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1 第 8 卷第 6 期 计算机辅助设计与图形学学报 Vol. 8 No 年 6 月 Journal of Computer-Aided Design & Computer Graphics Jun. 016 基于单目视觉的同时定位与地图构建方法综述 刘浩敏 1), 章国锋 1,)* 1), 鲍虎军 1) ( 浙江大学 CAD&CG 国家重点实验室杭州 ) ) ( 浙江大学工业信息物理融合系统协同创新中心杭州 ) (zhangguofeng@cad.zju.edu.cn) : 增强现实是一种在现实场景中无缝地融入虚拟物体或信息的技术, 能够比传统的文字 图像和视频等方式更高效 直观地呈现信息, 有着非常广泛的应用. 同时定位与地图构建作为增强现实的关键基础技术, 可以用来在未知环境中定位自身方位并同时构建环境三维地图, 从而保证叠加的虚拟物体与现实场景在几何上的一致性. 文中首先简述基于视觉的同时定位与地图构建的基本原理 ; 然后介绍几个代表性的基于单目视觉的同时定位与地图构建方法并做深入分析和比较 ; 最后讨论近年来研究热点和发展趋势, 并做总结和展望. : 增强现实 ; 同时定位与地图构建 ; 运动推断结构 ; 多视图几何 ; 摄像机跟踪 :TP A Survey of Monocular Simultaneous Localization and Mapping Liu Haomin 1), Zhang Guofeng 1,)*, and Bao Hujun 1) 1) (State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou ) ) (Collaborative Innovation Center for industrial Cyber-Physical System, Zhejiang University, Hangzhou ) Abstract: Augmented reality (AR) is a technique that allows to seamlessly composite virtual objects or information into real scene. Compared to traditional tet, images and videos, AR is a more effective and intuitive way for information presentation and has wide applications. Simultaneous localization and mapping (SLAM) is a key fundamental technique for augmented reality, which provides the ability of self-localization in an unknown environment and mapping the 3D environment simultaneously. The localization and mapping enables fusion of virtual objects and real scenes in a geometrically consistent way. In this paper, we describe the basic principles of Visual SLAM, and introduce some state-of-the-art monocular SLAM methods with deep analysis and comparison. Finally, we discuss some research tendency in recent years and make conclusions. Key words: augmented reality; simultaneous localization and mapping; structure-from-motion; multi-view geometry; camera tracking, ( )().,,., : ; : 基金项目 : (01BAH35B0); (613011, ); (015XZZX005-05); (0145). 刘浩敏 (1987),,, ; 章国锋 (1981),,,,,, ; 鲍虎军 (1966),,,,, CCF,.

2 856 计算机辅助设计与图形学学报第 8 卷,,,..,,., GPS, ; ;. (visual simultaneous localization and mapping, V-SLAM) ( ),., /, / V-SLAM,. (simultaneous localization and mapping, SLAM) [1-4],., (structurefrom-motion, SFM) [5]. SFM, SFM, V-SLAM. SLAM,, SLAM [3-4,6-9]. SLAM, SLAM, SLAM ; ( Durrant- Whyte [3-4] 006 SLAM, 10 ), SLAM., SLAM, 3 V-SLAM,., V-SLAM,.,, [5], 1. V-SLAM V-SLAM,. V-SLAM C 1 C m, X1 X n. C i, 3 3 Ri p i. X j R i, i pi C T ij ij ij i j i ( X, Y, Z ) R ( X p ) (1) h ( f X / Z c, f Y / Z c ) () ij ij ij y ij ij y, f, f y, y, ( c, cy ),. (1)(), h ij Ci X j, h hc (, X ) (3) ij i j V-SLAM ( 1, X 1 11, 1, 31 ). m arg min hc (, X ) ˆ (4), 1 1 C1Cm X1Xn i j n i j ij C 1 C m, X1 X n, X j Ci h ij ij. T 1 ij ~ N( ˆ ij, ij ), e e e. (4)(bundle adjustment, BA) [10], ij T 1 V-SLAM 的基本原理 V-SLAM 1

3 第 6 期, 等 : 857. V-SLAM,.,,.. V-SLAM IMU (). SLAM VIN(visual-aided inertial navigation) VI-SLAM (visual-inertial SLAM). ( Ci, Ci 1) IMU Z i { z 1 z n i }, VI-SLAM [11-13] arg min hc (, X ) ˆ C1Cm, X1Xn i1 j1 m1 i1 m n f( C, Z ) C i i i1 i i j ij ij (5) (4), VI-SLAM, f ( Ci, Zi) Z i C i, i. (Continuous Time System) [14] (Preintegration) [15]., VI-SLAM v i IMU b i, Ci ( Ri, pi, vi, b i)., GPS p G i,. SLAM. SLAM MonoSLAM [16] MSCKF [17]. MonoSLAM Davison SLAM. MonoSLAM t t C t X 1 X n, ( a );,,,, ( b );, Ct., ( c a. m arg min hc (, X ) ˆ C1Cm, X1Xn i1 j1 n i j ij m1 m1 G f( Ci, Zi) Ci1 i ˆ i i i i1 i1 GPS ij p p (6) G G i i i p ~ N( p ˆ, Λ ). b. 代表性单目 V-SLAM 系统, V-SLAM 3 : BA V-SLAM. V-SLAM,..1 基于滤波器的 V-SLAM V-SLAM : t, t ~ N ( ˆ t, P t), ˆt, Pt. c. MonoSLAM [16]

4 858 计算机辅助设计与图形学学报第 8 卷 ). MonoSLAM Shi-Tomasi [18], (active search) [19]. MonoSLAM (etended Kalman filter, EKF). (Prediction), Ct f( Ct1, avt, a t) (7) a v a, av ~ N(0, Γ v), a ~ N(0, Γ ), t. (Update), ˆ hc (, X ) n (8) j t j j, ˆ j X j, n j ~ N(0, j ). (5), MonoSLAM t, { C 1 Ct 1 },. EKF : 1) ( V-SLAM ), EKF, Levenberg-Marquardt [0],., ;,,. ), On ( 3 ),. EKF, Mourikis [17] 007 MSCKF. MSCKF VI-SLAM,, IMU [14] ;, MSCKF l C { Ct l 1 Ct}. C C i, C C i,., MSCKF (Marginalization), C i X j 3 { Ct l 1Ct}, On ( ) 3 Onl ( ). l n,,,.. 基于关键帧 BA 的 V-SLAM PTAM SFM, BA V-SLAM, Klein [1] 007, 009 iphone 3G []. PTAM : (Tracking) (Mapping). ( 3a ) ( 3b ), (4)( BA); BA,, C,. t a. b. 3 PTAM [1],, FAST [3], arg min wj h( Ct, X j) ˆ j (9) j Ct n j1 w Tukey [4], j (Outliers). (Inliers) (),, [5],,., C,, t

5 第 6 期, 等 : 859. (Epipolar Line) [5], (Triangulation) [5], BA,. PTAM V-SLAM, V-SLAM PTAM. Mur-Artal [6] 015 ORB-SLAM V-SLAM. ORB-SLAM PTAM,, 4 : 1) ORB-SLAM ORB [7], ORB [8], PTAM.,,.. ) ORB- SLAM,. [8] (), (Pose Graph). ( 4a ), i ; ( 4b ), ij ; go [9], ( 4c, 4d ),, (, ) 1 m ij ij 1 T 1 1 ij i j ij ij i j argmin ( ) ( ) (10), Σij ij (), a. () b. () c. d. 4 ORB-SLAM [6]. BA,, ORB-SLAM. BA ( 4 ). 3) PTAM,,. (Paralla),. ORB-SLAM. 4) PTAM,. ORB-SLAM, ;, BA. CAD&CG 013 RDSLAM [30], PTAM /, SIFT [31],,., RDSLAM RANSAC [3], RANSAC,,., V-SLAM..3 基于直接跟踪的 V-SLAM BA V-SLAM, ( )., (Direct Tracking),,. V-SLAM DTAM [33] LSD-SLAM [34]. DTAM Newcombe 011 V-SLAM, ( 5a )., DTAM AR ( 5b ),., DTAM

6 860 计算机辅助设计与图形学学报第 8 卷 C t C v, Cv, C v C t tv, arg min r(, D v ( ), tv ) (11) tv v, r(), r(, Dv, tv) Iv It( (, Dv( ), tv) (1) Iv D v C v, v, (, D v, tv ) v t. I g( ) e r (15) Huber, /, if 1 /, otherwise. DTAM (16) arg min R(, Dr) C(, Dr) d (17) Dr (total variation, TV) [36]. DTAM, DTAM,,, GPU,. Engel [37] 013 (visual odometry, VO), V-SLAM LSD-SLAM [34],. DTAM, LSD-SLAM ( 6a ),,. a. 5 DTAM [33], r D r ( 5c ). (Inverse Depth) [35]. 5d, DTAM M NS, M N, S. DTAM r m N() r, r d D r (Voel) C 1 (, d ) (,, mr ) 1 N() r r d (13) mn( r) r() (1). arg min C(, d), DTAM (Regularization Term) R(, d) g D r ( ) (14), g, d b. 6 LSD-SLAM [34] LSD-SLAM, k I k D k V k. N( Dk, Vk( )). LSD-SLAM t k tk, arg min r Dk tk k r Dk tk (, ( ), ) (, ( ), ) (18), k ; r() (1); (, ) r(),,

7 第 6 期, 等 : 861 r(, Dk, tk) I r(, Dk, tk) Vk Dk (19) Huber, Outliers. LSD-SLAM (), It Ik, d, EKF D k V k V d D k Dk Vk (0) Vk Vk Vk ORB-SLAM, LSD-SLAM,. k i [38] { k j }, ( k, k ) i j ij (10). ij.4 分析和比较 V-SLAM 1., MSCKF VI-SLAM V-SLAM,, V-SLAM, V-SLAM... MonoSLAM V-SLAM,, PTAM BA V-SLAM [39]. MSCKF,, IMU,. BA PTAM, RDSLAM ORB-SLAM SIFT ORB, PTAM BA, PTAM ; ORB-SLAM,. DTAM LSD-SLAM, ORB-SLAM. [6] TUM RGB-D [40], LSD-SLAM ORB-SLAM 5~10.. MonoSLAM On ( 3 ), n,. 3 MSCKF Onl ( ), n, l. MSCKF, l,,. PTAM ORB-SLAM,. RDSLAM PTAM ORB-SLAM, SIFT. DTAM LSD-SLAM,,,,.. MonoSLAM On ( 3 ),. MSCKF,. PTAM RDSLAM 表 1 各类单目 V-SLAM 系统比较 MonoSLAM MSCKF PTAM ORB-SLAM RDSLAM DTAM LSD-SLAM

8 86 计算机辅助设计与图形学学报第 8 卷 BA : PTAM ; RDSLAM BA, KDTree [41] PTAM,,. ORB-SLAM LSD-SLAM BA,. DTAM,.. ( ) V-SLAM., DTAM LSD-SLAM,. MSCKF VI-SLAM,, IMU,..,,. MonoSLAM EKF,. PTAM,, MonoSLAM.,,, MonoSLAM. PTAM, DTAM [4],. MSCKF, RDSLAM ORB- SLAM (MSCKF RDSLAM SIFT, ORB-SLAM ORB ), (RDSLAM KDTree [41], ORB-SLAM [43] ), (RDSLAM ). LSD-SLAM,,. PTAM, RDSLAM ORB-SLAM,, RDSLAM ORB-SLAM PTAM. MSCKF IMU,,. LSD- SLAM DTAM,,,..,. MonoSLAM, MSCKF. PTAM,,,.,,. RDSLAM, ORB-SLAM LSD-SLAM (RDSLAM KDTree [41], ORB-SLAM [43], LSD-SLAM FAB-MAP [38] ),, PTAM..,. MonoSLAM,. MSCKF,, MSCKF,, IMU,. PTAM RDSLAM,,,. ORB-SLAM, DTAM LSD-SLAM,. ORB-SLAM,, DTAM LSD-SLAM.. Mono-SLAM, MSCKF, PTAM, ORB-SLAM, DTAM, LSD-SLAM,. RANSAC [3] ( Huber, Tukey ),

9 第 6 期, 等 : 863, Outliers ;,,. MSCKF IMU,. RDSLAM,, RANSAC,,.,, RDSLAM.. MonoSLAM, ( ),. RDSLAM, SIFT, BA ;, Outliers,. MSCKF, PTAM DTAM. ORB-SLAM LSD-SLAM,.. Klein [5] 008, 7a. LSD-SLAM. 7b,. SFM VO [46-47]. Concha [48] ( 7c ), (Superpiel). Concha [48-49] PTAM LSD-SLAM,., V-SLAM. ( 7d ), [50] [51]. a. [5] b. [37] 3 近年研究热点与发展趋势, V-SLAM.,. 3.1 缓解特征依赖 V-SLAM. (.3 ), /,.,,, [44],. Forster [45] (semi-direct VO, SVO ),,. V-SLAM, (),, c. [48] d. [50] 7 3. 稠密三维重建 V-SLAM., [5], [53]. 010 RGB-D Kinect,.,. Newcombe [54] RGB-D SLAM KinectFusion. KinectFusion TSDF(truncated signed distance function) [55],,. TSDF, Marching Cube [56] TSDF 0, (Ray Cast) TSDF

10 864 计算机辅助设计与图形学学报第 8 卷 0., KinectFusion, ICP [57],.,, TSDF. KinectFusion : 1) ; ) ICP ; 3)., Whelan : [58],, ; [59] ICP, FOVIS [60] RGB-D [61] 3,, ; [6] DBoW [43], [63], ; [64](Surfel) [65],,,. V-SLAM,., AR,, V-SLAM RGB-D SLAM..3 DTAM LSD-SLAM V- SLAM. Schöps [44] LSD-SLAM,, AR ( 8a ). Pizzoli [66] REMODE,. Tanskanen [67] Kolev [68] ( 8b ), IMU. Pradeep [69] MonoFusion. Ondruska [70] MobileFusion, ( 8c ). Schöps [71] Project Tango, ( 8d ).,,., a. AR [44] b. [67] c. MobileFusion [70] d. [71] 8 (, I I ),. I I, (Patch) NCC(normalized cross correlation)., [67-68],,. MonoFusion [69] PatchMatch [7],.. DTAM REMODE ((14)),. REMODE [73], Inlier,.

11 第 6 期, 等 : 865 Kolev [68] [65],, Outliers. MonoFusion, MobileFusion Schöps [71] Project Tango TSDF [55] Outliers., GPU. AR, GPU., CPU [34,74],. 3.3 多传感器融合 : V-SLAM ; IMU ; SLAM,.,,. IMU,,. 1,,.,. t, C { C1, C,, C } t, 30 /s, 30,.,,., l { Ct l 1 Ct}, l.,,. SLAM ( l 1).,. MSCKF l. Li [75] MSCKF.0. MSCKF (Observability Analysis), (Linearization Point), (Yaw, ),., MSCKF.0 First-Estimate Jacobian [76],,. [77-78] (). [11-13,79]. EKF, SLAM, EKF,., [11-1] [15] IMU. [79] isam,. [13],. 3.4 其他实际问题 V-SLAM,., V-SLAM, BA V-SLAM (. ),.,,,, ;,,,, V-SLAM. [80-8],,., (Rolling Shutter),,., [83-86].,,, RANSAC, [30,87] IMU. 4 结语,

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