[Insight-users] Fitting a 2D mesh model to a 2D image?

[Zachary Pincus]

Luis,

Thanks for your (no pun) insight into the problem of putting a  
coordinate system on bacteria. Your option (c) is most clever: since  
one eventual endpoint of my mesh plan was to use that mapping to  
"canonicalize" bacteria, skipping the middleman is a great idea. Out of  
curiosity, from perusing the API docs it doesn't look like the BSpline  
methods can return inverse transforms. (Presumably because the mapping  
is not bijective so there is no well-defined inverse.) Am I mistaken on  
this point?

If I might ask a couple further questions, that I might try your  
patience further:

(1) Was I correct in my assumption about why the DeformableMesh3D  
filter wouldn't work (that it takes an edge mesh, not a dense  
area/volume mesh)? I ask because a related problem that I'm working on  
involves tracking moving, wiggling bacteria. In this case, having a  
deformable edge mesh that can follow the bacteria would be optimal. Can  
the DeformableMesh3D methods handle this case? It seems very analogous  
to the 3D case...

(2) Regarding your option (a), I was initially quite tempted by the  
spatial object registration methods. Nevertheless, going this route  
would still leave me with the need to implement/use some kind of  
image-based mesh deformation mechanism. Are there currently any good  
options here beside rolling my own FEM methods, as in your option (b)?

Thanks again,

Zach Pincus

On May 4, 2004, at 8:14 AM, Luis Ibanez wrote:

>
> Hi Zach,
>
>
> Here are several options:
>
> (Option (C) is probably the easiest to use at this point)
>
>
>
> A) You may want to use it the SpatialObjects and its
>    registration support: SpatialObjectToImage registration.
>
>    You will find the Hierarchy of spatial object under
>
>            Insight/Code/SpatialObject
>
>    There is a number of predefined SpatialObject in this directory.
>    Given that you are targeting a very specific problem, you probably
>    will have some advantages by creating your own variant of Spatial
>    Object.
>
>    An example about this type of registration is presented in the
>    SoftwareGuide.
>
>    This option is the most elegant but it will require some
>    programming effort on your part.    :-)
>
>
>
> B) You could use the FEM registration mechanism, but not through
>    the FEM registration filter. The reason is that this filter
>    takes control of most of the process. In your case you probably
>    want to create your own mesh, and control the iterations of
>    the registration.  Note that the FEM framework *do not* use the
>    itkMesh. There is a native FEM mesh that you should use in order
>    to create your object representation.
>
>    This is a very formal option, but it will require a lot of
>    programming effort on your part, plus some familiarization
>    with the intricacies of FEM solvers.
>
>
>
> C) You could create a "canonical" bacterial image and use the
>    BSPline transform for doing deformable registration against
>    your actual image.  This is probably the more straight forward
>    option at this point.   You could "fabricate" the canonical
>    bacterial image by straighten up the image from a real bacteria.
>    This can be done with the example:
>
>        Insight/Examples/Registration/LandmarkWarping2.cxx
>
>    You will place source landmarks on the original bacterial image,
>    and the target landmarks will be in a rectangular grid. Pretty
>    much like the one you attached to your email.
>
>    Once you get the canonical image, you simply use the Deformable
>    registration mechanisms illustrated in
>
>       Insight/Examples/Registration/DeformableRegistration4.cxx
>
>    Which is the basic ITK registration framework with a BSpline
>    DeformableTransform.  You use the Canonical bacterial as the
>    fixed image, and the real image as the moving image.  Note that
>    the BSplineTransform accepts a generic transform in order to
>    make composition. You can therefore use a Rigid2D  transform
>    in order to take care of global translation and rotation, while
>    leaving only deformations for the BSpline transform itself.
>
>
>    With this approach you will map all the bacterias into the
>    reference system of the canonical bacteria and will probably
>    be able to analyze the differences between specific patterns
>    of gene expression.
>
>    A great advantage here is that you will only have to deal
>    with the region of pixels that cover your canonical bacteria.
>    There will be good use of computation time in that case.
>
>
>
> In General:
>
> You may have to deal with the axial polarity  of the cells,
> and with the fact that due to the microscopy projection, you
> lose any 3D depth information as well as rotations of the
> bacteria along its axis, parallel to the microscope plate.
> But those issues affect any of the image processing methods
> that you may envisage....
>
>
>
> Please let us know if you have further questions.
>
>
>    Thanks
>
>
>
>      Luis
>
>
> ---------------------
> Zachary Pincus wrote:
>
>> Hello,
>> I've run across the need to place some sort of coordinate system on  
>> images of bent bacteria for the purposes of making measurements of  
>> protein localizations that can be compared across populations.
>> My first-pass idea was to make a 2D grid from an ITK mesh, and then  
>> use some of the FEM model-based segmentation/registration methods to  
>> fit the grid to the bacterial image. (See attached image for a vague  
>> idea of what I'm talking about.)
>> However, from reading the documentation for the DeformableMesh3D  
>> filter, I'm not sure if it will work off the shelf. It seems (and I  
>> am likely to be wrong) that this filter is more designed to work with  
>> the output of something like a marching cubes algorithm (or in my  
>> case, marching squares) that defines only the edge of the structure  
>> (that is, some manifold surface embedded in a higher-dimension space,  
>> like a 2D surface of a 3D object, or in my case, a 1D perimeter of a  
>> 2D object). Do the DeformableMesh3D methods work with dense meshes of  
>> the sort I'm proposing in the image below?
>> It almost seems like I need some hybrid between the FEM deformable  
>> image registration methods and the model based segmentation methods.  
>> If the DeformableMesh3D methods won't work, are there other things  
>> that I could try off-the-shelf from ITK? If not, does anyone have any  
>> suggestions as to which classes I might try to build off of?
>> Thanks for any input at all,
>> Zach Pincus
>> Department of Biochemistry and Program in Biomedical Informatics
>> Stanford University School of Medicine
>> Attached: Figure 0, in which my imagined inputs and outputs are  
>> illustrated in a most mediocre manner.
>> ---------------------------------------------------------------------- 
>> --
>
>
>
> _______________________________________________
> Insight-users mailing list
> Insight-users@itk.org
> http://www.itk.org/mailman/listinfo/insight-users
>