A Modified ICP Algorithm for 3D Point Cloud Registration Analysis - - PowerPoint PPT Presentation

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

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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
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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.

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Robots and environment

Introduction Iterative closest point algorithm Modified ICP Conclusions References

Principle of operation of a 3D laser scanner 1

1Paulus S. et.al 2014 - Limits of Active Laser Triangulation as an Instrument for High Precision

Plant Imaging

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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 face 2 3D scan of a navigable interior 3

3Texas Instruments, 01. Aug. 2014, Introduction to DLP 3D Machine Vision Reference Design 3http://www.undergroundcity3d.com/uvod/forum/3d-point-cloud/

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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

4http://artisynth.magic.ubc.ca/artisynth/pmwiki.php?n=OPAL.MarkoMarjanovic

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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.

5Salvi J., et.al, 2008 Overview of surface registration techniques including loop minimization for

three-dimensional modeling and visual inspection

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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.

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Iterative closest point algorithm

2D demo

Introduction Iterative closest point algorithm Modified ICP Conclusions References

https://www.youtube.com/watch?v=tfckXoa-wRQ

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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 point matching 6 Point to plane matching 6

6Bellekens B. et al, 2014 A survey of rigid 3D pointcloud registration algorithms.

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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.

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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: C =

1 2N

N

i=1((Si − M′ i)2)

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.

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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

7http://www.yaldex.com/game-development/1592730043_ch18lev1sec4.html

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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.

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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

8https://www.tum.de/en/about-tum/news/press-releases/long/article/30040/

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Modified ICP

Virtual measurement

Introduction Iterative closest point algorithm Modified ICP Conclusions References

Virtual measurement principle [Marani et al., 2016]

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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 Rt, Tt. Deletion mask is determined as: dj(Rt, Tt) =

• if |ρ

′υ

0,j(ˆ

z) − ρυ

0,j| > λ ∗ σn

1 if |ρ

′υ

0,j(ˆ

z) − ρυ

0,j| ≤ λ ∗ σn

σn standard deviation of noise λ mask strength

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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: C(Rt, Tt) =

1 2Q Q

• j=1

dj(Rt, Tt) × (ρυ

0,j(ˆ

z) − ρυ

1,j(ˆ

z|Rt, Tt))2 If a certain region in the environment is classified as ambiguous (and hence can cause cost function overestimation), it is discarded from the calculation.

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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]

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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.

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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.

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References

Introduction Iterative closest point algorithm Modified ICP Conclusions References

[Besl and McKay, 1992] Besl, P. J. and McKay, N. D. (1992). Method for registration of 3-d shapes. In Robotics-DL tentative, pages 586–606. International Society for Optics and Photonics. [Burgard et al., ] Burgard, W., Stachniss, C., Bennewitz, M., and Arras, K. Iterative closest point algorithm. [Chen and Medioni, 1992] Chen, Y. and Medioni, G. (1992). Object modelling by registration of multiple range images. Image and vision computing, 10(3):145–155. [Marani et al., 2016] Marani, R., Renò, V., Nitti, M., D’Orazio, T., and Stella, E. (2016). A modified iterative closest point algorithm for 3d point cloud registration. Computer-Aided Civil and Infrastructure Engineering. [Mitra, 2012] Mitra, N. J. (2012). The icp algorithm and its extensions. [Pomerleau et al., 2015] Pomerleau, F., Colas, F., and Siegwart, R. (2015). A review of point cloud registration algorithms for mobile robotics. Foundations and Trends in Robotics (FnTROB), 4(1):1–104.

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References (cont.)

Introduction Iterative closest point algorithm Modified ICP Conclusions References

[Rusinkiewicz and Levoy, 2001] Rusinkiewicz, S. and Levoy, M. (2001). Efficient variants of the icp algorithm. In 3-D Digital Imaging and Modeling, 2001. Proceedings. Third International Conference on, pages 145–152. IEEE. [Segal et al., 2009] Segal, A., Haehnel, D., and Thrun, S. (2009). Generalized-icp. In Robotics: Science and Systems, volume 2.

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