Laplacian Matrix Puns

I’m doing some filtering in matlab using the imfilter function. As I understand it, it is implemented with correlation/2D convolution.

The filter I am using is the Laplacian kernel, which is approximated by this matrix.

[ 0 -1 0; -1 4 -1; 0 -1 0]

But how is this matrix derived?

The reason I would like to know is because I am interested in better understanding the filtering process going on here so I can design my own filters to use with imfilter.

The Laplacian kernel essentially embosses the image but if I wanted to derive a filter that embosses, what process would I follow?

Edit: For those wondering about the 2D convolution of two matrices using the conv2 function with the parameter ‘same’, this is how it is done.

1. Your filter matrix, also called a kernel, or a mask, is flipped vertically and horizontally.

2. It is placed over the matrix of your image, with the center entry aligned with the first entry of your image matrix. Some of the entries of the two matrices will be superimposed. This is why the filter matrix is also called a mask.

3. The values of each of the super imposed entries are multiplied together and then add the products up. For example. If entry A(2,3) is superimposed with entry B(2,2) the values there are multiple together. If A(2,4) and B(2,3) are also superimposed, you multiple those together as well and then add the products. So N = A(2,3) * B(2,2) + A(2,4) * B(2,3)

4. The value, N, from step 3 is the entry for the place in new image matrix at the location in the original image matrix that is aligned with the center of the filter matrix.

5. The center of the filter matrix is moved to the next entry in the original image matrix and steps 2 through 5 repeat.

Hi, my question is that why here the x^(T)*A*x transitions the the sum?

I've been reading some applied math papers and the notion of the gradient of a matrix and Laplacian of a matrix keep coming up. I keep googling but nothing comes up (maybe I'm not googling the right things?).

If anyone knows how these are defined, please let me know!

Hello /r/Physics.

It's everyone's favorite day of the week, again. Time to share (or rant about) how your research/work/studying is going and what you're working on this week.

I am working on calculating entropy of a financial network. Researchers have tried to calculate density matrix for a graph by calculating a graph laplacian (see eq 10). However, accoriding to this answer on SO, correlation matrix can be substituted.
Please let me know if the SO answer is valid or not. Many thanks.

Do your worst!

It really does, I swear!

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

I'm surprised it hasn't decade.

There's this word that describes the phenomenon of a name that carries power due to the collective consciousness its devotees or venerators give to it.

Please what is it? I think it begins with "g". I can't really remember it. Thanks in advance!

They’re on standbi

Buenosdillas

Pilot on me!!

Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.

This sub is mostly just NSFW puns now.

If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.

Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.

When I got home, they were still there.

What did 0 say to 8 ?

" Nice Belt "

So What did 3 say to 8 ?

" Hey, you two stop making out "

I won't be doing that today!

You take away their little brooms

This morning, my 4 year old daughter.

Daughter: I'm hungry

Me: nerves building, smile widening

Me: Hi hungry, I'm dad.

She had no idea what was going on but I finally did it.

Thank you all for listening.

There hasn't been a post all year!

[Removed]

Why

It’s pronounced “Noel.”

After all his first name is No-vac

What, then, is Chinese rap?

Edit:

Notable mentions from the comments:

• Spanish/Swedish/Swiss/Serbian hits

• French/Finnish art

• Country/Canadian rap

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• Turkish/Tunisian/Taiwanese rap

There hasn't been a single post this year!

(Happy 2022 from New Zealand)

Nothing, it just waved