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GeodesicDilation
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GeodesicDilation

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GeodesicDilation[marker,mask]

gives the fixed point of the geodesic dilation of the marker constrained by the mask.

Details and Options

  • GeodesicDilation works with binary, grayscale, and multichannel images, operating on each channel separately.
  • GeodesicDilation works with 3D as well as 2D images, and also with data arrays of any rank.
  • GeodesicDilation[marker,mask] effectively starts with marker then repeatedly dilates it, masking with mask until the result no longer changes. For symbolic data, the geodesic dilation is done only once.
  • GeodesicDilation[marker,mask,n] iterates the dilation process at most n times.
  • GeodesicDilation effectively performs a morphological reconstruction by dilation.
  • The following options can be given:
  • CornerNeighborsTruewhether to include corner neighbors
    PaddingNonepadding method to use
  • The default setting Padding->None considers smaller neighborhoods at the edges of an image.

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Reconstruct the marked foreground objects:

In[1]:=1
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https://wolfram.com/xid/0pni89yjdpwyaj7u-7yggxw
Out[1]=1

Reconstruct the marked foreground objects in a 3D image:

In[1]:=1
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https://wolfram.com/xid/0pni89yjdpwyaj7u-ebfqb4
Out[1]=1

Scope  (1)Survey of the scope of standard use cases

Geodesic dilation of a vector:

In[1]:=1
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https://wolfram.com/xid/0pni89yjdpwyaj7u-fz397s
Out[1]=1

Interactive Examples  (1)Examples with interactive outputs

Iteratively apply geodesic dilation:

In[2]:=2
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https://wolfram.com/xid/0pni89yjdpwyaj7u-who2vd
Out[2]=2
Wolfram Research (2008), GeodesicDilation, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesicDilation.html (updated 2012).
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Wolfram Research (2008), GeodesicDilation, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesicDilation.html (updated 2012).

Text

Wolfram Research (2008), GeodesicDilation, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesicDilation.html (updated 2012).

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Wolfram Research (2008), GeodesicDilation, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesicDilation.html (updated 2012).

CMS

Wolfram Language. 2008. "GeodesicDilation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/GeodesicDilation.html.

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Wolfram Language. 2008. "GeodesicDilation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/GeodesicDilation.html.

APA

Wolfram Language. (2008). GeodesicDilation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeodesicDilation.html

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Wolfram Language. (2008). GeodesicDilation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeodesicDilation.html

BibTeX

@misc{reference.wolfram_2025_geodesicdilation, author="Wolfram Research", title="{GeodesicDilation}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesicDilation.html}", note=[Accessed: 25-March-2025 ]}

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@misc{reference.wolfram_2025_geodesicdilation, author="Wolfram Research", title="{GeodesicDilation}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesicDilation.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geodesicdilation, organization={Wolfram Research}, title={GeodesicDilation}, year={2012}, url={https://reference.wolfram.com/language/ref/GeodesicDilation.html}, note=[Accessed: 25-March-2025 ]}

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@online{reference.wolfram_2025_geodesicdilation, organization={Wolfram Research}, title={GeodesicDilation}, year={2012}, url={https://reference.wolfram.com/language/ref/GeodesicDilation.html}, note=[Accessed: 25-March-2025 ]}