MIN Faculty Department of Informatics A Modified ICP Algorithm for 3D Point Cloud Registration Analysis Olena Soroka University of Hamburg Faculty of Mathematics, Informatics and Natural Sciences Department of Informatics Technical Aspects of Multimodal Systems 21. November 2016 O. Soroka – Intelligent Robotics 1 / 23
Outline Introduction Iterative closest point algorithm Modified ICP Conclusions References 1. Introduction Robots and environment 3D point cloud Registration 2. Iterative closest point algorithm Core idea Problems 3. Modified ICP Description Performance Analysis 4. Conclusions 5. References O. Soroka – Intelligent Robotics 2 / 23
Robots and environment Introduction Iterative closest point algorithm Modified ICP Conclusions References Enabling robots to perform visual scanning of the environment can achieve various goals: ◮ localization ◮ mapping ◮ environmental awareness Most of the tasks rely on a 3-dimensional picture of the environment. O. Soroka – Intelligent Robotics 3 / 23
Robots and environment Introduction Iterative closest point algorithm Modified ICP Conclusions References Principle of operation of a 3D laser scanner 1 1 Paulus S. et.al 2014 - Limits of Active Laser Triangulation as an Instrument for High Precision Plant Imaging O. Soroka – Intelligent Robotics 4 / 23
3D point cloud Introduction Iterative closest point algorithm Modified ICP Conclusions References Data obtained from such scanners can be used for various purposes. 3D scan of a navigable interior 3 3D scan of a face 2 3 Texas Instruments, 01. Aug. 2014, Introduction to DLP 3D Machine Vision Reference Design 3 http://www.undergroundcity3d.com/uvod/forum/3d-point-cloud/ O. Soroka – Intelligent Robotics 5 / 23
3D point cloud Introduction Iterative closest point algorithm Modified ICP Conclusions References Treating the points of the 3D cloud as vertices allows to form faces and further process the data accordingly. Transformation of a 3D point cloud into a mesh 4 4 http://artisynth.magic.ubc.ca/artisynth/pmwiki.php?n=OPAL.MarkoMarjanovic O. Soroka – Intelligent Robotics 6 / 23
Registration Introduction Iterative closest point algorithm Modified ICP Conclusions References Registration of 3D point clouds 5 Problem Transforming a point set S in a way that the alignment error between it and a point set M from the same scene is minimal. 5 Salvi J., et.al, 2008 Overview of surface registration techniques including loop minimization for three-dimensional modeling and visual inspection O. Soroka – Intelligent Robotics 7 / 23
Iterative closest point algorithm Core idea Introduction Iterative closest point algorithm Modified ICP Conclusions References Algorithm first introduced in 1992 by two group of scientists. With two point sets that need to be matched, where point set S is static and point set M is moving: ◮ for each point in set M find the closest point in set S ◮ obtain a transformation to align the set M to the set S ◮ apply the transformation p ′ = R ¯ p + ¯ ¯ t R - rotation matrix ¯ t - translation vector p - original point vector ¯ p ′ - transformed point vector ¯ repeat until convergence. O. Soroka – Intelligent Robotics 8 / 23
Iterative closest point algorithm 2D demo Introduction Iterative closest point algorithm Modified ICP Conclusions References https://www.youtube.com/watch?v=tfckXoa-wRQ O. Soroka – Intelligent Robotics 9 / 23
Iterative closest point algorithm Point matching Introduction Iterative closest point algorithm Modified ICP Conclusions References Finding point pairs between sets S and M can be done in various ways: ◮ intersections of M with the normal to the point plane of S; ◮ projections of points in M onto the set S. Point to plane matching 6 Point to point matching 6 6 Bellekens B. et al, 2014 A survey of rigid 3D pointcloud registration algorithms. O. Soroka – Intelligent Robotics 10 / 23
Iterative closest point algorithm Point selection Introduction Iterative closest point algorithm Modified ICP Conclusions References To improve the reliability of calculations, outliers are disregarded. As to the point sets, it is possible to: ◮ use all samples; ◮ sample randomly; ◮ sample uniformly. O. Soroka – Intelligent Robotics 11 / 23
Iterative closest point algorithm Transformation matrix Introduction Iterative closest point algorithm Modified ICP Conclusions References The most commonly way is minimization of the squared sum of distance between the points - point-to-point : � N 1 i ) 2 ) i = 1 (( S i − M ′ C = 2 N where N is the number of points in the sample space. A variation of the method involves also considering the change in colors. Another option is taking the squared difference between a source point and an intersection of a normal vector with the moving set - point-to-plane distance. O. Soroka – Intelligent Robotics 12 / 23
Iterative closest point algorithm Problems Introduction Iterative closest point algorithm Modified ICP Conclusions References ICP algorithm is prone to stop at local minimum . Convergence and local minimum 7 7 http://www.yaldex.com/game-development/1592730043_ch18lev1sec4.html O. Soroka – Intelligent Robotics 13 / 23
Iterative closest point algorithm Problems Introduction Iterative closest point algorithm Modified ICP Conclusions References Primary cause is improper matching between 3D point clouds S and M. An important consideration, particularly in robotics, is the speed of calculations. O. Soroka – Intelligent Robotics 14 / 23
Modified ICP Description Introduction Iterative closest point algorithm Modified ICP Conclusions References Published in 2016, a modified ICP algorithm doesn’t rely on markers or positioning information, and introduces a concept of deletion masks . 3D laser scan of an indoor environment 8 8 https://www.tum.de/en/about-tum/news/press-releases/long/article/30040/ O. Soroka – Intelligent Robotics 15 / 23
Modified ICP Virtual measurement Introduction Iterative closest point algorithm Modified ICP Conclusions References Virtual measurement principle [Marani et al., 2016] O. Soroka – Intelligent Robotics 16 / 23
Modified ICP Deletion mask Introduction Iterative closest point algorithm Modified ICP Conclusions References Deletion mask is a result of virtually sampling the static set S (reference set) and transforming it via R t , T t . Deletion mask is determined as: � ′ υ 0 if | ρ 0 , j (ˆ z ) − ρ υ 0 , j | > λ ∗ σ n d j ( R t , T t ) = ′ υ 1 if | ρ 0 , j (ˆ z ) − ρ υ 0 , j | ≤ λ ∗ σ n standard deviation of noise σ n mask strength λ O. Soroka – Intelligent Robotics 17 / 23
Modified ICP Formulation Introduction Iterative closest point algorithm Modified ICP Conclusions References Deletion mask D is a binary matrix that can negate the influence of particular point matches on the calculation of the cost function: Q 1 � z | R t , T t )) 2 C ( R t , T t ) = d j ( R t , T t ) × ( ρ υ 0 , j (ˆ z ) − ρ υ 1 , j (ˆ 2 Q j = 1 If a certain region in the environment is classified as ambiguous (and hence can cause cost function overestimation), it is discarded from the calculation. O. Soroka – Intelligent Robotics 18 / 23
Modified ICP Performance Introduction Iterative closest point algorithm Modified ICP Conclusions References Minimum, maximum, and mean distance values [mm] between corresponding reflective markers extracted from the registrations of P1, P2, and P3 on P0. Best results are highlighted in bold (Lin: standard linear ICP; NL: nonlinear ICP; Pt2Pl: Point-to-Plane metrics; DM: Deletion Mask) [Marani et al., 2016] O. Soroka – Intelligent Robotics 19 / 23
Modified ICP Analysis Introduction Iterative closest point algorithm Modified ICP Conclusions References Provide situational improvements in the algorithm. Performs well with objects that consist of plane shapes. Initial positioning of the robot (sensor) is an important part of the algorithm. Virtual measurements are costly in terms of processing time. O. Soroka – Intelligent Robotics 20 / 23
Conclusions Introduction Iterative closest point algorithm Modified ICP Conclusions References 3D point cloud registration is performed for a wide variety of tasks. Iterative closest point is a well-known algorithm with a few problems. Most improvements to it are aimed at point matching and error function. Analyzed modification is useful for robotics, but is computationally expensive. O. Soroka – Intelligent Robotics 21 / 23
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