some questions about paper

[narutojxl]

Dear @jisehua,
Thanks for open source this excellent work! I have some stupid questions to seek your help, thanks a lot!

• Q1: I understand equ1. and equ2. are mean and cov of each clustered voxel, equ4, $S_i(p)$, is the pdf(probability density function) of each matched voxel? In paper, you say "where Fi(p) is the distribution probability of xi.", $x_i$ is one point in the current laser frame, \mathbf{x}_i, how to calcualte the pdf of the whole point cloud? Some places is bold symbols, while others do not, i'm a little confused.
• Q2: When p is zero, translation is zero, why $F_i(0) = 1$?
• Q3: According to equ9, Does each voxel has a degenerate factor, how to calculate the whole point cloud degenerate factor?
• Q4: According to equ16, you say $2*\mathbf{b_i}^T * \delta d$ is 1x6 vector. In equ12, $e_i$ is 3x1 vector, $J_i$ is 3x3 matrix, $\mathbf{b_i}^T$ is 1x3 vector, $\delta d$ is 3x1, the $2*\mathbf{b_i}^T * \delta d$ is a scalar? Degenerate factor D is also a scalar, but you say it is a 1x6 vector, Something i missunderstand?
• Q5: The degenerate direction is the eigenvector, 3x1 vector, corresponding max eigenvalue $\lambda_{max}$ of $\mathbf{H_i}$ ? Is degenerate direction is a 6x1 vector, x, y, z, roll, pitch, and yaw ?

BTW, could i have a chance to make a friend with you to stay in touch for convenient communication, i could not find your email ：）

Thanks a lot!
Best
narutojxl