Weird about the calculation of free space uniform sampling ?

[DeepDuke]

       # Part 3. free space uniform sampling
        repeated_dist = distances.repeat(freespace_sample_n,1)
        free_max_ratio = free_sample_end_dist_m_scaled / repeated_dist + 1.0
        free_diff_ratio = free_max_ratio - free_min_ratio

        free_sample_dist_ratio = torch.rand(point_num*freespace_sample_n, 1, device=dev)*free_diff_ratio + free_min_ratio

        free_sample_displacement = (free_sample_dist_ratio - 1.0) * repeated_dist

About the above caclualtion in https://github.com/PRBonn/SHINE_mapping/blob/master/utils/data_sampler.py, my understanding is samping points from 0.3m to 0.8m as the distance to the surface (for sigma=0.1 m, then surface sampling range should be [-0.3m, 0.3m] around the surface). But the above calculation is a bit weird to me

In most of the config files, we have free_sample_begin_ratio: 0.3 and free_sample_end_dist_m: 0.8. Suppose there is a scan point with range to the LiDAR as repeated_dist = 10m. Then free_max_ratio = 0.8 / 10 + 1.0 = 1.08, free_diff_ratio=1.08 - 0.3=0.78, then 0.3 <= free_sample_dist_ratio <= 1.08, finally -7m < free_sample_displacement < 0.8m. This means a high probability to sample a point from opposite direction with respect to the orignal scan point. Is it the meaning of free samping ? Or where is wrong with my understanding? Thank you!

[YuePanEdward]

Thanks a lot for your interest in our work. In my implementation, we have two types of samples:

1. the close-to-surface samples (indicated by the parameter surface_sample_range_m, which is sampled in the range [-surface_sample_range_m, surface_sample_range_m] along the ray from the endpoint)
2. the free space samples (indicated by the parameters free_sample_begin_ratio and free_sample_end_dist_m, which is sampled in the range [-free_sample_begin_ratio * ray_distance, free_sample_end_dist_m] along the ray from the endpoint).

Note that the sign is opposite from the SDF label (+: behind the surface, -: in front of the surface) here. This implementation is just for convenience since the free space samples may also lie in the close-to-surface region according to the current implementation. You may also split the free space into two parts ( [-free_sample_begin_ratio * ray_distance, -surface_sample_range_m] and [surface_sample_range_m, free_sample_end_dist_m] ) but I think the results will not have a big difference.

[DeepDuke]

@YuePanEdward Thanks for your kind explanation. I previously thought + is in front of the surface...