heatdiff 0.1.1

A package for image processing using the heat semigroup.

Heatdiff

The aim of this initial release is to demonstrate how the heat semigroup can be used as a lossy compression tool for image processing, in particular, for image corruption and restoration.

We also demonstrate that the heat semigroup can be used for image compression, via its use as a kernel in a weighted K-Means algorithm.

In addition, we will demonstrate that explicit diffusion equations can also be used as lossy compression for images. One can view this method as a 'learning free' denoising diffusion model. We replicate the experiments for the heat semigroup with diffusion equations, using their appropriate analogues.

You can visualise the heat semigroup and the diffusion process and examples can be found in the visualisation notebooks.

In the future, we aim to investigate further topics such as: regularised image restoration; lossless compression; and the integration of machine learning tools amongst others.

Installation

pip install heatdiff

Examples

The following notebooks demonstrate the most relevant features:

• Heat Semigroup
• Diffusion Process
• Visualising the Heat Seimgroup
• Visualiosing the Diffusion Process