# Question about markov random fields

1. Jun 28, 2011

### pamparana

Hello everyone,

I have a (noob!) question about Markov Random Field potential function.

So, I am looking at some literature where the markov random field potential function used is the so called Huber function, which is defined as:

V(t, a) = t^2 if (a < some_value)
V(t, a) = 2*a*|t| - t^2 if (a >= some_value)

So, I am looking at the computation of the MRF potential function in a first-neighborhood system, so looking at 4 adjacent neighbors:

What I notice is that the input to this V(t, a) function i.e. the t parameter is always the difference between the intensity at the site and the neighbor (I am looking at a 2D image).

So,

t = f(i) - f(i - 1) for left neighbor
t = f(i) - f(i + 1) for right neighbor

and similarly for top and bottom neighbor where 'f' is the intensity function.

My question is why that is...So why is the input parameter (t to the potential function V) the difference between the intensities....why not the sum of intensities or any other combination...?

Appreciate any replies you can give me!

Luc