LaplacianGaussianFilter

LaplacianGaussianFilter[data,r]

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

LaplacianGaussianFilter[data,{r,σ}]

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)

Filter a color image:

Apply the LoG filter to a 3D image:

Laplacian of Gaussian (LoG) of a list:

Scope  (8)

Data  (4)

Laplacian of Gaussian filtering of a numeric matrix:

Filter a TimeSeries object:

Filter an Audio signal:

Laplacian of Gaussian applied to a grayscale image:

Parameters  (4)

Laplacian of Gaussian filtering of a step sequence:

Use a larger radius:

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

Use different radii in the vertical direction:

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

Filtering of the horizontal planes only:

The default standard deviation is :

Vary the standard deviation:

Options  (7)

Method  (1)

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

Use the method "Gaussian":

Padding  (2)

LaplacianGaussianFilter using different padding methods:

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

Standardized  (1)

The default setting is True:

Use Standardized->False:

WorkingPrecision  (3)

MachinePrecision is used by default with integer arrays:

Perform an exact computation instead:

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

Specify the precision to use:

WorkingPrecision is ignored when filtering images:

An image of a real type is always returned:

Applications  (4)

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

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

Use LaplacianGaussianFilter to denoise an audio signal:

Get borders from a colored map:

Properties & Relations  (6)

LaplacianGaussianFilter is a linear filter:

LaplacianGaussianFilter is the result of a convolution:

Perform LaplacianGaussianFilter using GaussianFilter:

Impulse responses of Laplacian of Gaussian filter for selected radii:

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

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

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).

CMS

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

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: 23-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: 23-April-2025 ]}