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Erosion[image,ker]

gives the morphological erosion of image with respect to the structuring element ker.

Erosion[image,r]

gives the erosion with respect to a range-r square.

Erosion[data,…]

applies erosion to an array of data.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Parameters  
Options  
Padding  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
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Erosion

Erosion[image,ker]

gives the morphological erosion of image with respect to the structuring element ker.

Erosion[image,r]

gives the erosion with respect to a range-r square.

Erosion[data,…]

applies erosion to an array of data.

Details and Options

  • Erosion is also known as Minkowski subtraction.
  • Erosion works with arbitrary 2D and 3D images, operating separately on each channel, as well as data arrays of any rank.
  • The structuring element ker is a matrix containing s and s.
  • Erosion[image,r] is equivalent to Erosion[image,BoxMatrix[r]].
  • The structuring element is automatically padded with zeros to have odd dimensions. »
  • Erosion takes a Padding option that specifies the values to assume for pixels outside the image.
  • By default, Padding->1 is used for images, corresponding to pixel value for all channels.

Examples

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Basic Examples  (3)

Erosion of a binary image with a disk-shaped structuring element:

Wolfram Language code: Erosion[[image], DiskMatrix[3]]

Erosion of a grayscale image:

Wolfram Language code: Erosion[[image], DiskMatrix[3]]

Erosion of a 3D shape:

Wolfram Language code: Erosion[[image], 1]

Scope  (13)

Data  (7)

Erosion of a 2D binary array:

Wolfram Language code: Erosion[(⁠| | | | | | | | - | - | - | - | - | - | | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 |⁠), (⁠| | | | | - | - | - | | 0 | 0 | 0 | | 0 | 1 | 1 | | 0 | 0 | 1 |⁠)]//MatrixForm

Erosion of a binary image:

Wolfram Language code: Erosion[[image], (⁠| | | | | - | - | - | | 1 | 0 | 0 | | 0 | 1 | 0 | | 0 | 0 | 1 |⁠)]

Erosion of a numeric array:

Wolfram Language code: Erosion[(⁠| | | | | | | - | - | - | - | - | | 2 | 3 | 2 | 5 | 5 | | 1 | 4 | 2 | 3 | 5 | | 3 | 2 | 2 | 4 | 5 | | 2 | 1 | 2 | 3 | 1 | | 1 | 1 | 2 | 4 | 2 |⁠), 1]//MatrixForm

Erosion of a numeric vector:

Wolfram Language code: data = QuantityMagnitude@Values[FinancialData["AT&T", {{2012, 7, 1}, {2013, 1, 1}, "Day"}]];
Wolfram Language code: ListLinePlot[{data, Erosion[data, 5, Padding -> "Fixed"]}]

Erosion of a grayscale image:

Wolfram Language code: Erosion[[image], 3]

Erosion of a color image:

Wolfram Language code: Erosion[[image], 3]

Erosion on a symbolic array of data:

Wolfram Language code: Erosion[{a, b, c}, 1]

Parameters  (6)

Erode horizontally:

Wolfram Language code: Erosion[[image], {{1, 1, 1, 1, 1}}]

Erode vertically:

Wolfram Language code: Erosion[[image], {{1}, {1}, {1}, {1}, {1}}]

Erode with radius , equivalent to a BoxMatrix[r]:

Wolfram Language code: Erosion[[image], 1]

Erode using different radii:

Wolfram Language code: Table[Erosion[[image], r], {r, 1, 3}]

Erode with a diagonal structuring element:

Wolfram Language code: Erosion[[image], IdentityMatrix[5]]

Structuring elements with even dimensions are right-padded with zeros:

Wolfram Language code: Erosion[ArrayPad[ConstantArray[1, {3, 3}], 1], (⁠| | | | - | - | | 1 | 1 | | 1 | 1 |⁠)] === Erosion[ArrayPad[ConstantArray[1, {3, 3}], 1], (⁠| | | | | - | - | - | | 1 | 1 | 0 | | 1 | 1 | 0 | | 0 | 0 | 0 |⁠)]

Erode a 3D volume using a 3D kernel:

Wolfram Language code: Erosion[[image], DiskMatrix[{2, 2, 2}]]

Options  (2)

Padding  (2)

By default, the largest possible number is used for padding when applying erosion to arrays:

Wolfram Language code: Erosion[{1, 2, 3, 4, 5}, 1]

Specify a custom padding:

Wolfram Language code: Erosion[{1, 2, 3, 4, 5}, 1, Padding -> 0]

By default, Padding1 is used for images:

Wolfram Language code: i = [image];
Wolfram Language code: Erosion[i, 5]

Specify a custom padding:

Wolfram Language code: Erosion[i, 5, Padding -> Red]

Applications  (2)

Erosion reduces smaller, light features:

Wolfram Language code: Erosion[[image], 1]

Internal morphological gradient computed by subtracting the eroded image from the original image:

Wolfram Language code: i = [image]; i - Erosion[i, 1]

Properties & Relations  (2)

Erosion with a {0,0,1} kernel is effectively a translation to the left:

Wolfram Language code: Erosion[{1, 2, 3, 4, 5}, {0, 0, 1}, Padding -> 0]

Application of Erosion followed by Dilation is the same as Opening:

Wolfram Language code: Dilation[Erosion[[image], 3], 3]
Wolfram Language code: ImageDistance[%, Opening[[image], 3]]
Wolfram Research (2008), Erosion, Wolfram Language function, https://reference.wolfram.com/language/ref/Erosion.html (updated 2012).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_erosion, author="Wolfram Research", title="{Erosion}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Erosion.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_erosion, organization={Wolfram Research}, title={Erosion}, year={2012}, url={https://reference.wolfram.com/language/ref/Erosion.html}, note=[Accessed: 13-June-2026]}