LaplaceMeshSmoothing

This repository is about Laplacian filtering in the context of mesh denoising. The main contributions are

• compute the mean curvature of a mesh by Uniform Laplace and Cotangent Laplace respectively.
• compute mesh's Gaussian curvature.
• reconstruct the mesh with k eigenvectors.
• implementation of explicit and implicit Laplacian mesh smoothing.

More details can be found in this report.

Requirements

This code has been test under python 3.6.12, and the libraries I used as following,

• open3d==0.12.0
• trimesh==3.9.1
• numpy==1.19.2
• matplotlib==3.3.2
• argparse==1.4.0
• scipy==1.5.4

File structure

• data the data for testing our algorithm.
• docs the report of my experiment.
• src includes all of the source code.
  • part*.py in this files, I've done several experiment (check the report, you'll understand what I've done).
  • tools floder is a package I build to implement core algorithm
    • LaplaceOperator.py - the core code
    • tools.py - some tool function, like show mesh in open3d gui

Easy using

Fistly, you should import the nessary module.

import trimesh
import tools.LaplaceOperator  # our python package

For computing mean curvature matrix H and Gaussian curvature K of the mesh, you can do:

tm = trimesh.load(mesh_file_path)  # load mesh
Obj = LaplaceOperator.LaplaceOperator(tm)
H = Obj.getMeanCurvature(mode='uniform')  # also, you can use 'cotan'
K = Obj.getGaussianCurvature()

For spectral analysis which reconstruct the mesh with k eigenvectors, you can do:

newtm = Obj.decompose(k)  # k is the num of eigenvectors you want

For mesh smoothing, do following

# lr is the step size for every iteration. maxIter is the number of iteration
# you can also change mode to 'explicit' to do smooth
newtm = Obj.smooth(lr=step_size, maxIter=iteration, mode='implicit')

Experiment

You can read the code of my experiments to find out the usage with more detail.

The first experiment is about Uniform Laplace mean curvature and Gaussian curvature.

# Argument '--obj' is used to indicate the 3D object we use, and the mesh I use here can be found in data folder.
# and use'--mode mean' is to show the mean curvature.
python part1.py --obj lilium_s.obj --mode mean
python part1.py --obj plane.obj --mode mean
 
# Argument ‘--mode gaussian’ is to show the mean curvature.
python part1.py --obj plane.obj --mode gaussian
python part1.py --obj lilium_s.obj --mode gaussian

And then for the mean curvature by Cotangent laplace

python part3.py --obj plane.obj
python part3.py --obj lilium_s.obj

As for doing spectral analysis,

# Use '--k' to set the number of eigenvectors
pyhon part4.py --k 60

In terms of the explicit Laplacian mesh smoothing,

# '--step_size' is to set the step size lambda of iteration
# '--iteration' is to set the number of iteration
python part5.py --obj fandisk_ns.obj --step_size 1e-5 --iteration 50

To see the performace of the implicit Laplacian mesh smoothing,

# '--step_size' is to set the step size lambda of iteration
# '--iteration' is to set the number of iteration
python part5.py --obj fandisk_ns.obj --step_size 1e-5 --iteration 50

Some samples

For spectral analysis, if you run part4.py, finnaly you will get as following.

Besides, the picture below shows the results of the explicit Laplacian mesh smoothing.