Question about pruning threshold tp

[wzy-99]

Hello,

I hope this message finds you well. I am writing to seek clarification on the meaning of the threshold 'tp' mentioned in the paper. The paper discusses two thresholds, one being the distance threshold 'td' and the other being 'tp'.

In the paper, it is mentioned that less 3D Gaussians placed on the far edge of the scene are pruned out in order to preserve more points located at the far plane, relying on the relative depth. Specifically, the pruning threshold 'tp' is scaled by 'wp' to 1.0 depending on the relative depth, and the lowest threshold is applied to the farthest point.

However, I am still unclear about the exact definition and purpose of the threshold 'tp'. Could the author kindly provide an explanation or further clarification on this matter?

Thank you for your time and assistance. I look forward to your response.

[benhenryL]

Hi! Thanks for your attention to our work and feel sorry for the late reply.

The threshold ‘tp’ is exactly same as what 3D-GS uses to prune the points, which is set to 0.005 by default in its implementation. Maybe I can clarify what ‘wp’ does.
3D-GS uses the same, fixed threshold (tp) for pruning to all points regardless of their relative depth (I mean, z-axis values of the points) and large tp prunes out more points.

We tried to apply different pruning thresholds to each point to prune out fewer points lying on the far plane.
To do so, we introduced 'wp' which is multiplied to 'tp' so that all the points can have different pruning thresholds. i.e. tp * wp is a new threshold for pruning, and each point has a different wp as it is computed based on the point's position along the z-axis.
For instance, wp is set to smaller values for the points at the far plane to less prune out the points (keep more points), while it is set to larger ones for those at the near plane to remove some trivial points as 3D-GS does.

Simply, like figure 4 in the paper that I attached, we wanted to remove less number of points at the far plane like the rightmost case in the figure using wp*tp, while 3D-GS equivalently treats all the points with fixed tp which may prune lots of points at the far plane (middle case in the figure).

Hope this helps, and please let me know if you have any other questions.

Thanks!