Welcome to MathOverflow

Question

0

Does anyone know what a 3x3x3 Laplacian kernel looks like? I realize that might be an open-ended question, but I need to apply a Laplacian convolution using a 3x3x3 Laplacian kernel, and frankly I don't know what it looks like...

edit: and by what it "looks like" I'm hoping someone can just tell me in the form of

etc.

edited Jul 12 2010 at 20:01

Willie Wong
6,987●20●43

asked Jul 12 2010 at 18:24

Nick
37●7

3

What's the context to this question? Since you specified 3x3x3, do you know the kernel for other dimensions? Laplace has made many contributions to mathematics, and kernel is a really overloaded word in mathematics, so a little bit of clarification may help jog our memories to help you. – Willie Wong Jul 12 2010 at 18:41

Something tells me that the tag is inappropriate; although I must confess that I don't understand the question. – José Figueroa-O'Farrill Jul 12 2010 at 18:51

so I have an image I've applied a Gaussian blur too, which used a 3D kernel. I did not write the Gaussian kernel, but someone else did. Now I need to apply a Laplacian convolution to my image that was already convoluted with a Gaussian kernel. I found an example of a 2D Laplacian kernel (fourier.eng.hmc.edu/e161/lectures/gradient/…) but I can't figure out how to make a 3D kernel out of that. – Nick Jul 12 2010 at 18:51

this tag is definitely inappropriate, but i don't know which tag it belongs to and since I have low points, i couldn't add a simple and applicable tag like 'convolution' or 'laplace' because they don't exist. so i picked a random one. – Nick Jul 12 2010 at 18:52

In honour of J O'Rourke's answer, I am retagging this differential-operators. – Willie Wong Jul 12 2010 at 20:03

Joseph O'Rourke · Accepted Answer · 2010-07-12 19:32:17Z UTC

2

I think (perhaps?) you are looking for the discrete Laplacian operator. That Wikipedia page lists the $3 \times 3 \times 3$ convolution kernels explicitly.

edited Jul 12 2010 at 19:32

answered Jul 12 2010 at 19:15

Joseph O'Rourke
43.2k●1●49●214

	+1 for the link to a page with an ADE classification I didn't know about! – José Figueroa-O'Farrill Jul 12 2010 at 19:18
	you are my hero. – Nick Jul 12 2010 at 19:19
	@Nick: Hardly heroic, but ... thanks! @José: I was also unaware of that ADE classification. An informative page! – Joseph O'Rourke Jul 12 2010 at 19:27

3x3x3 Laplace Kernel?

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.