relax: 💤 relaxation Labelling to refine edge detection 💤.

This is an application of a niche algorithm named relaxation labeling to refine edge detection probabilities.

In the normal formulation relaxation is stated as a labelling problem. For an image we may wish to label each pixel as belonging to an edge, or being part of a region.

For example, we would normally have pixels as the objects, and the labels could be 'edge' or 'not edge'. Associated with each a_i is a set of measurements X_i, and also associated with each a_i is the contextual information of the other objects, which will depend on the current labels. Ideally, we would like to assign each object one label, but this will not in general be possible, and so we will have, for each object a set of probabilities of each label that logically sum to 1.

The contextual information is expressed by compatibility coefficients:

r([a_i:l_j], [a_k:l_l])

The value of r is a measure of how compatible it would be to label a_i with l_j and a_k with l_l. There will be one compatibility coefficient for each possible labelling of each pair of objects in the set.

It is an iterative process by defining compatibility coefficients and the region it is possible to refine the edge probabilities converted from intensities.

If you want to read more about it, here is a source better describing what is going on: Link

Building and Running

To install all the dependencies run:

pip install -r requirements.txt

Then you can just do e.g.:

python3 relax.py -d imgs/test.png -o test1.png -i 3 -c 2 0.5 0.5 2 -s 3 -v 1
-d Data input
-o Data output
-i Number of iterations
-c Compatibility matrix
-s Shape of the region matrix
-v Visualize the result

and voila!

Or a different compatibility matrix and a shape produces:

python3 relax.py -d imgs/test.png -o test2.png -i 3 -c 2 0.5 0.5 0.5 -s 5 -v 1

Credits

• All code was written by Martin Ferianc in 2017.