MorseMesh

This repo provides code for working with discrete Morse theory on meshes. It contains functions for Morse theory based edge detection and segmentation, a cluster based segmentation using the Morse theory based edges as well as a graphical user interface to use the methods. Jupyter notebooks are provided for pipelining many parameter combinations. The cluster segmentation is recommended for the graphical user interface, while the Morse segmentation is recommended for the pipline approach.

Contents

• Requirements
• Quick Guide
• Visualization
• License
• Authors
• Contact

Requirements

• Python 3.x (3.9 definitely works, probably also before)
• plyfile (pip install plyfile or: https://github.com/dranjan/python-plyfile)
• (required for gui) pyqt5
• (required for gui) vtk
• (optional for gui) qdarkstyle

Quick Guide

To start the GUI Tool run:

$ python3 gui.py

You need: A manifold like mesh (ply file) with a scalar function given in the quality property of the vertices (e.g. curvature values).

1. Open GUI Tool and load the mesh under File in
2. Press Compute Morse complex under Compute
3. Use sliders to get visually well recognized edges
4. Press Morse Segmentation Method (recommended for pipline) or Cluster Segmentation Method (recommended for GUI) under Segmentations
5. Save segmentation (label txt) under File or re-run with different parameters

1. Load ply file

Select Load ply under the File menu. Note that you need a .ply file that contains a function value under quality. Please ensure that your mesh has a manifold-like structure, i.e. especially there should be no edges with more than 2 adjacent triangles. Holes or boundaries in the mesh are no problem algorithmically, but depending on the application it might make sense to fill them. For mesh preprocessing, it is recommended using GigaMesh.

2. Compute Morse Complex

Compute the Morse complex for a loaded mesh from the Compute menu under Compute Morse complex.

3. Determine edges

You can now use the two sliders in the bottom to determine the edges correctly. Just move them and the mesh will be updated automatically.

The upper slider determines a strong threshold which includes all edges that exceed this threshold, while the lower slider determines the weak threshold, which adds only edges that are below the strong threshold, but above the weak threshold, hence refining the result a bit.

Under advanced edge detection in the sidebar you can select more edge settings, but the only ones that might be interesting though are the "Separatrix density* which could be set to All or Reversed and the Extremal line type, which can be switched between ridges and valleys.

4. Segmentation

Use the Morse segmentation method or the Cluster segmentation method in the Segmentations menu. The cluster segmentation is recommended for the GUI, while the Morse segmentation is recommended for the pipeline.

You can change the segmentation parameters in the sidebar under Morse segmentation or Cluster segmentation.

5. Save result

You can repeat the segmentation until you get a satisfactory result. The segmentation can be saved as a label.txt file in the File menu.

Visualization

There are different ways to visualize the label txt files: 1. Label .txt files can be visualized in the GUI tool using the Load labels txt function from the File menu 2. Label .txt files can be visualized in GigaMesh using File - Import - Import Labels (confirm YES when asked if the vertex is in the first column and select Labels-Connected Comp. on the right to see the results.)

License

The MorseMesh source code is released under the GPL License

Authors

Developed by Jan Philipp Bullenkamp.

Conforming Morse Complexes by Theresa Häberle.

Contact

Jan Philipp Bullenkamp: jan-philipp.bullenkamp (at) informatik.uni-halle.de