[Insight-users] Gradient Descent?

[motes motes]

Forgot to press reply to all :-)

On Tue, Jun 30, 2009 at 11:43 PM, motes motes <mort.motes at gmail.com> wrote:

>
>
> On Tue, Jun 30, 2009 at 11:34 PM, Luis Ibanez <luis.ibanez at kitware.com>wrote:
>
>>
>> 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 ?
>>
>>
>
> Well that was actually what I thought the optimization part of ITK was
> doing - finding extrema in the image.
>
> As I understand the cost function could be defined as eg.
> sum-of-squared-intensities. In each iteration this function is evaluated and
> we choose that "path" which minimizes this cost function.
>
> But is the cost function evaluated for the whole image or just for a local
> region?
>
> Maybe you can recommend some literature that covers this subject so I don't
> waste to much of your time :-) I have bought Digital Image Processing, Third
> Edition, Gonzalez et. al, but I could not find anything on gradient descent
> or cost functions/optimization.
>
>
>
>
>
>
>
>
>>
>>
>>    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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>>>
>>>
>
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