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LaplacianGaussianFilter

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convolves data with a Laplacian of Gaussian kernel of pixel radius r.

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convolves data with a Laplacian of Gaussian kernel of radius r and standard deviation σ.

Details and Options

Examples

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Basic Examples  (3)Summary of the most common use cases

Filter a color image:

In[75]:=75
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-eq1ru3
Out[75]=75

Apply the LoG filter to a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-gvz7fn
Out[1]=1

Laplacian of Gaussian (LoG) of a list:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-8ylu2i
Out[1]=1

Scope  (8)Survey of the scope of standard use cases

Data  (4)

Laplacian of Gaussian filtering of a numeric matrix:

In[35]:=35
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-ct07fd
In[36]:=36
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-c73fay

Filter a TimeSeries object:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-brhx0t
Out[1]=1

Filter an Audio signal:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-u9tjh0
In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-c7kjgb
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-j5yrn4
Out[3]=3

Laplacian of Gaussian applied to a grayscale image:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-8b3iu3
Out[1]=1

Parameters  (4)

Laplacian of Gaussian filtering of a step sequence:

In[88]:=88
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-fdqmi2
Out[89]=89

Use a larger radius:

In[90]:=90
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-s5zwi
Out[90]=90

Apply the Laplacian of Gaussian filter in the vertical direction only:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-bzqsge
Out[1]=1

Use different radii in the vertical direction:

In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-op3qwr
Out[2]=2

Laplacian of Gaussian derivative of a 3D image in the vertical direction only:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-ljvsn6
Out[1]=1

Filtering of the horizontal planes only:

In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-hidjao
Out[2]=2

The default standard deviation is :

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-eb87u4
Out[1]=1

Vary the standard deviation:

In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-bzh7l0
Out[2]=2

Options  (7)Common values & functionality for each option

Method  (1)

By default, the method "Bessel" is used to obtain the filter coefficients:

In[157]:=157
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-iaj2yk
Out[157]=157

Use the method "Gaussian":

In[158]:=158
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-ds9a3
Out[158]=158

Padding  (2)

LaplacianGaussianFilter using different padding methods:

In[428]:=428
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-ggz55e
Out[430]=430

Padding->None normally returns an image smaller than the input image:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-72b2z1
Out[1]=1

Standardized  (1)

The default setting is True:

In[65]:=65
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-iu3mq6
Out[65]=65

Use Standardized->False:

In[66]:=66
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-bxazhg
Out[66]=66

WorkingPrecision  (3)

MachinePrecision is used by default with integer arrays:

In[63]:=63
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-cdrg18
Out[63]=63

Perform an exact computation instead:

In[64]:=64
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-jt3a9c
Out[64]=64

With real arrays, by default, the precision of the input is used:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-2q79si
Out[1]=1

Specify the precision to use:

In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-7f69wx
Out[2]=2

WorkingPrecision is ignored when filtering images:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-pc6p9y
Out[1]=1

An image of a real type is always returned:

In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-o6dztt
Out[2]=2

Applications  (4)Sample problems that can be solved with this function

Detect edges by finding the zero crossings of a LoG filtered image:

In[135]:=135
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-e421i7
Out[135]=135

Segment an image by applying a LoG filter to the output of a distance transform:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-jouit6
Out[1]=1

Use LaplacianGaussianFilter to denoise an audio signal:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-hql8z3
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-g1tss
Out[2]=2

Get borders from a colored map:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-m7em2e
Out[1]=1

Properties & Relations  (6)Properties of the function, and connections to other functions

LaplacianGaussianFilter is a linear filter:

In[78]:=78
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-dktmv8
Out[80]=80

LaplacianGaussianFilter is the result of a convolution:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-uzbjxv
Out[1]=1

Perform LaplacianGaussianFilter using GaussianFilter:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-3dvv7v
Out[1]=1

Impulse responses of Laplacian of Gaussian filter for selected radii:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-n4jfuc
Out[1]=1

Impulse responses of Laplacian of Gaussian filter for selected standard deviations:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-cb3spd
Out[1]=1

Filtering of a binary image gives a real-valued image:

In[1]:=1
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-fblth
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-hznxi1
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bhgnqm0b13ems58he6y-bhcy14
Out[3]=3
Wolfram Research (2008), LaplacianGaussianFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html (updated 2016).
✖
Wolfram Research (2008), LaplacianGaussianFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html (updated 2016).

Text

Wolfram Research (2008), LaplacianGaussianFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html (updated 2016).

✖
Wolfram Research (2008), LaplacianGaussianFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html (updated 2016).

CMS

Wolfram Language. 2008. "LaplacianGaussianFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html.

✖
Wolfram Language. 2008. "LaplacianGaussianFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_laplaciangaussianfilter, author="Wolfram Research", title="{LaplacianGaussianFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html}", note=[Accessed: 30-April-2025 ]}

✖
@misc{reference.wolfram_2025_laplaciangaussianfilter, author="Wolfram Research", title="{LaplacianGaussianFilter}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html}", note=[Accessed: 30-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_laplaciangaussianfilter, organization={Wolfram Research}, title={LaplacianGaussianFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html}, note=[Accessed: 30-April-2025 ]}

✖
@online{reference.wolfram_2025_laplaciangaussianfilter, organization={Wolfram Research}, title={LaplacianGaussianFilter}, year={2016}, url={https://reference.wolfram.com/language/ref/LaplacianGaussianFilter.html}, note=[Accessed: 30-April-2025 ]}