I need shape (object contour) descriptors that are invariant to scaling and parallel wrapping, but not invariant to rotation. Something like Fourier descriptors. I want to make machine learning classifier (like SVM or ANN) that can automatically detect angle of object rotation. Object is simple binary blob, like human hand (binarized). Rotation angles interval is like (-45,45).
In my opinion you don't need ML algorithms for such task.
To caracterize the location of the angles you can compute the freeman chain code on the contour and then analyze when the deviation occur.
Or simply draw a circle centred on a pixel of the contour and then analiyze the content of that circle (if it corrspond to a straight line or a curve) while crossing all pixels of the contour.
https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/29518/versions/1/screenshot.gif
Your question is challenging from a design point of view.
A simple construction that could help you was to look at the unit normal vector (the direction) to the shape at every point on the shape contour. This I hope will be invariant to translation and scaling but assuming that you have a registration between the two shapes you can find the rotation by taking an average of the angles between the unit normal vectors at all points.
This method will breakdown for the shapes with rotational symmetry but I do not know whether you would be able to distinguish them easily with some other descriptors.
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