[ITK-users] Spatially variant morphological closing

[Daoued23]

Thank you very much for your help, but unfortunately  none of these
articles discussed the problem that I cited.

Best Regards
Daoued23

2015-09-30 21:49 GMT+01:00 Richard Beare [via ITK - Users] <
ml-node+s7n36269h60 at n7.nabble.com>:

> Spatially variant erosions and dilations are easy enough to visualise but,
> as you've discovered, openings and closings are less obvious. Some issues
> are discussed in the following papers.
>
> @Article{cuisenaire2006locally, title = "Locally Adaptable Mathematical
> Morphology Using Distance Transformations", author = "O. Cuisenaire", journal
> = "Pattern Recognition", volume = "39", number = "3", pages = "405--416", year
> = "2006", publisher = "Elsevier", } @Article{bouaynaya2007theoretical2, title
> = "Theoretical Foundations of Spatially-variant Mathematical Morphology
> Part {II}: Gray-level Images", author = "N. Bouaynaya and D. Schonfeld", journal
> = "IEEE Transactions on Pattern Analysis and Machine Intelligence", volume
> = "30", number = "5", pages = "837--850", year = "2008", publisher = "Published
> by the IEEE Computer Society", } @Article{bouaynaya2007theoretical1, title
> = "Theoretical Foundations of Spatially-variant Mathematical Morphology
> Part {I}: Binary Images", author = "N. Bouaynaya and D. Schonfeld", journal
> = "IEEE Transactions on Pattern Analysis and Machine Intelligence", volume
> = "30", number = "5", pages = "823--836", year = "2008", publisher = "Published
> by the IEEE Computer Society", }
>
> I've also done some work on the efficient implementations for
> circular/spherical structuring elements on binary images:
>
> @InProceedings{Beare2011j,
>
>   author =       {Beare, R. and Jackway, P.},
>
>   title =        {Parallel Algorithms Via Scaled Paraboloid Structuring
> Function
>
> s for Spatially-Variant and Label-Set Dilations and Erosions},
>
>   booktitle = {International Conference on Digital Image Computing:
> Techniques and Applications (DICTA) },
>
>   year =         2011,
>
>   month =        {December}}
>
>
> On Wed, Sep 30, 2015 at 11:05 PM, Daoued23 <[hidden email]
> <http:///user/SendEmail.jtp?type=node&node=36269&i=0>> wrote:
>
>> Hi everyone,
>>
>> I want to implement a spatially variant morphological closing, which its
>> structuring element is estimated for every pixel. I work on binary images.
>>
>>
>> So to apply the aspatially variant morphological closing, we estimate the
>> structuring element for every pixel surrounded by its neighborhood, apply
>> the dilation on every neighbouring window with the corresponding estimated
>> structring element. Then we get the dilated image as the union of all the
>> dilated windows. Now, we apply the erosion on every neighbouring window of
>> the dilated image with the transposed of the structuring element already
>> estimated. The adaptively closed image will be the union of the eroded
>> windows of the dilated image.
>>
>> Now the problem is that, we find background windows (all pixels are black)
>> in the image, so we cannot estimate a structuring element. when it's the
>> phase of the dilation we don't apply anything, but some pixels can appear
>> in
>> this windows as the result of the union of the surrounding windows that
>> have
>> been dilated. When applying the erosion on these new pixels which
>> structuring element should we consider knowing that we can't estimate one
>> based on the original image (background window)???
>>
>> Thank you
>>
>> Best regards
>>
>>
>>
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