[Insight-users] when to choose FEM, Demons or an optimizer ?

[Luis Ibanez]

Hi Cristian,

Unfortunately, NO.

It is not reasonable to expect that multiple deformable
registration methods will produce similar results. Each
method is solving a slightly different problems with
slightly different constraints.

Before going further, notice that your question is not
quite precise. Both FEM and DEMOS *ARE* running optimiza-
tion methods. Demons is using the equivalent of a gradient
descent method in order to minimize the sum of squared
differences between the images. FEM is also minimizing
the energy unbalance resulting from the internal and
external forces applied to an artificial physical model.
The minimization is done by linearizing the differential
equations of the physical model and computing iterative
solutions of a linear problem. This is equivalent to
running a gradient descent optimizer too. The basic
difference is that the optimization is somehow hidden in
the implicit procedure used for finding the solution of
the minimization problem, so you are not directly exposed
to the presence of the optimizer.


I assume that what you meant is: When to prefer FEM and/or
DEMONS over the open basic framework for registration in
ITK where the optimizer is set explicitly.

               Is that correct  ?



In the case of you hypothetical experiment, if you take
FEM and BSplines and use Mutual Information, it is very
*unlikely* that you will arrive to the same deformation
field and/or to the same final value of Mutual Information.


The main reasons that come to mind are:

1) FEM evaluates MI in small neighborhoods of the
    mesh nodes, while when you use a BSplineTransform
    in the basic ITK registration framework MI will be
    computed using samples over the entire image. So,
    from the very beginning the parts of the image that
    each method uses for evaluating the metric are not
    the same.

2) FEM has a set of physical constrains that *you*
    put in there, the constrains are implicit to the
    selection of the physical model (e.g. elastic).
    BSplines are a free form deformation, meaning
    that the will stretch as much as necessary for
    optimizing the value of the metric.

3) Both FEM and BSplines have *so many* parameters
    for you to tune up that in fact you cannot speak
    of "THE solution given by FEM" or "THE solution
    given by BSplines". The only thing that you can
    say is

      - *ONE* solution given by FEM when using this
        specific set of parameters,

      - *ONE* solution given by BSplines with using
        a set of optimization parameters.

Note that this doesn't mean that one is *better* than
the other. They are simply different approaches. The
deformation field produced by FEM *is not* more correct
than the one that you can obtain with BSplines. None of
them are revealing any "reality" anyways. They are only
giving you an artificial mechanism for fitting the
intensities of one image over the other.

The real deformation field that represents the deformation
of the tissue *cannot* be extracted from a medical image
unless you actually manage to mark and track cells.


The goal of Image Registration is not to find any physical
reality, but to facilitate the analysis of image information
in the chain of the clinical or research practice.

The quest for a "true" solution is an ill-posed problem.

In order to stay sane, you must look only for a "good enough"
solution. One that is accurate enough for the medical application
that you have at hand, and that is not too expensive given the
time and computational resources at your disposal.

The "goodness" of a registration algorithm cannot be evaluated
out of the context of an application. In practice what you do
is to define very well the purpose of the registration,

      is it for measuring volume changes ?
      is it for comparing multi-modality images ?
      is it for surgery planning ?
      is it for radiation treatment ?
      is it for performing a biopsy ?
      is it for building an atlas ?

Each one of them will have different requirements and different
trade-offs between the precision needed, the type of deformations
allowed, the computational time that is reasonable... etc.


The vicious tendency for stating that method "A" is better than
method "B" is only an example of lack of scientific rigor. Our
community is contaminated with this tendency due to the alienation
imposed by the practice of the "Publish of Perish" principle,
according to which every published paper is supposed to end up
in a paragraph stating why *this* method is better than every
other one previously published. Such discussions are only useful
for feeding researcher's egos and reputations, those discussions
offer a very poor service to the patients who pay taxes in order
to obtain a better health care delivery system.


Please post a better definition of your goal, in order to have
a context in which we could give you recommendations regarding
the advantages/disadvantages and trade-offs of different methods
available in ITK.




    Thanks



      Luis


----

    "Definition of the goal is critical to success"


----------------------
Cristian Becali wrote:

> Main question is if there is any good reason why
> methods like FEM or Demons would work better than a
> good old fashion optimization.
> 
> 
> If having two images and a metric like mutual
> information, supposing ideal parameters are found for
> both methods ( so that the methods converge ) and 
> same "resolution" is used in both methods ( for
> example a BSpline mesh density close to the FEM model
> ) the results are not supposed to be the same ? In the
> end, his methods are not supposed to arrive at same
> metric value if ideal conditions are met for them to
> converge ?
> 
> Or, put it in another way, selection of either FEM,
> Demons or other optimizer is part of the "What
> optimizer should be used with this images" problem or
> is there a good reason to choose a method over other ?
> 
> 
> 
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