MSF (Medial Skeletonization Flow)

A realization of Mean Curvature Skeleton

UCL COMP0119: Acquisition and Processing of 3D Geometry Project

Reference: Tagliasacchi, A., Alhashim, I., Olson, M. and Zhang, H. (2012), Mean Curvature Skeletons. Computer Graphics Forum, 31: 1735-1744. https://doi.org/10.1111/j.1467-8659.2012.03178.x

Project Structure

src: Source code of the implementation;

examples: Some example skeletons generated by our implementation;

docs: Paper and some files;

models: Some meshs used for testing and development.

Examples

How to use

If you want, you can adjust the parameters in src/config.json.

# Assuming you are in the root of project
from src.msf import MSF

# Initial a MSF Instance
msf = MSF()

# Load a mesh
msf.load_mesh("../models/armadillo.obj")

# Let's iterate! Of course you should repeate it.
msf.iterate() # msf.iterate(50) # or iterate 50 rounds directly

# Then see the skeletons in the latest folder of the `result` folder.

Parameter Explaination

Set the parameters in src/config.json

• wL: wL in the paper;

• wH: wL in the paper;

• wM: wL in the paper;

• use_dynamic_scale: If true, then allow adjusting scale between iterations. The scale will change between scale_min and scale_max repeatedly at intervals of scale_delta, which can speed up convergence;

• scale: The $\varepsilon$ in the paper will be scale multiply the diagonal length of the mesh's bounding box;

• scale_min: Only be used when use_dynamic_scale=true;

• scale_delta: Only be used when use_dynamic_scale=true;

• scale_max: Only be used when use_dynamic_scale=true;

• scale_fix: Be used to fix vertices;

• alpha: The $\theta$ in the paper;

• use_Laplacian_smoothing: If true, then use Implicit Laplacian smoothing before mesh optimizing, which is critical to produce a complete skeleton instead of meso-skeleton;

• smooth_lam: $\lambda$ in the Implict Laplacian Smoothing (step size);

• smooth_it: The iteration number of the Implict Laplacian Smoothing;

• use_reconstruction_in_voronoi: If true, use mesh reconstruction before calculating Voronoi poles, which can produce a better approximation of medial axis;

• k_voronoi:, Parameter in mesh reconstruction, only be used when use_reconstruction_in_voronoi=true, which means using the eigen vectors corresponding to the k_voronoi` smallest eigen values to perform reconstruction;

• use_reconstruction_in_skeletonization: If true, use reconstructed mesh in skeletonization, which can ignore details on the mesh that do not contribute to the skeletonization;

• k_skeleton: As k_voronoi, only be used when use_reconstruction_in_skeletonization=true;

• lsqr_args: Parameters for scipy.sparse.linalg.lsqr. Generally not modified.

Algorithm Procedure Code