Find out if overlaying polyline matches polygon centerline in qgis

Question

I have a polygon and a polyline and I need to find a scientific way of how close that polyline is to the actual polygon centerline. Is there any way of doing this in qgis? Any extensions, models, algorithms would be helpful!

Thoughts about this in my mind so far:

• Calculate centerline of polygon and then calculate distance of each point to nearest point of the other polyline. Problem: Calculating Voronoi polygons in qgis is crashing on my machine.
• Buffer that polyline, substract from that area the given polygon to calculate the difference area. The smaller, the better. Problem: I have no attributes in that polygon to distinguish between classes and so thin roads will give a different result than broad roads.
• Do a negative buffer so that the area is actually really small and clip it with the polyline. Same problem as above.

Answer 1

Taking into account your trouble with vector solution I suggest using approximate raster based technique. I’ll use ArcGIS (no QGIS) but most likely there are same tools in QGIS

Dissolve your polygons and convert them to polylines. Calculate Euclidean distance to lines using small cell size. The smaller it is, the more accurate result can be achieved. Clip raster using original polygons:

Calculate slope of above raster and select 'flat' areas. In my example I used <=40 degrees:

From here there are multiple paths to follow. You might want to clip ‘flat’ areas raster using small negative buffer first.

1. Convert result to points
2. Place points at the regular interval on existing centrelines
3. Find distance to nearest flat point for each centreline point
4. Summarise distances per street segment.

Picture below shows regularly placed points labelled by their distance to nearest ‘flat’ point.

Expect trouble at intersection and very narrow streets