[Insight-users] Re: model-to-image fitting for gaussian images

[Ali -]

> Hi Ali,
>
Hi  Luis,

Thanks for getting back to this.

> 1) By "Gaussian images" do you mean that the image has small sub regions
>     where the spatial distribution of pixel intensities is Gaussian ?

Yes, like I described, assume Gaussian regions with diameters of 3 - 10 pixels where  their centres are randomly distributed.
 
> 2) Is there anything else in the image, in addition to these Gaussians ?

Yes, salt-and-pepper noise : ). But apart from that, ideally, we should have just an ensamble of these Gaussian images.
 
> 3) How diverse are the Gaussians ? do you have a range of sigmas that
>     spans more than an order of magnitude ?

Diameters of 3 - 10 pixels mainly form the range.
 
> 4) Are the Gaussians radially symmetric ?
>     or do they form ellipsoids

Ideally they should be symmetrical. This is not true in case of optical abberations, but I would like to start with the ideal symmetrical case.
> 
> 5) What is the dimension of your image, 2D ?  3D ?

Only 2-D images.

> 
> If the Gaussians are not very diverse, you could use a FFT transform
> and filter them in Fourier space. That will be equivalent to doing
> convolution in physical space. That will give you peaks for solving
> the location problem. (e.g. finding where the Gaussians are).

That's right. Traditionally people use FFT masking for extracting the Gaussian image locations. However, this has some drawbacks such as locating the highly overlapped images. it is known now that algorithms like watershed can be much more efficient with this.

> 
>  From those locations you could estimate the sigma of each Gaussian
> by integrating its intensity values from the top of the peak, down
> to pixels with intensities > than peak / 3.0.  If you divide that
> integral by the peak value, you will have a number that can be
> correlated the sigma value. This has the advantage that you don't
> have to "fit" a gaussian model to the small intensity patch.

My main question was about the 'ITK implementation' of the algorithm, rather than the algorithm itself.

I guess it is possible to locate the peak of the guassian images by labeling the outcome of a watershed filter. In the second part, which is fitting a model to the available data, my understanding was that ITK already comes with some model-to-image fitting facilities. This, and the use of a metric is not quite clear to me.

(1) To avoid re-invening the wheel, does ITK come with the mentioned facilities?

(2) Could you describe a pipeline which can do this job by specifically addressing the required ITK classes.


Thanks.

> 
>    Regards,
> 
> 
>       Luis
> 
> 
> 
> -------------
> Ali - wrote:
> > Anyone?
> > 
> >  >Hi,
> >  >
> >  >Assume an image which contains a set of randomly distributed gaussian 
> > images with diameters of 3 - 10 pixels. The aim is to:
> >  >
> >  >(1) locate the gaussian images
> >  >
> >  >(2) fit a guassian model to these images
> >  >
> >  >The model-to-image registration approach, as described in itk software 
> > guide, seems to be a good way of implementing the 2nd part, is that 
> > right? Do I need to write a metric myself, or is there anything 
> > out-of-the-box currently in itk?
> > 


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