Not exactly science, but through it is a good place to put it.
For a calculus of variations class I took, we had to do a project of sorts. I choose to do it on the Mumford Shah functional. Below is the paper and a Octave and C++ implementation of the Simplified Mumford Shah functional. The Octave version is very slow which prompted me to do the C++ version later when I was done with the class. I plan on improving the C++ version while reading a data structures book I picked up, so if it still isn't fast enough for you come back later to see if there are any changes.
If you don't know what the Mumford Shah is, you can read the paper . I found it to be pretty interesting and thought I would share.