[Insight-users] Gradient Descent?

[Luis Ibanez]

Hi Motes,



       This is going to be a long conversation...   :-)


It seems that you are thinking of the image as the parametric
space itself.

If you are considering the image intensities to be the values
of a cost function, and you are assuming that the space of
image indexes is the parametric space, then,... yes... you
could perform a walk over this space using a gradient descent
approach.


This is done, for example, as part of the computation of
Watersheds...


Is that what you have in mind ?


Are you looking for a method for walking toward extrema
of intensities in an image ?



     Luis



---------------------
motes motes wrote:
> Ok it seems I need to find some resources concerning this kind of 
> optimization. But assume that I have a grayscale image when using the 
> gradient descent method are the gradient then calculated for a pixel and 
> the next pixel choosen is the one where the gradient has a negative growth?
> 
> 
> 
> On Tue, Jun 30, 2009 at 10:26 PM, Luis Ibanez <luis.ibanez at kitware.com 
> <mailto:luis.ibanez at kitware.com>> wrote:
> 
> 
>     Hi Motes,
> 
> 
>     The fact that this optimizer is applied to registration
>     of digital images is irrelevant.
> 
> 
>     All ITK optimizers are general purpose optimizers.
> 
> 
>     These Optimizers explore a parametric space looking
>     for good values of a cost function.
> 
>     When applied to image registration the Cost function
>     happens to be an ImageMetric, and the parametric
>     space happens to be the set of parameters of a
>     Transform.
> 
> 
>     The Image Registration chapter of the ITK Software Guide
>     http://www.itk.org/ItkSoftwareGuide.pdf shows many plots
>     of the Metric with respect to the optimizer iterations, as
>     well as many plots of the Transform parameters for multiple
>     iterations of the optimizer.
> 
>     Have you seen these figures ?
> 
> 
> 
>     Could you please clarify what kind of step-by-step
>     example are you looking for ?
> 
> 
> 
>     Simply "applying an optimizer to a digital image"
>     doesn't quite makes sense...
> 
> 
> 
>     Are you looking for image enhancement filters ?
>     maybe ?
> 
> 
>         Please elaborate on the context of your question,
> 
> 
>               Thanks
> 
> 
>                     Luis
> 
> 
> 
>     ----------------------------------------------------------------
>     On Tue, Jun 30, 2009 at 4:13 PM, motes motes <mort.motes at gmail.com
>     <mailto:mort.motes at gmail.com>> wrote:
> 
>         A lot of the examples in the itkSoftwareGuide uses the optimizer
>         defined in itkRegularStepGradientDescentOptimizer.h.
> 
>         As I understand this i a gradient descent optimzer. There is not
>         much details about this method in the guide (I assume its rather
>         basic)  but it could be very nice to read some examples showing
>         how this optimizer works for a few iterations.
> 
>         I have tried googling articles and websites that show how
>         gradient descent is applied in the context of digital image
>         processing but cannot seem to find anything. Does anyone on this
>         mailing list know of any good resources to a step-by-step
>         example using the gradient descent method on a digital image?
> 
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>