Erosion
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
open all close allBasic Examples (3)
Erosion of a binary image with a disk-shaped structuring element:
Erosion of a grayscale image:
Erosion of a 3D shape:
Scope (13)
Data (7)
Erosion of a 2D binary array:
Erosion of a binary image:
Erosion of a numeric array:
Erosion of a numeric vector:
Erosion of a grayscale image:
Erosion of a color image:
Erosion on a symbolic array of data:
Parameters (6)
Erode horizontally:
Erode vertically:
Erode with radius , equivalent to a BoxMatrix [r]:
Erode using different radii:
Erode with a diagonal structuring element:
Structuring elements with even dimensions are right-padded with zeros:
Erode a 3D volume using a 3D kernel:
Options (2)
Padding (2)
By default, the largest possible number is used for padding when applying erosion to arrays:
Specify a custom padding:
By default, Padding 1 is used for images:
Specify a custom padding:
Applications (2)
Erosion reduces smaller, light features:
Internal morphological gradient computed by subtracting the eroded image from the original image:
Tech Notes
Related Guides
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_2025_erosion, author="Wolfram Research", title="{Erosion}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Erosion.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_erosion, organization={Wolfram Research}, title={Erosion}, year={2012}, url={https://reference.wolfram.com/language/ref/Erosion.html}, note=[Accessed: 04-January-2026]}