When I started computer vision the most common term, I found was Image derivation. In my school I learned derivation on the function, but the images are collection discreet value in terms of pixel. Its value ranges from 0 to 255 in terms of intensity. How can we apply derivative to discrete value it is not some function? Initially, I was confused and spend lots of time to figured out what exactly it means. With more digging I found Image differentiation refer to different to its pixel value.
It has three ways to calculate differentiation
df/dx = f(x) – f(x-1) = f’(x) backward difference
df/dx= f(x) – f(x+1) = f’(x) forward difference
df/dx= f(x+1) – f(x+1) = f’(x) Central difference
[10 20 10 200 210 250 250]
Central derivative [ -1 0 1]
Derivative at index 3 = 210 – 10 = 200
Derivative mask for image
derivative
Example given in shah lecture with x and y derivative
Reference
https://mccormickml.com/2013/02/26/image-derivative/
https://www.youtube.com/watch?v=1THuCOKNn6U
http://www.cs.cmu.edu/~16385/s17/Slides/4.0_Image_Gradients_and_Gradient_Filtering.pdf
