有界泊松曲面约束的曲面样点法向稳健估计
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摘要
对存在噪声、非均匀采样等缺陷的曲面样本,基于样点及其邻近样点构成的局部样本通常无法稳健逼近曲面局部区域,导致样点法向难以准确估计。为抑制样本缺陷对样点法向估计的影响,提出一种以有界泊松曲面逼近局部样本作为约束的样点法向加权估计算法。对待估计法向的样点,该算法对其所属曲面局部样本作增益优化处理,使得曲面局部样本具备边界保护区域;在样点的Frenet标架中以泊松曲面逼近该样本,基于样本的边界保护区域将泊松曲面的离散网格转化为有界形式,从而建立样点邻域的曲面约束,以有界泊松曲面离散网格中距样点最近的网格面片作为样点的参考面片,基于顶点邻域面的正则度及邻域面到该顶点的测地距离估计参考面片顶点法向,将参考面片各顶点法向的加权求和结果作为样点法向的估计结果。实验结果表明:曲面样本噪声水平不高于20%时,可将法向计算误差控制在π/18以内,且所得法向过渡较为光滑。证明了该算法适用于复杂曲面样本,可稳健处理存在噪声以及采样不均匀等缺陷的曲面样本的样点法向估计问题,实现曲面样点法向的光滑过渡。
For each point of the surface obtained from organized point cloud,the normal can be estimated by fitting a local surface approximation to the surface local sample.However,for a surface sample with defects,it is difficult to robustly approximate the local area.Therefore,it is difficult to accurately estimate the normal of the sample points.To suppress the influence of sample defects on the normal estimation of sample points,a weighted normal estimation algorithm was presented for sample points,which uses the bounded Poisson surface as a constraint of the surface local sample.For the sample point whose normal needs to be estimated,this algorithm optimized the surface local sample by obtaining more auxiliary points,which form the surface local sample with the boundary protection area.The Poisson surface was used to approximate this local sample in the Frenet frame of the sample point,and the discrete meshes of the Poisson surface were transformed into the bounded form based on the boundary protection area of this local sample.Then,the surface constraint of the neighborhood of the sample point was built.In the discrete meshes of the bounded Poisson surface,the nearest triangular facet of the sample point was used as the reference facet of the sample point.The vertex normal of the reference facet was estimated based on the vertex neighbor facet regularity and the geodesic distance from the neighbor facet to the vertex,and the weighted summation of the vertex normals of the reference facet was used as the estimation result of the sample point's normal.The experimental results show that the deviation of normal calculation can be controlled within when the noise level of the surface sample is not higher than 20%and the normal transition is smooth.The proposed algorithm is suitable for complex surface samples and can robustly deal with the problem of normal estimation of surface samples with noise and non-uniform sampling.In addition,the transition of the obtained normals is smooth.
For each point of the surface obtained from organized point cloud,the normal can be estimated by fitting a local surface approximation to the surface local sample.However,for a surface sample with defects,it is difficult to robustly approximate the local area.Therefore,it is difficult to accurately estimate the normal of the sample points.To suppress the influence of sample defects on the normal estimation of sample points,a weighted normal estimation algorithm was presented for sample points,which uses the bounded Poisson surface as a constraint of the surface local sample.For the sample point whose normal needs to be estimated,this algorithm optimized the surface local sample by obtaining more auxiliary points,which form the surface local sample with the boundary protection area.The Poisson surface was used to approximate this local sample in the Frenet frame of the sample point,and the discrete meshes of the Poisson surface were transformed into the bounded form based on the boundary protection area of this local sample.Then,the surface constraint of the neighborhood of the sample point was built.In the discrete meshes of the bounded Poisson surface,the nearest triangular facet of the sample point was used as the reference facet of the sample point.The vertex normal of the reference facet was estimated based on the vertex neighbor facet regularity and the geodesic distance from the neighbor facet to the vertex,and the weighted summation of the vertex normals of the reference facet was used as the estimation result of the sample point's normal.The experimental results show that the deviation of normal calculation can be controlled within when the noise level of the surface sample is not higher than 20%and the normal transition is smooth.The proposed algorithm is suitable for complex surface samples and can robustly deal with the problem of normal estimation of surface samples with noise and non-uniform sampling.In addition,the transition of the obtained normals is smooth.
引文
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[18]高健,陈岳坪,邓海祥,等.复杂曲面零件加工精度的原位检测误差补偿方法[J].机械工程学报,2013,49(19):133-143.GAO J,CHEN Y P,DENG H X,et al..Insitu inspection error compensation for machining accuracy improvement of complex components[J].Journal of Mechanical Engineering,2013,49(19):133-143.(in Chinese)
[19]段黎明,邵辉,李中明,等.高效率的三角网格模型保特征简化方法[J].光学精密工程,2017,25(2):460-468.DUAN L M,SHAO H,LI ZH M,et al..Simplification method for feature preserving of efficient triangular mesh mode[J].Opt.Precision Eng.,2017,25(2):460-468.(in Chinese)
[20]BROUMI S,BAKAL A,TALEA M,et al..Applying Dijkstra algorithm for solving neutrosophic shortest path problem[C].International Conference on Advanced Mechatronic Systems.IEEE,2017:412-416.
[21]孙殿柱,刘华东,史阳,等.基于核密度估计的散乱点云边界特征提取[J].农业机械学报,2013,44(12):275-279.SUN D ZH,LIU H D,SHI Y,et al..Boundary feature abstraction of unorganized points based on kernel density estimation[J].Transactions of the Chinese Society for Agricultural Machinery,2013,44(12):275-279.(in Chinese)
[22]张应中,谢馥香,罗晓芳,等.采用半边编码的三角网格拓扑数据结构[J].计算机辅助设计与图形学学报,2016,28(2):328-334.ZHANG Y ZH,XIE F X,LUO X F,et al..A topological data structure using coding of half-edges for triangle meshes[J].Journal of Compuer-Aided Design&Computer Graphics,2016,28(2):328-334.(in Chinese)
[2]吴禄慎,史皓良,陈华伟.基于特征信息分类的三维点数据去噪[J].光学精密工程,2016,24(6):1465-1473.WU L SH,SHI H L,CHEN H W.Denoising of three-dimensional point data based on classification of feature information[J].Opt.Precision Eng.,2016,24(6):1465-1473.(in Chinese)
[3]孙殿柱,郭洪帅,李延瑞,等.基于局部泊松曲面重建的点云刚性配准方法[J].机械工程学报,2018,54(15):141-149.SUN D ZH,GUO H SH,LI Y R,et al..Method of rigid registration based on Poisson reconstruction of local sample points[J].Journal of Mechanical Engineering,2018,54(15):141-149.(in Chinese)
[4]HOOPE H,DEROSE T,DUCHAMP T,et al..Surface reconstruction from unorganized points[C].Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques.New York,ACM Press,1992:71-78.
[5]KAZHDAN M,HOPPE H.Screened Poisson surface reconstruction[J].ACM Transactions on Graphics,2013,32(3):1-13.
[6]MITRA N J,NGUYEN A,GUIBAS L.Estimating surface normals in noisy point cloud data[J].International Journal of Computational Geometry&Applications,2004,14(45):261-276.
[7]YOON M,LEE Y,LEE S,et al..Surface and normal ensembles for surface reconstruction[J].Computer-Aided Design,2007,39(5):408-420.
[8]王兆丰,闫镔,童莉,等.自适应邻域尺寸选择的点云法向量估计算法[J].红外与激光工,2014,43(4):1322-1326.WANG ZH F,YAN B,TONG L,et al..Normal estimate method of point clouds based on adaptive neighbor size[J].Infrared&Laser Engineering,2014,43(4):1322-1326.(in Chinese)
[9]CAO J,CHEN H,ZHANG J,et al..Normal estimation via shifted neighborhood for point cloud[J].Journal of Computational and Applied Mathematics,2018,329:57-67.
[10]GUENNEBAUD G,GROSS M.Algebraic point set sufaces[J].ACM Transactions on Graphics(TOG),2007,26(3):23-32.
[11]PAULY M,KEISER R,KOBBELT L P,et al..Shape modeling with point-sampled geometry[J].ACM Trans Graph,2003,22(3):641-650.
[12]GROSS M,PFISTER H.Point-based Graphics[M].The Morgan Kaufmann Series in Computer Graphics.San Francisco:Morgan Kaufmann Publishers Inc,2007.
[13]NURUNNABI A,BELTON D,WEST G.Robust statistical spproaches for local planar surface fitting in 3Dlaser scanning data[J].Isprs Journal of Photogrammetry&Remote Sensing,2014,96(4):106-122.
[14]王醒策,蔡建平,武仲科,等.局部表面拟合的点云模型法向估计及重定向算法[J].计算机辅助设计与图形学学报,2015,27(4):614-620.WANG X C,CAI J P,WU ZH K,et al..Normal estimation and normal orientation for point cloud model based on improved local surface fitting[J].Journal of Computer-Aided Design&Computer Graphics,2015,27(4):614-620.(in Chinese)
[15]孙殿柱,魏亮,李延瑞,等.基于局部样本增益优化的α-shape曲面拓扑重建[J].机械工程学报,2016,52(3):136-142.SUN D ZH,WEI L,LI Y R,et al..Surface reconstruction withα-shape based on optimization of surface local sample[J].Journal of Mechanical Engineering,2016,52(3):136-142.(in Chinese)
[16]CIME M V M,Pedrini H.Marching cubes technique for volumetric visualization accelerated with graphics processing units[J].Journal of the Brazilian Computer Society,2013,19(3):223-233.
[17]刘健,孙殿柱,李延瑞,等.散乱点云局部点集最小包围盒快速求解算法[J].农业装备与车辆工程,2010(6):27-29.LIU J,SUN D ZH,LI Y R,et al..Accelerating algorithm of minimum bounding box for local scattered points[J].Agricultural Equipment&Vehicle Engineering,2010(6):27-29.(in Chinese)
[18]高健,陈岳坪,邓海祥,等.复杂曲面零件加工精度的原位检测误差补偿方法[J].机械工程学报,2013,49(19):133-143.GAO J,CHEN Y P,DENG H X,et al..Insitu inspection error compensation for machining accuracy improvement of complex components[J].Journal of Mechanical Engineering,2013,49(19):133-143.(in Chinese)
[19]段黎明,邵辉,李中明,等.高效率的三角网格模型保特征简化方法[J].光学精密工程,2017,25(2):460-468.DUAN L M,SHAO H,LI ZH M,et al..Simplification method for feature preserving of efficient triangular mesh mode[J].Opt.Precision Eng.,2017,25(2):460-468.(in Chinese)
[20]BROUMI S,BAKAL A,TALEA M,et al..Applying Dijkstra algorithm for solving neutrosophic shortest path problem[C].International Conference on Advanced Mechatronic Systems.IEEE,2017:412-416.
[21]孙殿柱,刘华东,史阳,等.基于核密度估计的散乱点云边界特征提取[J].农业机械学报,2013,44(12):275-279.SUN D ZH,LIU H D,SHI Y,et al..Boundary feature abstraction of unorganized points based on kernel density estimation[J].Transactions of the Chinese Society for Agricultural Machinery,2013,44(12):275-279.(in Chinese)
[22]张应中,谢馥香,罗晓芳,等.采用半边编码的三角网格拓扑数据结构[J].计算机辅助设计与图形学学报,2016,28(2):328-334.ZHANG Y ZH,XIE F X,LUO X F,et al..A topological data structure using coding of half-edges for triangle meshes[J].Journal of Compuer-Aided Design&Computer Graphics,2016,28(2):328-334.(in Chinese)