Raster effects?

Question

Mathematics

Where can I find _mathematical_ formulas for creating various effects (sepia, grayscale, etc.)?
Does Qt have out of the box functions for applying effects? Does it work with images pixel by pixel to apply formula-based effects?
If not, are there cross-platform C++ frameworks that will allow you to work with images pixel by pixel?
PS: I need to write some effects that could be applied to images obtained from the camera using openCV, but in the future I would like to apply the same formulas to ordinary images obtained from files.
Solution:
1) Gonzalez R. and Woods R. will help with the math.
2) The ready-made effects are in QGraphicsEffect, and QImage::bits() to work with an array of bits.
3) From other libraries, you can take libpng, libjpeg, ImageMagic, etc. to help.
Thank you very much for your help!

Answer 1

So, if openCV is already in use, what's the problem with taking all the necessary functions from there?
I understand, if it would be necessary to do without bold libraries ...
PS In general, the vast majority of "filters" are implemented in the most elementary way using simple matrix operations.

Answer 2

I once wrote a small article just about effects in Qt, maybe it will come in handy.

Answer 3

Here is an article about sepia.
And so, look there for articles in Russian and English , in my opinion, a lot of interesting things in terms of image processing.