In medias res

It is an important question to ask. Why is image segmentation particular? Well, it is not interesting in particular, but it belongs to a very special category of problems. Mathematics is the framework that aims to describe the world. Every exact science uses mathematics as its way of description. Basically (and I am sure, that lots of people would argue on this) in every exact science you define a set of axioms, and try to build a system up on them. These axioms come from the experiences. They can either be results from a particle accelerator, or from the stack market.

Now, your job is simple, find the axioms and build a system up on them. It is here that it becames difficult. A system is based on a set of rules. In mathematics they are called theorems. You state a theorem and you try to proove it. In fact wouldn't it be really cool if you could just build a computer, give it any set of axioms and then have it build the system up all by itself? Unfortunately it is not as easy as this.

The proof of  unprovability

In the begining of a century there was a mathematitan-philosopher called Godel, who ruined all the hopes of the classic mathematics. It is know because of his contribution, that given any set of axioms, doesn't matter how complete, there exist theorems that are true but you cannot prove that they are true. That means that you cannot find all the rules of the world and what is even more inconvinient: given a theorem, you can't prove, you can never know wether it is only extraordinarily difficult, or unprovable.

Trivia

Given Godel's incompleteness I think images are an elegant escape from the uncertainty. Most of the people find it difficult to understand why is segmenation of images so difficult. Particularly because a 5 years old child can do it. This where it lays the philosophy of my science. When I am trying to segment images I can be sure that there exists a solution. We already have a solution. My interest is searching the algorithms and methods which can perceive the world as people can. I don't know wether I can ever understand these methods, but I do my best.