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Opening[image,ker]

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

Opening[image,r]

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

Opening[data,…]

applies opening to an array of data.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Kernel  
Applications  
Properties & Relations  
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Opening

Opening[image,ker]

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

Opening[image,r]

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

Opening[data,…]

applies opening to an array of data.

Details

  • Morphological opening is typically used to break thin connections, remove small objects and smooth the boundaries.
  • Opening is effectively erosion followed by dilation using a specific structuring element.
  • Opening 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 0s and 1s.
  • Opening automatically pads structuring elements to have odd dimensions.
  • Opening[image,r] is equivalent to Opening[image,BoxMatrix[r]].

Examples

open all close all

Basic Examples  (4)

Opening of a binary image using a disk-shaped structuring element:

Wolfram Language code: Opening[[image], DiskMatrix[9]]

Opening of a grayscale image using a disk-shaped structuring element:

Wolfram Language code: Opening[[image], DiskMatrix[5]]

Opening of a color photo with a diamond-shaped structuring element:

Wolfram Language code: Opening[[image], DiamondMatrix[11]]

Opening of a 3D image using a cubic structuring element:

Wolfram Language code: Opening[[image], 5]

Scope  (9)

Data  (6)

Use Opening to remove short sequences of 1s from a numeric vector:

Wolfram Language code: Opening[{1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1}, {1, 1, 1}]

Opening 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, Opening[data, 10]}]

Opening of a 2D binary array:

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

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

Wolfram Language code: Opening[[image], DiskMatrix[5]]

Opening of a grayscale image:

Wolfram Language code: Opening[[image], 6]

Opening of a symbolic array of data:

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

Kernel  (3)

Open horizontally:

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

Open vertically:

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

Open using a uniform, square structuring element:

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

Applications  (2)

Use morphological opening to extract objects larger than the structuring element:

Wolfram Language code: Opening[[image], DiskMatrix[6]]

Extract 3D objects larger than the structuring element:

Wolfram Language code: Opening[\!\(\*Graphics3DBox[«8»]\), DiskMatrix[{8, 8, 8}]]

Properties & Relations  (3)

Even-length kernels get right-padded with zeros:

Wolfram Language code: i = RandomImage[];
Wolfram Language code: Opening[i, (⁠| | | | - | - | | 0 | 1 | | 1 | 1 |⁠)] == Opening[i, (⁠| | | | | - | - | - | | 0 | 1 | 0 | | 1 | 1 | 0 | | 0 | 0 | 0 |⁠)]

For symmetric kernels, Opening corresponds to an Erosion followed by a Dilation:

Wolfram Language code: i = RandomImage[]; ker = (⁠| | | | | - | - | - | | 0 | 1 | 0 | | 1 | 1 | 1 | | 0 | 1 | 0 |⁠); Opening[i, ker] == Dilation[Erosion[i, ker], ker]

For non-symmetric kernels, Opening corresponds to Erosion followed by a Dilation with a reflected structuring element:

Wolfram Language code: i = RandomImage[]; ker = (⁠| | | | | - | - | - | | 0 | 1 | 0 | | 1 | 1 | 0 | | 0 | 0 | 0 |⁠);
Wolfram Language code: Opening[i, ker] == Dilation[Erosion[i, ker], Reverse[ker, {1, 2}]]
Wolfram Research (2008), Opening, Wolfram Language function, https://reference.wolfram.com/language/ref/Opening.html (updated 2012).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_opening, author="Wolfram Research", title="{Opening}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Opening.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_opening, organization={Wolfram Research}, title={Opening}, year={2012}, url={https://reference.wolfram.com/language/ref/Opening.html}, note=[Accessed: 13-June-2026]}