Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures

This repository provides an example application that implements the curvature estimators on oriented point clouds presented at Symposium on Geometry Processing 2023, Genova, Italy, July 3-7:

Jacques-Olivier Lachaud, David Coeurjolly, Céline Labart, Pascal Romon, Boris Thibert, Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures, Comput. Graph. Forum, 42(5), 2023.

Authors of the code:

• Jacques-Olivier Lachaud
• David Coeurjolly

Building

Once cloned, proceed as follows on Linux/macos:

mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j 8

It will automatically fetch and install the dependencies polyscope and eigen.

Usage

Computing curvatures of point clouds approximating simple shapes

./curvatures

Run the program with a GUI that allows you to generate point clouds approximating simple shapes (sphere, torus, cube, dodecahedron).

Computing curvatures of an oriented point cloud (given as text file)

./curvatures ../data/bearded-man-xyz-nxyz.pts

Text file should be composed of lines of the form x y z nx ny nz for each point, determining the coordinates (x,y,z) of each point and the components (nx,ny,nz) of its oriented normal vector.

Computing curvatures of an oriented point cloud (given as a wavefront OBJ file)

./curvatures ../data/bunnyhead.obj

The OBJ file should contained the vertices as v x y z and normal vectors as vn nx ny nz.

Using the interface

• Shape generation

  • Sphere generates a sphere of size R with N points
  • Torus generates a torus of great radius R and small radius r with N points
  • Cube generates a cube of size R with N points
  • Dodecahedron generates a dodecahedron of size R with N points
  • InputFile generates a set of points from the given input file
  • all shapes can be perturbated in position (parameter x) and in normals (parameter xi)
  • you may toggle between fast display (better when N > 5 millions) or nice display

• Curvature computation

  • Curvatures computes all curvature information (mean, Gaussian, principal curvatures and directions.
  • parameter K is the chosen number of nearest neighbors
  • parameter L is the chosen number of triangles (only for Uniform generation)
  • you may choose for triangle random generation methods among Uniform, Independent, Hexagram, Avg-Hexagram (see paper for details)
  • method Avg-Hexagram is the fastest, very accurate while staying robust to noise
  • parameter W balances between the normal to the points and the average normals of its neighbors to define the local sampling plane, 0.5 works well.

• Information

  • the total computation time of curvatures is displayed
  • l2 and loo errors are displayed for Sphere and Torus shape.

Replicate paper results

We provide additional datasets to be able to reproduce the paper results. To exactly get the paper visual after clicking on Curvatures the button, for each interested curvature quantity, change polyscope's colormap from viridis to coolwarm and use the clamping values given in the following table (to specify the colormap min/max values, just CTRL-click to the min/max text area for the selected curvature quantities).

Pointcloud	Paper figure	Params	curvature colormap clamping ranges
./curvatures ../data/goursat/goursat_025000.pts	Fig6	K=50, L=100	Mean: [-0.107, 0.345], Gaussian: [-0.034, 0.119]
./curvatures ../data/torus/torus_025000.pts	supplem Fig2	K=50, L=100	Mean: [ 0.125, 0.32], Gaussian: [-0.125, 0.0625]
./curvatures ../data/goursat/goursat_025000.pts	supplem Fig3	K=50, L=200	Mean: [-0.107, 0.345], Gaussian: [-0.034, 0.119]
./curvatures ../data/torus/torus_025000.pts	supplem Fig4	K=50, L=200	Mean: [ 0.125, 0.32], Gaussian: [-0.125, 0.0625]
./curvatures ../data/anisotropic/goursat-filter.pts	supplem Fig5	K=50, L=200	Mean: [-0.107, 0.345], Gaussian: [-0.034, 0.119]
./curvatures ../data/anisotropic/torus-filter.pts	supplem Fig6	K=50, L=200	Mean: [ 0.125, 0.32], Gaussian: [-0.125, 0.0625]
./curvatures ../data/lidarSim/goursat-lidar.pts	supplem Fig5	K=50, L=200	Mean: [-0.107, 0.345], Gaussian: [-0.034, 0.119]
./curvatures ../data/lidarSim/torus-lidar.pts	supplem Fig6	K=50, L=200	Mean: [ 0.125, 0.32], Gaussian: [-0.125, 0.0625]

Examples

Mean curvature (Avg-Hexagram, N=20)

Mean curvature on torus (N=10000, N=20)	First principal direction	Second principal direction