建筑物边界规则化的混合LS-TLS平差方法
|
摘要
针对基于传统平差方法的建筑物边界规则化建模和解算复杂问题,利用基于海森法线和正交距离的直线方程,构建顾及边界垂直和平行条件的变量含误差(EIV)模型.该模型是附有二次型限制条件的齐次EIV模型,且设计矩阵由含误差元素的矩阵和不含误差的矩阵组成.针对该模型,推导了基于奇异值(SVD)分解的混合最小二乘-总体最小二乘(LS-TLS)直接解法以及精度评定方法.通过LiDAR点云的建筑物边界规则化算例表明:该方法易于建模,避免了条件方程线性化问题,且解算不需要迭代,重建精度高,可广泛用于基于摄影测量和LiDAR数据的建筑物重建.
Considering the modeling and computational complexity of building boundary regularization task of the traditional least squares adjustment methods,an EIV(errors-in-variables)model considering the vertical and parallel relations of building boundary was presented by using Hessian normal vector and orthogonal distance's line equation.The proposed model is a homogeneous EIV model with a quadratic condition,and the design matrix consists of a matrix with random errors and an error free matrix.A direct adjustment method based on singular value decomposition(SVD)of mixed least squares-total least squares(LS-TLS)with accuracy evaluation was proposed.The building boundary regularization from LiDAR point cloud shows that the proposed modelling and numerical algorithm can avoid solving a complicated nonlinear conditional equations and have the advantages of simplicity of modeling,stability and efficiency in numerical computation,and better accuracy.It can be widely used for building reconstruction from photogrammetry or LiDAR data points.
Considering the modeling and computational complexity of building boundary regularization task of the traditional least squares adjustment methods,an EIV(errors-in-variables)model considering the vertical and parallel relations of building boundary was presented by using Hessian normal vector and orthogonal distance's line equation.The proposed model is a homogeneous EIV model with a quadratic condition,and the design matrix consists of a matrix with random errors and an error free matrix.A direct adjustment method based on singular value decomposition(SVD)of mixed least squares-total least squares(LS-TLS)with accuracy evaluation was proposed.The building boundary regularization from LiDAR point cloud shows that the proposed modelling and numerical algorithm can avoid solving a complicated nonlinear conditional equations and have the advantages of simplicity of modeling,stability and efficiency in numerical computation,and better accuracy.It can be widely used for building reconstruction from photogrammetry or LiDAR data points.
引文
[1]WEIDNER U,FRSTNER W.Towards automatic building extraction from high-resolution digital elevation models[J].ISPRS Journal of Photogrammetry and Remote Sensing,1995,50(4):38-49.
[2]SAMPATH A,SHAN J.Segmentation and reconstruction of polyhedral building roofs from aerial LiDAR point clouds[J].IEEE Transactions on Geoscience and Remote Sensing,2010,48(3):1554-1567.
[3]YANG B S,XU W X,DONG Z.Automated building outlines extraction from airborne laser scanning point clouds[J].IEEE Geoscience and Remote Sensing Letters,2013,10(6):1399-1403.
[4]BEGER R,GEDRANGE C,HECHT R,et al.Data fusion of extremely high resolution aerial imagery and LiDAR data for automated railroad centre line reconstruction[J].ISPRS Journal of Photogrammetry and Remote Sensing,2011,66:40-51.
[5]CHEN L C,TEO T A,KUO C Y,et al.Shaping polyhedral buildings by the fusion of vector maps and LiDAR point clouds[J].Photogrammetric Engineering&Remote Sensing 2008,74(9):1147-1157.
[6]MAAS H G,VOSSELMAN G.Two algorithms for extracting building models from raw laser altimetry data[J].ISPRS Journal of Photogrammetry and Remote Sensing,1999,54(2):153-163.
[7]童小华,邓愫愫,史文中.数字地图合并的平差原理与方法[J].武汉大学学报(信息科学版),2007,32(7):621-625.TONG Xiaohua,DENG Susu,SHI Wenzhong.A new least squares adjustment method for map conflation[J].Geomatics and Information Science of Wuhan U-niversity,2007,32(7):621-625.
[8]刘鹏程,艾廷华,邓吉芳.基于最小二乘的建筑物多边形的化简与直角化[J].中国矿业大学学报,2008:37(5):699-704.LIU Pengcheng,AI Tinghua,DENG Jifang.Simplification and rectangularity of building-polygon based on least squares adjustment[J].Journal of China University of Mining&Technology,2008,37(5):699-704.
[9]BEDER C.Grouping uncertain oriented projective geometric entities with application to automatic building reconstruction[D].Germany:Bonn University,2007:71-79.
[10]MEIDOW J,BEDER C,FRSTNER W.Reasoning with uncertain points,straight lines,and straight line segments in 2D[J].ISPRS Journal of Photogrammetry and Remote Sensing,2009,64(2):125-139.
[11]SAMPATH A,SHAN J.Building boundary tracing and regularization from airborne LiDAR point clouds[J].Photogrammetric Engineering&Remote Sensing,2007,73(7):805-812.
[12]ZHOU Yongjun,ZHOU Yu.Constrained homogeneous errors-invariables modelling and extended weighted total least squares solutions[J/OL].Survey Review,2018,DOI:10.1080/00396265.2018.1516394.
[13]邓才华,周拥军,朱建军,等.一类新函数模型及通用加权总体最小二乘平差方法[J].中国矿业大学学报,2015,44(5):952-958.DENG Caihua,ZHOU Yongjun,ZHU Jianjun,et al.General weighted total least square method for a type of new functional model[J].Journal of China University of Mining&Technology,2015,44(5):952-958.
[14]王乐洋,余航,李毅.一种加权总体最小二乘问题的解法[J].中国矿业大学学报,2016,45(6):1263-1270.WANG Leyang,YU Hang,LI Yi.A method for weighted total least squares problem[J].Journal of China University of Mining&Technology,2016,45(6):1263-1270.
[15]SCHAFFRIN B,WIESER A.On weighted total least-squares adjustment for linear regression[J].Journal of Geodesy,2008,82:415-421.
[16]KRYSTEK M,ANTON M.A least-squares algorithm for fitting data points with mutually correlated coordinates to a straight line[J].Measurement Science&Technology,2011,22:3438-3442.
[17]JI Q,HARALICK R M.Breakpoint detection using covariance propagation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1998,20(8):845-851.
[18]KAPP A,GRLL L.Optimal estimation of line segments in noisy LiDAR data[J].Signal Processing,2006,86:2304-2317.
[19]XU Peiliang,LIU Jingnan,SHI Chuang.Total least squares adjustment in partial errors-in-variables models:Algorithm and statistical analysis[J].Journal of Geodesy,2012,86(8):661-675.
[20]FANG Xing.Weighted total least-squares with constraints:A universal formula for geodetic symmetrical transformations[J].Journal of Geodesy,2015,89(5):459-469.
[21]於宗俦,于正林.测量平差原理[M].武汉:武汉大学出版社,1990:63-71.YU Zongchou,YU Zhenglin.Principle of surveying adjustment[M],Wuhan:Wuhan University Press,1990:63-71.
[2]SAMPATH A,SHAN J.Segmentation and reconstruction of polyhedral building roofs from aerial LiDAR point clouds[J].IEEE Transactions on Geoscience and Remote Sensing,2010,48(3):1554-1567.
[3]YANG B S,XU W X,DONG Z.Automated building outlines extraction from airborne laser scanning point clouds[J].IEEE Geoscience and Remote Sensing Letters,2013,10(6):1399-1403.
[4]BEGER R,GEDRANGE C,HECHT R,et al.Data fusion of extremely high resolution aerial imagery and LiDAR data for automated railroad centre line reconstruction[J].ISPRS Journal of Photogrammetry and Remote Sensing,2011,66:40-51.
[5]CHEN L C,TEO T A,KUO C Y,et al.Shaping polyhedral buildings by the fusion of vector maps and LiDAR point clouds[J].Photogrammetric Engineering&Remote Sensing 2008,74(9):1147-1157.
[6]MAAS H G,VOSSELMAN G.Two algorithms for extracting building models from raw laser altimetry data[J].ISPRS Journal of Photogrammetry and Remote Sensing,1999,54(2):153-163.
[7]童小华,邓愫愫,史文中.数字地图合并的平差原理与方法[J].武汉大学学报(信息科学版),2007,32(7):621-625.TONG Xiaohua,DENG Susu,SHI Wenzhong.A new least squares adjustment method for map conflation[J].Geomatics and Information Science of Wuhan U-niversity,2007,32(7):621-625.
[8]刘鹏程,艾廷华,邓吉芳.基于最小二乘的建筑物多边形的化简与直角化[J].中国矿业大学学报,2008:37(5):699-704.LIU Pengcheng,AI Tinghua,DENG Jifang.Simplification and rectangularity of building-polygon based on least squares adjustment[J].Journal of China University of Mining&Technology,2008,37(5):699-704.
[9]BEDER C.Grouping uncertain oriented projective geometric entities with application to automatic building reconstruction[D].Germany:Bonn University,2007:71-79.
[10]MEIDOW J,BEDER C,FRSTNER W.Reasoning with uncertain points,straight lines,and straight line segments in 2D[J].ISPRS Journal of Photogrammetry and Remote Sensing,2009,64(2):125-139.
[11]SAMPATH A,SHAN J.Building boundary tracing and regularization from airborne LiDAR point clouds[J].Photogrammetric Engineering&Remote Sensing,2007,73(7):805-812.
[12]ZHOU Yongjun,ZHOU Yu.Constrained homogeneous errors-invariables modelling and extended weighted total least squares solutions[J/OL].Survey Review,2018,DOI:10.1080/00396265.2018.1516394.
[13]邓才华,周拥军,朱建军,等.一类新函数模型及通用加权总体最小二乘平差方法[J].中国矿业大学学报,2015,44(5):952-958.DENG Caihua,ZHOU Yongjun,ZHU Jianjun,et al.General weighted total least square method for a type of new functional model[J].Journal of China University of Mining&Technology,2015,44(5):952-958.
[14]王乐洋,余航,李毅.一种加权总体最小二乘问题的解法[J].中国矿业大学学报,2016,45(6):1263-1270.WANG Leyang,YU Hang,LI Yi.A method for weighted total least squares problem[J].Journal of China University of Mining&Technology,2016,45(6):1263-1270.
[15]SCHAFFRIN B,WIESER A.On weighted total least-squares adjustment for linear regression[J].Journal of Geodesy,2008,82:415-421.
[16]KRYSTEK M,ANTON M.A least-squares algorithm for fitting data points with mutually correlated coordinates to a straight line[J].Measurement Science&Technology,2011,22:3438-3442.
[17]JI Q,HARALICK R M.Breakpoint detection using covariance propagation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1998,20(8):845-851.
[18]KAPP A,GRLL L.Optimal estimation of line segments in noisy LiDAR data[J].Signal Processing,2006,86:2304-2317.
[19]XU Peiliang,LIU Jingnan,SHI Chuang.Total least squares adjustment in partial errors-in-variables models:Algorithm and statistical analysis[J].Journal of Geodesy,2012,86(8):661-675.
[20]FANG Xing.Weighted total least-squares with constraints:A universal formula for geodetic symmetrical transformations[J].Journal of Geodesy,2015,89(5):459-469.
[21]於宗俦,于正林.测量平差原理[M].武汉:武汉大学出版社,1990:63-71.YU Zongchou,YU Zhenglin.Principle of surveying adjustment[M],Wuhan:Wuhan University Press,1990:63-71.