HBS - Harmonic Beltrami Signature

This is a Python library for computing Harmonic Beltrami Signature(HBS). It provides a set of tools for boundary conditions, mesh generation, conformal welding and other mathematical problems, particularly suited for numerical computations in complex analysis.

Reference

This implementation is based on the paper:

Harmonic Beltrami Signature: A Novel 2D Shape Representation for Object Classification
Chenran Lin, Lok Ming Lui DOI: 10.1137/22M1470852

Installation

Install directly from PyPI:

pip install hbs

Or install from source:

1. Clone this repository:

   git clone https://github.com/ChanceAroundYou/hbs_python.git

2. Install dependencies:

   pip install -r requirements.txt

Main Modules

• hbs.py: HBS algorithm for computing HBS and recontructing shape from HBS
• conformal_welding.py: Conformal welding algorithm implementation
• mesh.py: Mesh generation and processing
• utils/:
  • boundary.py: Boundary processing tools
  • geodesic_welding.py: Geodesic welding
  • mobius.py: Möbius transformations
  • poisson.py: Poisson integral implementation
  • tool_functions.py: Utility functions
  • zipper.py: Zipper algorithm implementation
• qc/: Quasiconformal mapping algorithms
  • bc.py: Beltrami coefficient computation
  • lsqc.py: Least squares quasiconformal mapping algorithm

Usage Example

Compute HBS from image

from hbs.utils.boundary import get_boundary
from hbs import get_hbs

# Boundary points extraction
# 
# we don't actually restrict the method of boundary extraction,
# but this package provides a simple implementation as follows
img_path = 'img/example.jpg'
circle_point_num = 1000
bound = get_boundary(img_path, bound_point_num)

# HBS computing
# 
# it requires boundary points arranged in clockwise order as input, in `np.complex`
density = 0.01
bound_point_num = 250
hbs, hbs_mapping, cw, disk = get_hbs(bound, circle_point_num, density)

Reconstruct shape from HBS

from hbs import reconstruct_from_hbs

## `disk` must be a DiskMesh corresponding to give `hbs`
bound, _, _, _ = reconstruct_from_hbs(hbs, disk)

Compute conformal welding from image

from hbs.utils.boundary import get_boundary
from hbs.conformal_welding import get_conformal_welding

# Boundary points extraction
img_path = 'img/example.jpg'
bound_point_num = 250
bound = get_boundary(img_path, bound_point_num)

# Conformal welding computing
# 
# it also requires boundary points arranged in clockwise order as input, in `np.complex`
cw = get_conformal_welding(bound)

Please also refer to example.ipynb

Dependencies

• NumPy
• SciPy
• Matplotlib
• Opencv

Contributing

Contributions are welcome via pull requests.

Code Author

• Chenran Lin