mlsanityData to 7 Oct 2026

A compact formula for the derivative of a 3-D rotation in exponential coordinates

arXiv 1312.0788 ↗First posted 3 Dec 2013cs.CV math.OCcited by 14

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Abstract (arXiv)

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Dec 2013.

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Citing papers per year: 2021: 4; 2022: 2; 2023: 1; 2024: 3; 2025: 3; 2026: 1.

14 papers.

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  1. 2021Deep Regression on Manifolds: A 3D Rotation Case Studycited by 67
  2. 2021RePOSE: Fast 6D Object Pose Refinement via Deep Texture Renderingcited by 63
  3. 2022Event Collapse in Contrast Maximization Frameworkscited by 33
  4. 2022A Fast Geometric Regularizer to Mitigate Event Collapse in the Contrast Maximization Frameworkcited by 16
  5. 2025Simultaneous Motion And Noise Estimation with Event Camerascited by 5
  6. 2024Event-based Photometric Bundle Adjustmentcited by 3
  7. 2024Motion Segmentation for Neuromorphic Aerial Surveillancecited by 2
  8. 2025E-VLC: A Real-World Dataset for Event-based Visible Light Communication And Localizationcited by 1
  9. 2021Registration Techniques for Deformable Objectscited by 0
  10. 2021Camera Motion Agnostic 3D Human Pose Estimationcited by 0
  11. 2023Surface Geometry Processing: An Efficient Normal-based Detail Representationcited by 0
  12. 2024ESC: Evolutionary Stitched Camera Calibration in the Wildcited by 0
2 more
  1. 2025Nonlinear Motion-Guided and Spatio-Temporal Aware Network for Unsupervised Event-Based Optical Flowcited by 0
  2. 2026FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolutioncited by 0