[ITK-users] Spatially variant morphological closing

[Richard Beare]

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 <mlt.khawla at gmail.com> 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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