There are many well defined measures for many basic geometrical objects such as rectangularity (area coverage of minimum bounding rectangle), triangularity (area coverage of minimum enclosing triangle), circularity ratio (area/perimeter$^2$), etc.
I am looking for relevant measures to classify C-shaped objects (or similarly U-shaped objects). By classify I simply mean to assign a membership to the set "C-shaped objects" if the measure (or aggregate of measures) reach a certain threshold. The measure itself together with the threshold level will thus define what a constitutes a "C-shaped object".
None of the articles I have found on shape measurements and feature extraction ever mention C-shapes. I know that defining a C-shape might be difficult and rather subjective, and therefore a single measure might be difficult to construct.
If no single measurement that can be used to describe C-shapes exists, maybe there is a good aggregate of measures that can help in classifying C-shapes?
I know that various forms of template matching methods could do the trick, but I am looking for a measure that is not reliant on a model and less computationally expensive.
The only idea I could come up with is some kind of radial density distribution (see pic below). But I am unsure on how to utilize the density information to create a relevant measure with good discriminatory properties.
Any input would be helpful.