素,提出了提高曲面品质的方法。控制点数目影响最终的曲面重构精度,对于百万点云数量,100个四边域剖分区域,选用60-80个控制点进行曲面拟合比较适宜。分析了曲面阶次、节点数和光顺系数对曲面-点云误差的影响,对于6082个点云数据,采用曲面阶次为4×4,节点数为5×5,光顺系数为0.7000进行拟合时,曲面-点云最大偏差仅为0.0408mm。在满足曲面-点云误差情况下,采用减少冗余控制点以及动态调整控制点空间位置的方法提高曲面光顺性。
研究了人体面部三维数据检测、曲面重建和快速成形加工。通过双光栅三维扫描仪将正弦光栅投射到人体面部,将被面部调制的变形光栅转换成两片分立点云。点云经自动拼接处理后,采用三角剖分和曲面拟合生成三角面片。通过消除孔洞边界杂乱三角形,并对面部孔洞进行填充、消差和平滑处理获得光滑封闭面片。经过四边形网格剖分和曲面拟合等处理,生成面部NURBS曲面。最终将逆向过程生成的STL文件导入到快速成形设备加工人体面部曲面,实现逆向工程整个流程。
Point clouds preprocessing and surface reconstruction with fringe projection take fringe scanning as measuring ways, entities, samples as research objects. The main content of the research includes 3D data detecting, point clouds preprocessing, surface reconstruction and rapid manufacture. It is one of the most important techniques to realize rapid products development and manufacture. It is of wide application prospect in remodeling and creation design of automobiles, motors, airplanes, home appliances, molds, crafts, clothing, medical fields and so on.
The relevant theories of phase measurement with fringe projection are studied. Phase demodulation principle of fringe projection measurement is explained, and the relation between object height and fringe phase is obtained. The phase demodulation effect of 1D FTP and 2D FTP methods is compared, and it shows that 2D FTP can precisely reflect the change along arbitrary directions. Phase demodulation principle with phase shifting profilometry is thoroughly analyzed, and phase solving method adopting 4-step phase shifting method is explained. Solving formula of deformation fringe is established. Wrapping phase and its effect on 3D surface measurement is analyzed, and minimum differential algorithm is adopted to implement phase unwrapping to realize real phase continuity.
The registration and simplification of point clouds are studied in the paper. In the manual registration of the point clouds, inheriting and optimizing algorithm is proposed to realize precise point clouds registration. Rotating matrix and translation vector can be obtained after 25 iterations, while the registration error is 0.10mm. Compared to ICP algorithm, it has advantages of higher registration precision and less iteration times. In the automatic registration of point clouds, the sum of squares of Euclidean distance between surfaces is reduced by Gauss-Markoff model, and overlapping area is matched by the least squares algorithm to realize automatic point clouds registration without mark points. In the simplification of point clouds, various mesh sizes are chosen corresponding to object profile and point clouds curvature, and point clouds simplification is implemented by medium value filtering method to reduce redundant points. Not only can it inherit quick and effective merits of uniform mesh method, but also it can retain detail data of the object shape.
Triangle division, quadrilateral division and NURBS reconstruction are studied in the paper. Triangle growth method based on LABN (least angle between normal) is adopted to implement the direct division of the scattered point clouds. Firstly, a threshold range is given to define points set of the extension side. Then the third point by counterclockwise triangle alignment is found out. Finally triangle meshes are optimized by the local optimization rules. Quadrilateral deformation factor is calculated out according to the quality of triangles to implement maximum weigh matching. Two adjacent triangles are merged to implement quadrilateral division. NURBS surface is obtained through triangle division, curvature detecting, contour lines construction, quadrilateral division, UV parameter lines construction and surface fitting.
Surface-point clouds error, surface smoothness and their influence factors are studied, and the methods to improve surface quality are proposed. The number of control points has great effect on reconstruction precision. For the point clouds including about 1 million points, if the number of quadrilateral meshes is 100, it is suitable to choose 60 to 80 control points. The effect of surface order, span and smoothness on the error of surface-point clouds is analyzed. If the point clouds include 6082 points, when the surface order is 4×4, span is 5×5, smoothness is 0.7000, the maximum error of surface-point clouds is 0.0408mm. If the surface-point clouds error meets the requirement, the smoothness property of the surface can be improved by reducing redundant control points and adjusting the position of the control points.
3D data detecting, surface reconstruction and rapid prototyping manufacture of the face are studied. Firstly, sinusoidal fringe is projected to the face by double fringe scanner, and fringe image is modulated by the face profile. Two separate point clouds of the face are obtained by the conversion of the deformation fringe. After the automatic registration of the point clouds, triangle surface of the face is obtained by triangle division and surface fitting. Irregular triangles around holes boundary of the face are eliminated, and holes are filled, relaxed and smoothed to form closed and smooth surface. Finally NURBS face surface reconstruction is implemented by quadrilateral meshes division and surface fitting. STL file obtained from reverse process is input to rapid prototyping equipment to implement the manufacturing of the face model to realize the entire procedure of reverse engineering.
研究了光栅投影位相测量的相关理论。分析了光栅投影三维测量的相位调制原理,建立了物体高度与光栅相位之间的对应关系。比较了一维傅里叶变换和二维傅里叶变换相位解调效果,结果表明二维傅里叶变换能更精确反映物体表面任何方向上的变化。分析了相移法相位解调的原理,采用四步相移法求解光栅相位,并建立了变形光栅相位的求解公式。研究了包裹相位产生的原因以及对三维面型测量的影响,采用最小差分算法进行相位去包裹处理,实现了真实相值相位连续。
研究了点云数据预处理中的点云配准与精简技术。在点云手动拼接中,提出了继承与优化算法,经过迭代25次可获取配准所需的旋转矩阵和平移向量,实现了无序点云拼接,拼接误差为0.10mm,相比最邻近点迭代算法,具有拼接偏差小和迭代次数少等优点。在点云数据自动拼接中,通过Gauss-Markoff模型减小曲面间的欧氏距离平方和,采用最小二乘原理对重叠区域进行匹配,实现了无需标志点的点云自动拼接。在点云精简技术中,根据物体形貌及点云曲率采用不同的网格尺寸,并通过中值滤波删减冗余点云数据,既能继承均匀网格法速度快且有效的优点,又能保留物体细节信息。
研究了无序点云三角剖分、四边域剖分和NURBS曲面重建。采用基于法矢量夹角最小原则的三角形生长法对空间离散点直接剖分,它首先根据阈值范围规定扩展边的点集,然后寻找构成三角形逆时针排列的第三点,最后用局部优化准则三角网格进行优化。根据三角形质量计算四边形变形因子进行最大权匹配,实现了四边域的划分。通过对物体三维点云进行三角剖分、曲率检测、构造轮廓线、四边域剖分、建立UV参数线和曲面拟合,最终生成NURBS曲面。
研究了曲面-点云误差和曲面光顺特性及其影响因素,提出了提高曲面品质的方法。控制点数目影响最终的曲面重构精度,对于百万点云数量,100个四边域剖分区域,选用60-80个控制点进行曲面拟合比较适宜。分析了曲面阶次、节点数和光顺系数对曲面-点云误差的影响,对于6082个点云数据,采用曲面阶次为4×4,节点数为5×5,光顺系数为0.7000进行拟合时,曲面-点云最大偏差仅为0.0408mm。在满足曲面-点云误差情况下,采用减少冗余控制点以及动态调整控制点空间位置的方法提高曲面光顺性。
研究了人体面部三维数据检测、曲面重建和快速成形加工。通过双光栅三维扫描仪将正弦光栅投射到人体面部,将被面部调制的变形光栅转换成两片分立点云。点云经自动拼接处理后,采用三角剖分和曲面拟合生成三角面片。通过消除孔洞边界杂乱三角形,并对面部孔洞进行填充、消差和平滑处理获得光滑封闭面片。经过四边形网格剖分和曲面拟合等处理,生成面部NURBS曲面。最终将逆向过程生成的STL文件导入到快速成形设备加工人体面部曲面,实现逆向工程整个流程。
Point clouds preprocessing and surface reconstruction with fringe projection take fringe scanning as measuring ways, entities, samples as research objects. The main content of the research includes 3D data detecting, point clouds preprocessing, surface reconstruction and rapid manufacture. It is one of the most important techniques to realize rapid products development and manufacture. It is of wide application prospect in remodeling and creation design of automobiles, motors, airplanes, home appliances, molds, crafts, clothing, medical fields and so on.
The relevant theories of phase measurement with fringe projection are studied. Phase demodulation principle of fringe projection measurement is explained, and the relation between object height and fringe phase is obtained. The phase demodulation effect of 1D FTP and 2D FTP methods is compared, and it shows that 2D FTP can precisely reflect the change along arbitrary directions. Phase demodulation principle with phase shifting profilometry is thoroughly analyzed, and phase solving method adopting 4-step phase shifting method is explained. Solving formula of deformation fringe is established. Wrapping phase and its effect on 3D surface measurement is analyzed, and minimum differential algorithm is adopted to implement phase unwrapping to realize real phase continuity.
The registration and simplification of point clouds are studied in the paper. In the manual registration of the point clouds, inheriting and optimizing algorithm is proposed to realize precise point clouds registration. Rotating matrix and translation vector can be obtained after 25 iterations, while the registration error is 0.10mm. Compared to ICP algorithm, it has advantages of higher registration precision and less iteration times. In the automatic registration of point clouds, the sum of squares of Euclidean distance between surfaces is reduced by Gauss-Markoff model, and overlapping area is matched by the least squares algorithm to realize automatic point clouds registration without mark points. In the simplification of point clouds, various mesh sizes are chosen corresponding to object profile and point clouds curvature, and point clouds simplification is implemented by medium value filtering method to reduce redundant points. Not only can it inherit quick and effective merits of uniform mesh method, but also it can retain detail data of the object shape.
Triangle division, quadrilateral division and NURBS reconstruction are studied in the paper. Triangle growth method based on LABN (least angle between normal) is adopted to implement the direct division of the scattered point clouds. Firstly, a threshold range is given to define points set of the extension side. Then the third point by counterclockwise triangle alignment is found out. Finally triangle meshes are optimized by the local optimization rules. Quadrilateral deformation factor is calculated out according to the quality of triangles to implement maximum weigh matching. Two adjacent triangles are merged to implement quadrilateral division. NURBS surface is obtained through triangle division, curvature detecting, contour lines construction, quadrilateral division, UV parameter lines construction and surface fitting.
Surface-point clouds error, surface smoothness and their influence factors are studied, and the methods to improve surface quality are proposed. The number of control points has great effect on reconstruction precision. For the point clouds including about 1 million points, if the number of quadrilateral meshes is 100, it is suitable to choose 60 to 80 control points. The effect of surface order, span and smoothness on the error of surface-point clouds is analyzed. If the point clouds include 6082 points, when the surface order is 4×4, span is 5×5, smoothness is 0.7000, the maximum error of surface-point clouds is 0.0408mm. If the surface-point clouds error meets the requirement, the smoothness property of the surface can be improved by reducing redundant control points and adjusting the position of the control points.
3D data detecting, surface reconstruction and rapid prototyping manufacture of the face are studied. Firstly, sinusoidal fringe is projected to the face by double fringe scanner, and fringe image is modulated by the face profile. Two separate point clouds of the face are obtained by the conversion of the deformation fringe. After the automatic registration of the point clouds, triangle surface of the face is obtained by triangle division and surface fitting. Irregular triangles around holes boundary of the face are eliminated, and holes are filled, relaxed and smoothed to form closed and smooth surface. Finally NURBS face surface reconstruction is implemented by quadrilateral meshes division and surface fitting. STL file obtained from reverse process is input to rapid prototyping equipment to implement the manufacturing of the face model to realize the entire procedure of reverse engineering.
引文
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