Evaluate the smoothness of curve

I have a binary immage, like in the figure, with different curves which I've skeletonized and from which I have the coordinates xy.

I was wondering if there is a way to evaluete how intese the curvature is: more like a circle, an hyperbola, a corner. For exemple by defining a parameter which is bigger (or smaller) regarding the curvature.

Thank you

Answer 1

[darova]

I used find() function to exract all white pixels. Reduced number of points and interpolated them to get smooth curve (look HERE)

Once i found position (x,y) of pixels i had to sort them: i calculated angle for each pixel and sorted data by angle

I used dot product (angle between radius and curve )

→

And made a system of equations ( - intersection points )

Look also here: Radius of curvature

[Sebastian Ursarescu]

Thank you darova for the answer it is very interesting. However I have a randomic line with different curvatures and different orientations, how can I set a reference system a priori? Anyway it is enough to determinate if the curve is endgy.

[darova]

Did you try the script i attached?

[darova]

still waiting

[Sebastian Ursarescu]

I still have some issues chosing the interpolation method and the number of interpolated elements but your answer is very usefull. Thank you

[darova]

happy to help

you are welcome

[darova]

spline() doesn't work? What kind of problems do you have

[Sebastian Ursarescu]

All interpac's methos work. The results are pretty similar. Using few points the line is a little bit rude, using too much points too, usinig 1/5 of the initial points seems to work very good. The point is if the curve is too sharp it cuts it a little bit the edge in some cases. Anyway, from the tries I made until now it is not a big deal.