You really strengthened your membership in the information theory fraternity during that summer of 2006 in Lausanne, didn’t you? One result of the connections you developed then was that Sonia and I were able to enjoy the wedding of Dinkar Vasudevan last week in Delhi. It was a good event. Even though Dinkar and I had never met before, he knew exactly who I was when he received us – thanks to you.
That summer of 2006 was good for me as well. Getting to know Nikos Paragios, getting going with variational level set methods, and doing a bit of work on medical imaging turned out well. I ended up using variational level set methods in my recently completed Ph.D. thesis: to develop a new algorithm for the machine learning problem of supervised classification, which I termed the geometric level set (GLS) classifier.
Typically, level set methods are employed when the data is on a pixel or voxel grid. With the GLS classifier, I broke away from that mold and allowed the data to be in any general Euclidean feature space. In the final section of my thesis, I suggest that variational level set methods and other similar geometric partial differential equation-based techniques be applied not in pixelized spaces, nor even in general Euclidean spaces, but in the space of probability distributions with associated information geometry. Any thoughts?