Strength
What it is useful for
- Decoupled from translation and model scale, making rotation failures easy to diagnose.
- Independent of mesh sampling density.
3DoF / pose components · error
Geodesic Rotation Error
Uses the shortest rotation angle between predicted and ground-truth rotations as the error.
Evaluates orientation alone, without considering distance from the camera; often reported alongside Translation Error or n° mcm thresholds.
Principle
The formulas define the computation. The diagrams show whether the error concerns a 3D model, visible surfaces, the image plane, or aggregation across thresholds.
The relative rotation R_gt^T R_hat expresses the rotation needed to move from the ground-truth orientation to the prediction; its trace recovers this minimum rotation angle.
Reduces 3D orientation error to a scalar, making it useful for category-level methods or tasks without a reliable CAD surface.
How to compute
Read the ground-truth rotation R_gt and predicted rotation R_hat.
Compute the relative rotation and recover the angle from its trace.
Compute the mean or median across instances, or the proportion below a specified angular threshold.
Strength
Caveat
Paper atlas
Links are derived by normalizing the metric names used in each paper. Directly reported metrics are distinguished from metrics associated through a broader protocol.
ICRA / IEEE RA-L · Thomas Jantos, Stephan Weiss, Jan Steinbrener
ECCV · Li Jin, Yuchen Yang, Weikai Chen et al.
ICRA · Xingjian Yang, Ashis G. Banerjee
CVPR · Huan Ren, Yihan Chen, Chuxin Wang et al.
CVPR · Li Zhang, Mingyu Mei, Ailing Wang et al.
ICRA · Jiahong Chen, Jinghao Wang, Zi Wang et al.
ICRA / IEEE RA-L · Xiangting Meng, Jiaqi Yang, Mingshu Chen et al.
ICRA · Zhe Wang, Qijin Song, Zihao Li et al.
ICRA · Zhichao Li, Chiara Bartolozzi, Lorenzo Natale et al.
CVPR · Jae-Young Kang, Hoonhee Cho, Taeyeop Lee et al.
ECCV · Siddhant Bansal, Zhifan Zhu, Shashank Tripathi et al.
ICRA · Panagiotis Sapoutzoglou, Orestis Vaggelis, Athina Zacharia et al.
ICRA · Pengfei Ye, Yuxiang Ma, Yi Zhou et al.
CVPR · Marwan Taher, Ignacio Alzugaray, Kirill Mazur et al.
ICRA · Miquel Oller, Qiyang Qian, Radu Corcodel et al.
ECCV · Xiao Lin, Minghao Zhu, Yun Peng et al.
AAAI · Wei Li, Long Ji, Ying Wang et al.
IJCV · Jian Liu, Wei Sun, Hui Yang et al.
CVPR · Wubin Shi, Shaoyan Gai, Feipeng Da
AAAI · Xianhui Meng, Yukang Huo, Li Zhang et al.
CVPR · Can Zhang, Gim Hee Lee
ICRA · Yufeng Jin, Niklas Funk, Vignesh Prasad et al.
CVPR · Sheng Yu, Di-Hua Zhai, Yuanqing Xia
ICRA · Lorenzo Shaikewitz, Tim Nguyen, Luca Carlone
ICRA / IEEE RA-L · Mark Van der Merwe, Kei Ota, Dmitry Berenson et al.
ICRA · Wen Yang, Zhixian Xie, Yiting Wang et al.
ECCV · Junwen Huang, Jiaqi Hu, Peter KT Yu et al.
ICRA · Hakjin Lee, Junghoon Seo, Jaehoon Sim
ICCV · Yufeng Jin, Vignesh Prasad, Snehal Jauhri et al.
CVPR · Jingshun Huang, Haitao Lin, Tianyu Wang et al.
ICRA · Zicai Peng, Te Cui, Guangyan Chen et al.
ICCV · Shaobo Zhang, Yuhang Huang, Wanqing Zhao et al.
WACV · Yujing Sun, Caiyi Sun, Yuan Liu et al.
3DV · Chin-Hsuan Wu, Yen-Chun Chen, Bolivar Solarte et al.
IROS · Yunzhi Lin, Yipu Zhao, Fu-Jen Chu et al.
IEEE RA-L · Ryo Okumura, Tadahiro Taniguchi
IROS · Marios Glytsos, Panagiotis P. Filntisis, George Retsinas et al.
ICCV · Junwen Huang, Shishir Reddy Vutukur, Peter KT Yu et al.
IROS · Teng Guo, Jingjin Yu
IROS · Nassim Ali Ousalah, Anis Kacem, Enjie Ghorbel et al.
ICCV · Tom Fischer, Xiaojie Zhang, Eddy Ilg
AAAI · Haixin Shi, Yinlin Hu, Daniel Koguciuk et al.
ICRA · Jingshun Huang, Haitao Lin, Tianyu Wang et al.
WACV · Arkadeep Narayan Chaudhury, Leonid Keselman, Christopher G. Atkeson
ECCV · Chuanrui Zhang, Yonggen Ling, Minglei Lu et al.
3DV · Zehao Zhu, Jiashun Wang, Yuzhe Qin et al.
CVPR · Tianfu Wang, Guosheng Hu, Hongguang Wang
CVPR · Yijia Weng, Bowen Wen, Jonathan Tremblay et al.
CVPR · Chen Zhao, Tong Zhang, Zheng Dang et al.
ICRA · Arren J. Glover, Luna Gava, Zhichao Li et al.
ICRA · Yufan Kang, Guillaume Caron, Ryoichi Ishikawa et al.
WACV · Gerald Ebmer, Adam Loch, Minh Nhat Vu et al.
ECCV · Jingyi Tang, Gu Wang, Zeyu Chen et al.
ECCV · Florian Langer, Jihong Ju, Georgi Dikov et al.
ICRA · Marwan Taher, Ignacio Alzugaray, Andrew J. Davison
3DV · Hanwen Jiang, Zhenyu Jiang, Kristen Grauman et al.
CVPR · Linfang Zheng, Tze Ho Elden Tse, Chen Wang et al.
ECCV · Pengyuan Wang, Takuya Ikeda, Robert Lee et al.
CVPR · HyunJun Jung, Shun-Cheng Wu, Patrick Ruhkamp et al.
ICRA · Matteo Bortolon, Theodore Tsesmelis, Stuart James et al.
CVPR · Agastya Kalra, Guy Stoppi, Dmitrii Marin et al.
CVPR · Jingtao Sun, Yaonan Wang, Mingtao Feng et al.
ECCV · Ruida Zhang, Ziqin Huang, Gu Wang et al.
CVPR · Liyuan Zhu, Shengyu Huang, Konrad Schindler et al.
WACV · Janis Rosskamp, Rene Weller, Gabriel Zachmann
AAAI · JongMin Lee, Yohann Cabon, Romain Brégier et al.
CVPR · Zhiyuan Yu, Zheng Qin, Lintao Zheng et al.
IROS · Jiaqi Yang, Yucong Chen, Xiangting Meng et al.
ICRA · Ronghan Chen, Yang Cong, Yu Ren
CVPR · Van Nguyen Nguyen, Thibault Groueix, Georgy Ponimatkin et al.
ECCV · Mengchen Zhang, Tong Wu, Tai Wang et al.
ECCV · Jiyao Zhang, Weiyao Huang, Bo Peng et al.
ECCV · Akshay Krishnan, Abhijit Kundu, Kevis-Kokitsi Maninis et al.
ECCV · Yuchen Che, Ryo Furukawa, Asako Kanezaki
WACV · Jiahao Yang, Wufei Ma, Angtian Wang et al.
ECCV · Yang You, Kai Xiong, Zhening Yang et al.
3DV · Rama Krishna Prasad Kandukuri, Michael Strecke, Joerg Stueckler
ECCV · Yiyao Ma, Kai Chen, Hon-Sing Tong et al.
CVPR · Tsu-Ching Hsiao, Hao-Wei Chen, Hsuan-Kung Yang et al.
CVPR · Yamei Chen, Yan Di, Guangyao Zhai et al.
ECCV · Yuliang Guo, Abhinav Kumar, Cheng Zhao et al.
ICRA · Jenny Wang, Octavian Donca, David Held
ECCV · Li Zhang, Weiqing Meng, Yan Zhong et al.
CVPR · Leonhard Sommer, Artur Jesslen, Eddy Ilg et al.
IROS · Francesco Di Felice, Alberto Remus, Stefano Gasperini et al.
3DV · Van Nguyen Nguyen, Yuming Du, Yang Xiao et al.
Next
Compare metrics at the same level to understand why one score improves while another stays unchanged.
3D Translation Error
Rotation–Translation Threshold Accuracy
Average Distance of Model Points
Maximum Symmetry-Aware Surface Distance