Classifying 2D shapes by the smoothness of their boundaries
Fourier shape descriptors are quite easy to use and can do well to differentiate smooth objects from jagged ones. Imagine a polar coordinate system with the origin at the centroid of the 2D object. Store a vector of $r$ values as $\theta$ varies in $[0, 2\pi)$ where $r$ is the distance of the boundary from the centroid at each fixed angle $\theta$. Next, take the Fourier transform (FT) of this vector of $r$ values. If the boundary of the 2D object is jagged, the FT will have lot of non-zeros even at high frequencies. On the other hand, imagine doing this with a perfectly smooth circular object---you will end up with a vector of constant $r$ values whose FT is simply a non-zero DC term.

The DFT vector can be used as a feature vector.

See slides 16-20 in this pdf:
http://homepages.cae.wisc.edu/~ece533/project/f06/karrels_ppt.pdf