# Shape measure for C-shaped objects

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.