Polygon Shape Similarity using QGIS

There is a script available at https://github.com/anitagraser/QGIS-Processing-tools/blob/master/1.1/scripts/hausdorff_distance_pairwise.py

It needs to be updated by changing the following line:

from processing.core.VectorWriter import VectorWriter

to

from processing.tools.vector import VectorWriter

Save the script in .qgis2/processing/scripts/hausdorff_distance_pairwise.py

Now when you open QGIS and the Processing Toolbox you can search for 'hausdorff'

Add your two layers to compare

Open the script and set the options - you need some key fields so the correct features can be compared to each other.

Once the tool has run the output file has a new field - HAUSDORFF - added to it with the similarity score. Smaller is better.

I found the script worked with polylines rather than polygons and you can use the Vector > Geometry Tools > Polygons to Lines tool to convert.