Norman MacLeod of the The Natural History Museum in London has put a series of articles online about quantitative analysis of paleontological data. These describe how shapes can be quantified, compared and classified mathematically. Link here.
The most interesting technique is "Elliptic Fourier Analysis". Using this technique any shape, even the most complex one, can be described by a series of 2-dimensional harmonics. This is demonstrated by this very cool picture:
|The Centre Cannot Hold II: Elliptic Fourier Analysis by Norman MacLeod|
More background literature - The morphometric techniques are explained in other documents as well:
- A very short introduction to circular harmonics.
- The morphometrics website of Stony Brook. It also has a long list of morphometric software packages.
- A personal site with morphometric research (used in archaeology) and some software.
Other relevant image software - I've found more interesting software that could be useful for my project but I'll only investigate that further if SHAPE does not work as expected:
- Potrace and autotrace : these software packages translate a bitmap picture into a scalable vector drawing. I don't know how easy it would be to do fourier analysis on their output. (E: Thanks anyway for the tip!)
- PyNGL : a Python language module used to visualize scientific data. A very interesting software package but it has no image processing functionality. But it might be useful for GPS mapping plots.
- SHTOOLS : an archive of software that can be used for spectral analyses on the sphere. This may do the job of spherical harmonic analysis. But it looks too powerful and too complex for my purposes.
- Fiji and ImageJ : image processing software written in Java. Fiji has a GUI with menus.
- SonEnvir : a research project that investigates sonification in a number of scientific disciplines. It uses SuperCollider.
- MAX/MSP was mentioned as useful software. In the meantime I realize that PureData is a branch of this development and that it has fourier transforms. So maybe I'll have to dive into that too.