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.