LaplacianFilter[data,r]
convolves data with a radius-r Laplacian kernel.
LaplacianFilter[data,{r1,r2,…}]
uses radius ri at level i in data.


LaplacianFilter
LaplacianFilter[data,r]
convolves data with a radius-r Laplacian kernel.
LaplacianFilter[data,{r1,r2,…}]
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:
-
list arbitrary-rank numerical array tseries temporal data such as TimeSeries, TemporalData, … image arbitrary Image or Image3D object audio an Audio object video a Video 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 Automatic the precision to use - With setting Padding->None, LaplacianFilter[data,…] normally returns a result smaller than data.

Examples
open all close allScope (9)
Data (7)
Options (5)
WorkingPrecision (3)
With real arrays, by default the precision of the input is used:
WorkingPrecision is ignored when filtering images:
Applications (3)
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:
History
Introduced in 2008 (7.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2016 (11.0) ▪ 2025 (14.3)
Text
Wolfram Research (2008), LaplacianFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/LaplacianFilter.html (updated 2025).
CMS
Wolfram Language. 2008. "LaplacianFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/LaplacianFilter.html.
APA
Wolfram Language. (2008). LaplacianFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LaplacianFilter.html
BibTeX
@misc{reference.wolfram_2025_laplacianfilter, author="Wolfram Research", title="{LaplacianFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/LaplacianFilter.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_laplacianfilter, organization={Wolfram Research}, title={LaplacianFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/LaplacianFilter.html}, note=[Accessed: 08-August-2025]}