Metrics for 3D Rotations: Comparison and Analysis

By Du Q. Huynh. Journal of Mathematical Imaging and Vision, 2009

752 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/56178de1001efe54792ad93f6980de5d5e91906b

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In Aerospace Engineering

In Computer Vision and Pattern Recognition

Citations in the corpus

Automatic generation and detection of highly reliable fiducial markers under occlusion (2014, methodology): “The 3D rotation error is computed using the inner product of unit quaterions[47]”
Domain Separation Networks (2016, background): “The first term is the classification loss, similar to the rest of the experiments, the second term is the log of a 3D rotation metric for quaternions [13], and ξ is the weight for the pose loss.”
Geometry-Aware Learning of Maps for Camera Localization (2017, methodology): “We also implemented other metrics for rotation [26], and found they did not improve the performance.”
DeceptionNet: Network-Driven Domain Randomization (2019, background): “where the first term is the classification loss and the second term is the log of a quaternion rotation metric [19].”
Benchmarking Simulated Robotic Manipulation Through a Real World Dataset (2019, background): “The inner product of the unit quarternion for a data point is a value between 0 and π2 [29].”
Dynamic Multiscale Graph Neural Networks for 3D Skeleton Based Human Motion Prediction (2020, neutral): “In s1, we consider 20 joints with non-zero exponential maps [18]; In s2 and s3, we consider 10 and 5 parts, respectively.”
Comparing ICP variants on real-world data sets (2013, neutral): “Addressing the problem of multiple rotation metrics, Huynh [12] proposes an evaluation of 6 types of diﬀerent distance for SO (3) used in the scientiﬁc litterature.”
Real-time Deep Pose Estimation with Geodesic Loss for Image-to-Template Rigid Registration (2018, methodology): “To achieve this, we formulated a regression problem for 3D pose estimation based on the angle-axis representation of 3D rotations that form a Special Orthogonal Group SO(3); and used the biinvariant geodesic distance, which is a natural Riemannian metric on SO(3) [22], as the loss function.”
Unsupervised Pixel-Level Domain Adaptation with Generative Adversarial Networks (2016, background): “where the first and second terms are the classification loss, similar to Equation 3, and the third and fourth terms are the log of a 3D rotation metric for quaternions [23].”
Learning Action Recognition Model from Depth and Skeleton Videos (2017, methodology): “Using Euclidean Distance between the Euler Angles [10], we apply k-means clustering to each body-part features independently.”
Large-Scale, High-Resolution Comparison of the Core Visual Object Recognition Behavior of Humans, Monkeys, and State-of-the-Art Deep Artificial Neural Networks (2018, methodology): “Pose differences were computed as distances in unit quaternion representations: the 3D pose ( r xy , r xz , r yz ) was first converted into unit quaternions, and distances between quaternions , were estimated as (cid:0) (cid:2) (Huynh, 2009).”
Generative Models for Graph-Based Protein Design (2019, background): “Quaternions represent 3D rotations as four-element vectors that can be efficiently and reasonably compared by inner products [39].”
MSM: a new flexible framework for Multimodal Surface Matching☆ (2014, neutral): “This is proportional to the angle θpq between the start and end points of the two consecutive rotations (Huynh, 2009; Moakher, 2002) (since the rotation is related to its axis angle representation through an exponential map, logR = ([k]×θ), and the Frobenius norm of the skew symmetric matrix is √…”
Rolling Rotations for Recognizing Human Actions from 3D Skeletal Data (2016, background): “Here, the second last equality follows from the fact that dSO3 is bi-invariant [14].”