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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

1 1 1
2 2 2
3 3 3

4 4 4 
5 5 5 
6 6 6

7 7 7
8 8 8 
9 9 9

etc.

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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 '10 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 '10 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/node8.html) but I can't figure out how to make a 3D kernel out of that. –  Nick Jul 12 '10 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 '10 at 18:52
    
In honour of J O'Rourke's answer, I am retagging this differential-operators. –  Willie Wong Jul 12 '10 at 20:03
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1 Answer

up vote 2 down vote accepted

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

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+1 for the link to a page with an ADE classification I didn't know about! –  José Figueroa-O'Farrill Jul 12 '10 at 19:18
    
you are my hero. –  Nick Jul 12 '10 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 '10 at 19:27
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