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MorphologicalEulerNumber[image]

computes the morphological Euler number of regions in a binary image.

MorphologicalEulerNumber[image,t]

treats values above t as foreground.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
2D Images  
3D Images  
Options  
CornerNeighbors  
Padding  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

MorphologicalEulerNumber

MorphologicalEulerNumber[image]

computes the morphological Euler number of regions in a binary image.

MorphologicalEulerNumber[image,t]

treats values above t as foreground.

Details and Options

Examples

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Basic Examples  (1)

Count the number of white objects minus the number of holes:

Wolfram Language code: MorphologicalEulerNumber[ [image]]

Scope  (5)

2D Images  (1)

Euler number of a single object with no holes:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Single object with one hole:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Single object with two holes:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Two objects with no holes:

Wolfram Language code: MorphologicalEulerNumber[[image]]

3D Images  (4)

Euler number of a single 3D solid:

Wolfram Language code: MorphologicalEulerNumber[\!\(\*Graphics3DBox[«8»]\)]

Euler number of a single 3D solid with one hole:

Wolfram Language code: volume = Image3D[{[image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image]}]; MorphologicalEulerNumber[volume]

Euler number of a tunnel:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Morphological Euler number of a torus:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Options  (4)

CornerNeighbors  (2)

By default, all eight neighbors around a given pixel are treated as being neighbors:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Treat only the four non-corner pixels as neighbors:

Wolfram Language code: MorphologicalEulerNumber[[image], CornerNeighbors -> False]

Padding  (2)

By default, zero padding is assumed:

Wolfram Language code: MorphologicalEulerNumber[[image]]

Specify the padding value:

Wolfram Language code: MorphologicalEulerNumber[[image], Padding -> 1]

Properties & Relations  (1)

Euler number is computed as the number of connected components minus the number of holes:

Wolfram Language code: i = [image];

The number of connected components:

Wolfram Language code: componentCount = Max[MorphologicalComponents[i]]

The number of holes:

Wolfram Language code: holesCount = Max[MorphologicalComponents[ImageSubtract[FillingTransform[i], i]]]
Wolfram Language code: MorphologicalEulerNumber[i]
Wolfram Research (2008), MorphologicalEulerNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/MorphologicalEulerNumber.html (updated 2014).

Text

Wolfram Research (2008), MorphologicalEulerNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/MorphologicalEulerNumber.html (updated 2014).

CMS

Wolfram Language. 2008. "MorphologicalEulerNumber." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/MorphologicalEulerNumber.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_morphologicaleulernumber, author="Wolfram Research", title="{MorphologicalEulerNumber}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MorphologicalEulerNumber.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_morphologicaleulernumber, organization={Wolfram Research}, title={MorphologicalEulerNumber}, year={2014}, url={https://reference.wolfram.com/language/ref/MorphologicalEulerNumber.html}, note=[Accessed: 13-June-2026]}