Voxel downsampling with geometry preservation

How far can bigpointcloud_001.ply be reduced before its geometry starts to go? Measured, not eyeballed.

Input

11,357

points, with normals + RGB

Native resolution

0.140

mean nearest-neighbour spacing

Safe voxel

0.210

8,832 pts — 78% kept

Aggressive voxel

0.279

5,592 pts — 49% kept

Method

Voxel size is chosen against an error budget rather than by guesswork. Every candidate is scored by how far the surface actually moved — the distance from each original point to the nearest kept point — plus how much the normals rotated and whether the bounding box shrank. The natural yardstick is the cloud's own nearest-neighbour spacing (0.140): a downsample that perturbs the surface by less than that has not degraded it beyond the noise the original sampling already carries.

safe — largest voxel whose 95th-percentile error stays under one NN spacing
aggressive — largest voxel whose mean error stays under one NN spacing

Voxel-size sweep

voxel	× NN	points	kept	mean err	RMS	p95	Hausdorff	normal dev	bbox shrink
0.070	0.5×	11,320	99.7%	0.0002	0.0022	0.0000	0.0409	0.1°	0.00%
0.105	0.7×	11,138	98.1%	0.0015	0.0080	0.0000	0.0788	0.4°	0.00%
0.140	1.0×	10,705	94.3%	0.0058	0.0179	0.0540	0.0952	1.4°	0.18%
0.210	1.5×	8,832	77.8%	0.0315	0.0507	0.0990	0.1598	5.7°	0.28%	safe
0.279	2.0×	5,592	49.2%	0.0829	0.0960	0.1536	0.2145	13.3°	0.35%	aggressive
0.419	3.0×	2,620	23.1%	0.1467	0.1567	0.2357	0.3530	23.0°	1.15%	geometry degrading
0.559	4.0×	1,511	13.3%	0.1999	0.2139	0.3175	0.4801	28.3°	1.50%	geometry degrading
0.838	6.0×	655	5.8%	0.3102	0.3330	0.5034	0.7154	33.4°	4.69%	geometry degrading
1.117	8.0×	385	3.4%	0.4017	0.4271	0.6343	0.9313	39.4°	11.05%	geometry degrading
1.676	12.0×	163	1.4%	0.5899	0.6305	0.9446	1.2392	45.3°	15.01%	geometry degrading

Geometry holds to about 0.28 — half the points, surface displaced 0.083 units on average (0.4% of the 20.7-unit bbox diagonal), normals within 13°. Past 0.42 it degrades quickly: normals swing 23°+, and by voxel 1.1 the bounding box itself has lost 11%, meaning thin structure is being erased outright rather than merely thinned.

Points kept, surface error and normal deviation versus voxel size — Point count falls off a cliff well before the error curves rise steeply — the region left of the green line buys a large reduction almost for free.

Visual comparison

Original, safe voxel, aggressive voxel and random baseline, in two views — Original · voxel 0.210 · voxel 0.279 · random subsample at the same budget. Colours are the cloud's own RGB; point size is identical across panels, so density differences are real.

Open the interactive 3-D viewer → (rotate/zoom, original vs downsampled side by side)

Why voxel, not random

method (5,592 pts)	mean	RMS	p95	Hausdorff	normal dev
voxel 0.279	0.0829	0.0960	0.1536	0.2145	13.3°
random subsample	0.0860	0.1261	0.2310	0.6478	12.9°

Mean error is nearly the same; the tails are not. Random subsampling is 50% worse at p95 and 3× worse at the Hausdorff bound — it thins uniformly-dense regions and leaves holes wherever the dice fall badly. Voxel downsampling caps the worst-case gap by construction, and averages positions, colours and normals within each cell instead of picking a survivor.

Per-point error heat maps for the two voxel sizes and the random baseline — Original points coloured by distance to the kept surface, shared scale. Voxel error is dim and uniform; the random baseline is speckled with bright hotspots — the same average, a much worse worst case.

Files

bigpointcloud_001.ply — original, 11,357 pts (0.58 MB)
bigpointcloud_001_voxel0.210_safe.ply — 8,832 pts (0.45 MB)
bigpointcloud_001_voxel0.279_aggressive.ply — 5,592 pts (0.29 MB)
sweep.csv — full metric table
voxel_downsample.py — the script that produced all of this

Normals and colours survive the downsample (averaged per voxel), so the outputs drop straight into a PointNet++ pipeline that expects them.

Reproduce

python voxel_downsample.py --input bigpointcloud_001.ply — auto-selects both operating points. Override with --voxel 0.28 or --target-points 3000. Needs open3d, numpy, matplotlib, and optionally plotly for the interactive viewer.