[Registration] Evaluation Metircs: RRE, RTE, RSE, RDE, RR(Success Ratio), ATE

Reference

GaussReg: Fast 3D Registration with Gaussian Splatting

DReg-NeRF

Relative Rotation Error (RRE), Relative Translation Error (RTE), and Relative Scale Error (RSE) between the estimated transformation and ground truth transformation as the evaluation metric of the registration accuracy.

• Relative Rotational Error (RRE), the geodesic distance between the estimated and ground-truth rotation matrix.
  • $\text{RRE} = \arccos\left(\frac{\text{Tr}(\mathbf{R}_\text{est}^\top \mathbf{R}_\text{gt}) - 1}{2}\right)$
• Relative Translation Error (RTE), the ratio of the Euclidean distance between the estimated and ground-truth translation vectors to the norm of the ground-truth translation vector.
  • $\text{RTE} = \frac{| \mathbf{t}_\text{est} - \mathbf{t}_\text{gt} |}{| \mathbf{t}_\text{gt} |}$
• Relative Scale Error (RSE), the ratio of the Euclidean distance between the estimated and ground-truth scale factors to the ground-truth scale factor.

  • $\text{RSE} = \frac{

    s_\text{est} - s_\text{gt}

    }{s_\text{gt}}$

• Relative Depth Error (RDE), the ratio of the Euclidean distance between the estimated and ground-truth depth to the ground-truth depth.
  • $\text{RDE} = \frac{| \text{estimated depth} - \text{ground-truth depth} |}{\text{ground-truth depth}}$
• Recall Rate(RR) or Success Ratio, the ratio of successful registration. –> Dataset에 대해 registration이 실패 없이 수행된 비율
  • The quantitative results are shown in Table 1, where the Success Ratio indicates the portion of successful registrations. As shown in Table 1, for 82 scenes in ScanNet-GSReg, HLoc only registers 75.6% of them successfully, while our method achieves a 100% success ratio.
  • We first compared our method with GaussReg on the ScanNet-GSReg dataset. As is shown in Tab. 2, both methods can handle this dataset with a 100% success ratio, …
• Absolute Translational Error (ATE), the Euclidean distance between the estimated and ground-truth translation vectors.