Computing first derivative--image processing

I need help understanding computer first derivative

I don't understand how to derivative of [5 5 5 4 4 3 4 3 4 5 2 2 2 2 1 1 1]

is

[X 0 -1 0 -1 1 -1 1 1 -3 0 0 0 -1 0 0 X]

Answer 1

[Image Analyst]

It's just the (n+1)st element minus the nth element. Same as you'd get from diff(). There are also imgradient(), and imgradientxy() functions in the Image Processing Toolbox.

[MLnoob5340]

Okay! how would I find the second derivative do the same process again?

[Image Analyst]

Yeah, you can do that. What do you really want to do anyway? Why don't you post your image and say what you want to measure in it or do to it?

Answer 2

[Youssef Khmou]

In general diff(X,n) of N by 1 vector returns an N-n by 1 vector, second derivative is diff(X,2), using gradient is better because it offers a possibility to choose the sample rate, if its 1 then :

 d2x=gradient(gradient(x));