I have $n$ curves in the 3d space, which I represented with a certain amount of points. (That is, for every curve $i$, there is a vector $v_i$ with $m$ points which belong to the curve)
My goal is to make a regression based on different geometrical properties of this curves. Which parameters can I use?
I have thought of length, centroid, (mean) curvature, but then I'm out of ideas. I'd appreciate any suggestion, the more "independent" the measures the better (to avoid collinearity in the regression).
Thank you in advance!
P.S. the curves here are supposed to represent axons, so if you have any reference on how this is done in bioengineering I'd appreciate it!
A few more ideas, in addition to the ones you mentioned:
Direction. Fit a straight line to the curve, and then look at the direction of the line. Direction can be expressed by two angles.
Moments of inertia. These measure the "distribution" of matter in the curves, in some vague sense.
Some things with bounding boxes. For example, the ratio of the arclength to the diagonal of the bounding box gives some indication of how "bent" the curve is.
Similar things with minimum bounding sphere. The diameter of the sphere is a measure of the size of the curve. Ratio of diameter to arclength is a measure of straightness.
Total turning angle. Add up the turning angles at each point.
Some of these are measures of curvature, in some sense. Since your curves are really just polylines (strings of points), real curvature is a bit hard to estimate.