The issue with Equation 2 in the paper

[Wuzheng02]

This is a very solid work, and I’m quite interested in it.

However, I have a minor question about Equation (2) in the paper: Should there be a coefficient of $\frac{1}{2\pi\sigma_x\sigma_y}$ missing before the $\exp$ term in Equation (2)?

You wrote $R_{\text{point}}$ as a Gaussian distribution, but the integral of your current formula does not equal 1.

If you want to ensure that the value of $R_{\text{point}}$ remains between 0 and 1, you should not write it as equal to $N(\mu_p; \mu_{\text{gt}}, \Sigma_{\text{gt}})$.

[sugarandgugu]

Sorry for the late reply!

We've experimented with adding the normalization factor ((\frac{1}{2\pi\sigma_x\sigma_y})), but found it makes rewards excessively small even when centers are very close. Comparative tests showed the unnormalized form performs better, peaking at 1 and decaying to 0 for bounded RL signals.

Thanks for your interest

[Wuzheng02]

Thanks for your reply. I understand the rationale behind keeping the reward normalized between 0 and 1.

I just think

$$R_{\text{point}} =\mathcal{N}(\mu_p; \mu_{gt}, \Sigma_{gt})$$

should be written as:

$$R_{\text{point}} = (2\pi\sigma_x\sigma_y) \cdot \mathcal{N}(\mu_p; \mu_{gt}, \Sigma_{gt})$$

This typo does not detract from my belief that this is a meaningful work.