# 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

• 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 allclose all

## Basic Examples(4)

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

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

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

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

## Scope(9)

### Data(6)

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

Opening of a numeric vector:

Opening of a 2D binary array:

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

Opening of a grayscale image:

Opening of a symbolic array of data:

### Kernel(3)

Open horizontally:

Open vertically:

Open using a uniform, square structuring element:

## Applications(2)

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

Extract 3D objects larger than the structuring element:

## Properties & Relations(3)

Even-length kernels get right-padded with zeros:

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

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

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_2024_opening, author="Wolfram Research", title="{Opening}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Opening.html}", note=[Accessed: 21-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_opening, organization={Wolfram Research}, title={Opening}, year={2012}, url={https://reference.wolfram.com/language/ref/Opening.html}, note=[Accessed: 21-July-2024 ]}