基于Lie群表示的保体积2D-3D点集配准算法

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (3): 90-97.

• 自动化技术与计算机技术 • 上一篇下一篇

基于Lie群表示的保体积2D-3D点集配准算法

喻莹¹, 蔡晨炜¹, 应时辉¹, 李策^*2

1.上海大学理学院, 上海 200444;
2.兰州理工大学电气工程与信息工程学院, 甘肃兰州 730050

收稿日期:2022-03-31 出版日期:2024-06-28 发布日期:2024-07-02
通讯作者: 李策(1974-),男,辽宁营口人,博士,教授,博导.Email:xjtulice@qmail.com
基金资助:
国家自然科学基金(11971296,61866022,62363025),甘肃省高校产业支撑计划(2023CYZC-26)

Volume-preserving 2D-3D point set registration algorithm based on Lie group representation

YU Ying¹, CAI Chen-wei¹, YING Shi-hui¹, LI Ce²

1. College of Science, Shanghai University, Shanghai 200444, China;
2. School of Electrical Engineering and Information Engineering, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2022-03-31 Online:2024-06-28 Published:2024-07-02

摘要/Abstract

摘要： 2D-3D点集配准的目标是寻找三维原始点集与二维目标投影点集之间的对应关系和最优变换.为了给出配准问题的解析解,避免投影引起的体积退化,提出基于Lie群表示的保体积2D-3D点集配准算法.首先,考虑投影矩阵和旋转矩阵的非交换性,引入Lie群表示,将配准问题形式化为一个Lie群优化问题.利用局部线性化方法,将Lie群优化问题转化为一个可计算的二次规划问题.其次,为了避免体积退化,考虑约束变换后的三维点集的投影与二维目标点集的投影具有相同的体积.为便于计算,引入Jensen-Bregman LogDet散度作为保体积正则项,将计算点集的体积差异转化为计算协方差矩阵之间的差异.然后,通过交替求解对应关系和最优变换,形成完整且可解的迭代策略.最后,在两个经典数据集上进行对比实验和消融实验,验证了该算法的精确性和有效性.

关键词: 2D-3D点集配准, Lie群, 保体积正则, 二次规划

Abstract: The aim of 2D-3D point set registration is to find the optimal transformation and correspondence between 3D source point set and 2D target projection point set. In order to obtain the closed-form solution to the registration problem and avoid the volume degradation caused by projection, a volume-preserving 2D-3D point set registration algorithm based on Lie group representation was proposed. Firstly, considering the non-commutativity of the projection matrix and the rotation matrix, the Lie group representation is introduced to formalize the registration problem into an optimization problem based on Lie group. The Lie group optimization problem is transformed into a computationally quadratic programming problem by the local linearization method. Secondly, in order to avoid volume degradation, the projection of 3D transformed point set is constrained to have the same volume as that of 2D target point set. In order to facilitate calculation, the Jensen-Bregman LogDet divergence is introduced as a volume-preserving regularization term, converting the volume difference calculation into a covariance matrix difference calculation. Subsequently, a complete and solvable iteration strategy is developed by alternately solving for the correspondence and the optimal transformation. Finally, comparative experiments and ablation experiments on two classical data sets verify the accuracy and effectiveness of the proposed approach.

Key words: 2D-3D point set registration, Lie group, volume-preserving regularization, quadratic programming

中图分类号:

TP399

喻莹, 蔡晨炜, 应时辉, 李策. 基于Lie群表示的保体积2D-3D点集配准算法[J]. 兰州理工大学学报, 2024, 50(3): 90-97.

YU Ying, CAI Chen-wei, YING Shi-hui, LI Ce. Volume-preserving 2D-3D point set registration algorithm based on Lie group representation[J]. Journal of Lanzhou University of Technology, 2024, 50(3): 90-97.

参考文献

[1] BROWN M,WINDRIDGE D,GUILLEMAUT J.Globally optimal 2D-3D registration from points or lines without correspondences [C]//15th IEEE International Conference on Computer Vision (ICCV).Washington,DC:IEEE,2015:2111-2119.
[2] FELDMAR J,AYACHE N,BETTING F.3D-2D projective registration of free-form curves and surfaces [J].Computer Vision and Image Understanding,1997,65(3):403-424.
[3] ZHU J,LI H,AI D,et al.Iterative closest graph matching for non-rigid 3D/2D coronary arteries registration [J].Computer Methods and Programs in Biomedicine,2021,199:1-15.
[4] KIM J,LEE J,JIN W,et al.Locally adaptive 2D-3D registration using vascular structure model for liver catheterization [J].Computers in Biology and Medicine,2016,70:119-130.
[5] MIAO S,WANG Z,LIAO R.A CNN regression approach for real-time 2D/3D registration [J].IEEE Transactions on Medical Imaging,2016,35(5):1352-1363.
[6] MARKELJ P,TOMAZVIC D,LIKAR B,et al.A review of 3D/2D registration methods for image-guided interventions [J].Medical Image Analysis,2012,16(3):642-661.
[7] BESL P,MCKAY N.A method for registration of 3-D shapes [J].IEEE Trans-actions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[8] 李策,卢冰,肖利梅,等.基于相对坐标ICP的室内场景三维重建算法 [J].兰州理工大学学报,2017,43(3):96-101.
[9] 林玉萍,毕泊,孙飞鹏,等.基于图像配准的古代西夏文活字印刷术鉴别方法 [J].兰州理工大学学报,2016,42(4):97-101.
[10] 李策,罗欣颖,杜少毅.面向地图点集的多尺度层级ICP算法 [J].兰州理工大学学报,2012,29(4):83-86.
[11] YING S,PENG J,DU S,et al.A scale stretch method based on ICP for 3D data registration [J].IEEE Transactions on Automation Science and Engineering,2009,6(3):559-565.
[12] 应时辉,彭济根,郑红,等.含各向异性尺度形变数据集匹配问题的Lie群方法 [J].自动化学报,2009,35(7):867-874.
[13] DU S,ZHENG N,YING S,et al.Affine iterative closest point algorithm for point set registration [J].Pattern Recognition Letters,2010,31(9):791-799.
[14] DU S,ZHENG N,LEI X,et al.Scaling iterative closest point algorithm for registration of m-D point sets [J].Journal of Visual Communication and Image Representation,2010,21(5/6):442-452.
[15] CHEN H,ZHAG X,DU S,et al.A correntropy-based affine iterative closest point algorithm for robust point set registration [J].IEEE Journal of Automatica Sinica,2019,6(4):981-991.
[16] BENSEGHIR T,MALANDAIN G,VAILLANT R.Iterative closest curve: a framework for curvilinear structure registration application to 2D/3D coronary arteries registration [C]//International Conference on Medical Image Computing and Computer- Assisted Intervention.Berlin:Springer,2013:179-186.
[17] KHOO Y,KAPOOR A.Non-iterative rigid 2D/3D point-set registration using semidefinite programming [J].IEEE Transactions on Image Processing,2016,25(7):2956-2970.
[18] DONG J,PENG Y,YING S,et al.LieTrICP:an improvement of trimmed iterative closest point algorithm [J].Neurocomputing,2014,140:67-76.
[19] ROHLFING T,MAURER C R,BLUEMAKE D A,et al.Volume-preserving non-rigid registration of MR breast images using free-form deformation with an incompressibility constraint [J].IEEE Transactions on Medical Imaging,2003,22(6):730-741.
[20] CHERIAN A,SRA S,BANERJEE A,et al.Jensen-Bregman LogDet divergence with application to efficient similarity search for covariance matrices [J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(9):2161-2174.

基于Lie群表示的保体积2D-3D点集配准算法

Volume-preserving 2D-3D point set registration algorithm based on Lie group representation

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