[Insight-users] Regularization type with Demons

[Miki Maric]

Hello Luis and group,

Thank you for your reply.
Yes I look at the Demons filter code and I know that be a lot of modifications
there :(

For now, my understanding is the following:
1. demons now calculate updates according Thirions equation namely U
   and then smooth it Unew=U*G(U) where G is gaussian filter * is
convolution oper.

2. maybe simplest modifications can go in SmoothUpdateField
   instead of Gaussian smoothing to introduce another type of regularization
  (if can we write it that it only depends on part S from functional
F=D+lambda*S).
  Now in Demons Gaussian smoothing is applied only on S part, and separated from
  forces calculation. Small refactoring  will be necessary if
regularizer is applied
  only on S. According to 1. that means that we replace G filter with
another filter.

3. If we want to apply another type of regularizer for example L1, then
   modifications go to both parts of F functional, and bigger modifications is
   necessary in the whole Demons filter because now smoother must be somehow
   incorporated in forces calculation?

4. Question is now: Can we reorganize functional F where S is L1 smoothing
   (approximate not exact), by just using convolution on updates U=U*G(U)?

Thanks,

Miki





On 6/20/10, Luis Ibanez <luis.ibanez at kitware.com> wrote:
> Hi Miki,
>
> The Demons filter takes advantage of the fact that a
> Gaussian smoothing is "equivalent" to a L2 regularization.
>
> Where "equivalent" here means: "is close enough"
>
> If you want to replace this norm, you will have to make
> significant modifications to the code of the Demons
> filter.
>
> It will be interesting to see if you find a way of refactoring
> the filter in such a way that different types of regularization
> can be used. That will be a great paper for the Insight
> Journal  (http://www.insight-journal.org).     :-)
>
>
>       Luis
>
>
>
> ----------------------------------------------------------------------
> On Fri, Jun 11, 2010 at 4:55 AM, Miki Maric <mikimaric1975 at gmail.com> wrote:
>
>> Hello to all,
>>
>> As I understand PDE implementation of Thirion Demons,  Tikhonov type of
>> regularizer is used (L2 norm).
>> Is there are possibility to implement other type of regularizer namely L1?
>>
>> How to change smoother in this framework? (How to integrate Total
>> Variation
>> norm in it? Is it possible? Maybe by implementing
>> itkTotalVariationDenoisingFilter instead of Gaussian?)
>>
>>
>> Thanks,
>>
>> Miki
>>
>>
>>
>>
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