Question

How would you differentiate a matrix ?

Answer 1

gosh, that was a crass generalistaion

post the question if you have a specific example but i still reckon you should "just differentiate"... :-)

Answer 2

Matrix calculus

Answer 3

so I am studying a book in computer vision, and they are mentioning some sort of differentiation procedure using "Gassuan derivate filters"... I am tyring to understand how Gaussian derivative filters work ... So I guessed that in order to get to that first I should get to how you simply differentiate the matrix.. They have to be similar, I just dont know how they are connected. Guassian filters with simple differentiation that is

Answer 4

what i remember ..you can either choose to differentiate either by row or column
like
if you would start with a row you will differentiate the row leaving rest of the matrix untouched, then the second one leaving the other two untouched and same with the third
and its a choice to go either with the column or the row whichever makes it work

Answer 5

!s there @ gl!tch in the matr!x?

Answer 6

I'm looking into it here trying to figure it out and at slide 9 I think it gets into it: http://crcv.ucf.edu/REU/2013/P1_filters.pdf

It looks less like a derivative where the limit goes to zero and more like they're taking finite differences between adjacent pixels. So for instance instead of:

\[\lim_{h \to 0} \frac{f(x+h) -f(x)}{h}\]

The 'derivatives' you'll be doing are not needed to be limits, since h=1:

\[f(x+1)-f(x)\]

But this is just for 1D input, not a 2D input like a matrix, but it looks like it sorta generalizes it a little here.

Answer 7

Actually this is pretty damn good I think, they start talking about derivatives at slide 36 but reading up to that point isn't too difficult I think.
http://www.cs.cornell.edu/courses/cs6670/2011sp/lectures/lec02_filter.pdf

Tell me how that goes and I think I can explain it depending on how much time you have and what kind of understanding of other stuff you have coming into this. Also, have you taken differential equations before and know what the heat equation is?

Answer 8

This is actually really cool, I didn't realize that this is how all this image processing stuff was done

Answer 9

Ok so your original assumption that we have to differentiate a matrix isn't right it seems. Really what's happening is that the matrix itself is acting as the derivative on an image.

So basically it just looks at points on the picture, and then combines them just like the derivative normally combines f(x+h) with f(x) to make a single function f'(x). Except since it's a matrix it looks at and combines f(x+h,y), f(x,y+h), f(x+h,y+h), and f(x,y) and possibly other points, depending on what kind of filter you want to do.