convolves data with a radius-r Laplacian kernel.


uses radius ri at level i in data.

Details and Options

  • LaplacianFilter is commonly used in image processing to highlight regions of rapid-intensity change by approximating the second spatial derivatives of an image.
  • The data can be any of the following:
  • listarbitrary-rank numerical array
    tseriestemporal data such as TimeSeries, TemporalData,
    imagearbitrary Image or Image3D object
    audioan Audio object
  • For multichannel images and audio signals, LaplacianFilter operates separately on each channel.
  • LaplacianFilter[data,] by default returns a result of the same dimensions as data.
  • The following options can be given:
  • Padding "Fixed"padding method
    WorkingPrecision Automaticthe precision to use
  • With setting Padding->None, LaplacianFilter[data,] normally returns a result smaller than data.


open allclose all

Basic Examples  (2)

Laplacian filter of a list:

Laplacian filtering of a color image:

Scope  (8)

Data  (6)

Laplacian filter of a 2D Array:

Filter a TimeSeries object:

Filter an Audio signal:

Filter a grayscale image:

Filter a color image:

Filter a 3D image:

Parameters  (2)

Apply the Laplacian filter in the horizontal direction only:

Use different radii in the horizontal direction:

Filter a 3D image in the vertical plane only:

Filtering of the horizontal planes only:

Options  (5)

WorkingPrecision  (3)

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:

Padding  (2)

Laplacian filtering using different padding schemes:

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

Applications  (3)

Find edges in an image:

Subtract the Laplacian filter from the original image to emphasize details:

Get borders from a colored map:

Properties & Relations  (3)

LaplacianFilter is a linear filter:

Impulse response of LaplacianFilter of radius 2:

Perform Laplacian filtering using ImageConvolve:

Laplacian filtering of a binary image gives a real-valued image:

Neat Examples  (1)

Create a random texture from uniform noise:

Wolfram Research (2008), LaplacianFilter, Wolfram Language function, (updated 2016).


Wolfram Research (2008), LaplacianFilter, Wolfram Language function, (updated 2016).


Wolfram Language. 2008. "LaplacianFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016.


Wolfram Language. (2008). LaplacianFilter. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_laplacianfilter, author="Wolfram Research", title="{LaplacianFilter}", year="2016", howpublished="\url{}", note=[Accessed: 24-July-2024 ]}


@online{reference.wolfram_2024_laplacianfilter, organization={Wolfram Research}, title={LaplacianFilter}, year={2016}, url={}, note=[Accessed: 24-July-2024 ]}