Level set machine learning

Level set image segmentation with velocity field from machine learning methods

Example 1	Example 2

Installation

Linux

Install via pip:

pip install lsml

MacOS and Windows

Not on pip; install locally:

# Clone the repo
git clone git@github.com:notmatthancock/level-set-machine-learning.git
# Change working directory to the cloned repo
cd level-set-machine-learning
# Install via pip locally
pip install -e .

Description of the method

In the standard level set segmentation approach, the boundary of the approximating segmentation is given by the zero level set of some scalar field u (also called the "level set function"), and the movement of zero level set of u is prescribed to move in the normal direction with velocity ν, which usually takes into account underlying image information.

This prescribed movement is summarized in the following PDE [1]:

u_t = v ||Du||₂

In this extension of the level set method method [2], the velocity field v is learned from data via machine learning regression methods, rather than fixing the velocity function a priori based on expected image appearance (e.g., assuming object boundaries being defined by strong image gradients).

[1]: Malladi, Ravi, James A. Sethian, and Baba C. Vemuri. "Shape modeling with front propagation: A level set approach." IEEE transactions on pattern analysis and machine intelligence 17.2 (1995): 158-175.

[2]: Hancock, Matthew C., and Jerry F. Magnan. "Lung nodule segmentation via level set machine learning." arXiv preprint arXiv:1910.03191 (2019). https://arxiv.org/abs/1910.03191

Examples

See examples directory for the method illustrated on some synthetic data.