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

Details and Options

  • GeodesicErosion works with binary, grayscale, and multichannel images, operating on each channel separately.
  • GeodesicErosion works with 2D as well as 3D images, and also with data arrays of any rank.
  • GeodesicErosion[marker,mask] effectively starts with marker then repeatedly erodes it, masking with mask until the result no longer changes. For symbolic data, the geodesic erosion is done only once.
  • GeodesicErosion[marker,mask,n] iterates the erosion process at most n times.
  • GeodesicErosion effectively performs a morphological reconstruction by erosion.
  • 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.


open allclose all

Basic Examples  (2)

Reconstruct the marked background objects:

Reconstruct the marked background objects in a 3D image:

Scope  (1)

Geodesic erosion of a vector:

Applications  (1)

Select the extended minimum that includes the specified point:

Properties & Relations  (1)

When computing geodesic erosion on symbolic arrays, only one iteration is performed:

Interactive Examples  (1)

Extract objects of varying sizes:

Wolfram Research (2008), GeodesicErosion, Wolfram Language function, (updated 2012).


Wolfram Research (2008), GeodesicErosion, Wolfram Language function, (updated 2012).


Wolfram Language. 2008. "GeodesicErosion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012.


Wolfram Language. (2008). GeodesicErosion. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_geodesicerosion, author="Wolfram Research", title="{GeodesicErosion}", year="2012", howpublished="\url{}", note=[Accessed: 17-July-2024 ]}


@online{reference.wolfram_2024_geodesicerosion, organization={Wolfram Research}, title={GeodesicErosion}, year={2012}, url={}, note=[Accessed: 17-July-2024 ]}