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MorphologicalBinarize
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MorphologicalBinarize

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MorphologicalBinarize[image,{t1,t2}]

creates a binary image from image by replacing all values above the upper threshold t2 with 1, also including pixels with intensities above the lower threshold t1 that are connected to the foreground.

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uses t as the upper threshold, automatically choosing a suitable value for the lower threshold.

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chooses the lower and the upper threshold automatically.

Details and Options

  • MorphologicalBinarize effectively performs hysteresis thresholding and is typically used as part of edge-detection methods.
  • MorphologicalBinarize works with 2D as well as 3D images. It converts multichannel and color images into grayscale images, then produces an image in which every pixel has value 0 or 1.
  • The following short forms can be used for the second argument:
  • t{Automatic,t}t1 computed automatically
    {t}{t,Automatic}t2 computed automatically
    {func}{t1,t2}t1=func[t2] with t2 automatic
    {t,func}{t,t2}t2=func[t]
  • The following options can be given:
  • CornerNeighbors Truewhether to include corner neighbors
    Method "Cluster"method to use to specify the upper threshold
  • MorphologicalBinarize[image,{t},Method->method] specifies the method to use to determine the threshold. See the reference page for FindThreshold for full documentation of available methods.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Binarization of an image using double thresholding:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-ezcdgs
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

Find connected foreground regions between the two specified thresholds:

In[2]:=2
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https://wolfram.com/xid/0cf1mfbhsb0sshy-25qnud
Out[2]=2

Use a fixed upper threshold and compute the lower threshold automatically:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-86124r
Out[1]=1

Use a fixed lower threshold and compute the upper threshold automatically:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-wwehrc
Out[1]=1

Compute the lower threshold as a function of the automatically computed upper threshold:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-88jc12
Out[1]=1

Find the upper and lower thresholds automatically:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-gsymo9
Out[1]=1

Binarize a 3D image:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-fccall
Out[1]=1

Options  (3)Common values & functionality for each option

CornerNeighbors  (2)

Treats all 8 pixels surrounding a given pixel as adjacent:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-bphx0w
Out[1]=1

Treats only the 4 pixels surrounding a given pixel along the coordinate axes as adjacent:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-9f4izp
Out[1]=1

Method  (1)

Compute the upper threshold using Kapur's entropy method:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-8e72bn
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

Edge detection typically involves hysteresis thresholding perfomed on the gradient magnitude:

In[2]:=2
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https://wolfram.com/xid/0cf1mfbhsb0sshy-bze6dw
Out[2]=2

Binarize using hysteresis thresholding:

In[3]:=3
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https://wolfram.com/xid/0cf1mfbhsb0sshy-ccuww1
Out[3]=3

Properties & Relations  (5)Properties of the function, and connections to other functions

With color images, the thresholding is performed on intensity values:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-jggcri
In[3]:=3
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https://wolfram.com/xid/0cf1mfbhsb0sshy-d3w9k
Out[3]=3

With ColorSpace->Automatic multi-channel images, the mean of channel values is used:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-n6nsr5
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cf1mfbhsb0sshy-qe3ac6
Out[2]=2

If both the upper threshold and a Method option are specified, the method is ignored:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-vih21f
In[2]:=2
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https://wolfram.com/xid/0cf1mfbhsb0sshy-zvz8ps
Out[2]=2

MorphologicalBinarize operates on pixel values considering neighboring pixel values:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-x061l6
Out[1]=1

Binarize operates on a pixel value regardless of neighboring pixels:

In[2]:=2
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https://wolfram.com/xid/0cf1mfbhsb0sshy-rl17o
Out[2]=2

MorphologicalBinarize[image,{t1,t2}] is effectively the geodesic dilation of two binary images:

In[1]:=1
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https://wolfram.com/xid/0cf1mfbhsb0sshy-xs3gux
Out[1]=1

The marker image is binarized using t2 and the mask image is binarized using t1:

In[2]:=2
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https://wolfram.com/xid/0cf1mfbhsb0sshy-hrcdr6
Out[2]=2
Wolfram Research (2010), MorphologicalBinarize, Wolfram Language function, https://reference.wolfram.com/language/ref/MorphologicalBinarize.html (updated 2012).
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Wolfram Research (2010), MorphologicalBinarize, Wolfram Language function, https://reference.wolfram.com/language/ref/MorphologicalBinarize.html (updated 2012).

Text

Wolfram Research (2010), MorphologicalBinarize, Wolfram Language function, https://reference.wolfram.com/language/ref/MorphologicalBinarize.html (updated 2012).

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Wolfram Research (2010), MorphologicalBinarize, Wolfram Language function, https://reference.wolfram.com/language/ref/MorphologicalBinarize.html (updated 2012).

CMS

Wolfram Language. 2010. "MorphologicalBinarize." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/MorphologicalBinarize.html.

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Wolfram Language. 2010. "MorphologicalBinarize." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/MorphologicalBinarize.html.

APA

Wolfram Language. (2010). MorphologicalBinarize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MorphologicalBinarize.html

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Wolfram Language. (2010). MorphologicalBinarize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MorphologicalBinarize.html

BibTeX

@misc{reference.wolfram_2025_morphologicalbinarize, author="Wolfram Research", title="{MorphologicalBinarize}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/MorphologicalBinarize.html}", note=[Accessed: 30-March-2025 ]}

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@misc{reference.wolfram_2025_morphologicalbinarize, author="Wolfram Research", title="{MorphologicalBinarize}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/MorphologicalBinarize.html}", note=[Accessed: 30-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_morphologicalbinarize, organization={Wolfram Research}, title={MorphologicalBinarize}, year={2012}, url={https://reference.wolfram.com/language/ref/MorphologicalBinarize.html}, note=[Accessed: 30-March-2025 ]}

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@online{reference.wolfram_2025_morphologicalbinarize, organization={Wolfram Research}, title={MorphologicalBinarize}, year={2012}, url={https://reference.wolfram.com/language/ref/MorphologicalBinarize.html}, note=[Accessed: 30-March-2025 ]}