Perona-Malik Solver

This package includes 3 three different solvers for the Perone-Malik equation and an optimizer for retrieving the best timestep (dt) and lambda (ld) for different images. Users are also able to change the g function (a variable function within the Perona-Malik equation).

The Perona-Malik equation is used to smooth images and is described in the following link.

http://people.maths.ox.ac.uk/trefethen/pdectb/perona2.pdf

Although the equation is good at conserving the edges initially, at long time scales it starts to ignore them and begins to behave like the heat equation. This can be seen when opening Results/animated_dog.gif.

Prerequisites and Installing

First clone the following github.

 git clone https://github.com/SABS-R3-projects/Perona-Malik.git

Then go to the Perona-Malik directory you just cloned and create a virtual environment using pip or conda. The following shows how to do it with pip.

python3 -m venv my_env

Then activate the environment and install the requirements.

source my_env/bin/activate
pip install -r requirements.txt

All prerequisities are in the requirement.txt file.

Getting Started

The package consists of two parts.

1. Smoothing of a picture (smoothpicture.py)
2. Optimize for the best variables to smooth picture (opt.py)
3. Creating an animation showing the imaging smoothing (animation.py)

To smooth your picture you open the smoothpicture.py and manually insert the path to your image and run the code. This will result in three different smoothings of your picture from three different solvers (allowing you to chose the best one). Additionally, information about the smoothing process is also saved. You are also given the option to change the time step (dt), lambda (ld) and g function.

The three solvers consists are:

1. a finite difference (FD) solver (fd_solver),
2. a FD written in numpy solver (numpy_solver),
3. and an anisotropic lib solver (at_lib_solver)

To optimize for the best dt and ld for your image open opt.py. This will run, but will not optimize properly due to the nature of the similarity function in ld and dt space being very irregular.

To create an animation of the image smoothing to open animation.py and manually insert the path to your image and run the code. This will create a gif of the smoothing using the numpy solver. WARNING: This script takes around 5 minutes for a large image.

All results are saved in the Results folder.

Running the tests

Run tests by running test_image.py

Authors

• Brennan
• Itai
• Simon
• Tobias

License

This project is licensed under the BSD 3-Clause License.