applying newton rapshon method

I have an image 'cameraman.tif'.I have to apply newton rapshon method using the formula to that image

Cj=Ci-f(Ci)/f'(Ci)

f(Ci)=i^2-i-1

f'(Ci)=2i-1

Ci is the central pixel

Cj is the neighboring pixel of Ci

please hel how to process

[Jan]

What is "the neighboring pixel of Ci"? There are either 4 or 8 neighboring pixels.

[FIR]

8 nighbours

[Amith Kamath]

Also, I believe images need two indices, as in C(x,y). Could you rephrase the question based on two indices?

Additionally, I fail to understand how the left hand side of the equation is already known to be the neighboring pixel (?)