Question about markov random fields

[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

 

[mmwave]

y

Hello Lucy,

That is a great question! The input parameter for the MRF potential function is often the difference between intensities because it allows for a more localized and specific representation of the relationship between neighboring pixels. By using the difference in intensities, the potential function can capture how similar or dissimilar neighboring pixels are, rather than just their overall intensity levels.

Additionally, using the difference in intensities allows for the potential function to be more robust to noise and outliers in the image. If the sum of intensities was used, a single outlier pixel could greatly affect the potential function, whereas using the difference in intensities allows for a more gradual change in potential.

I hope this helps clarify why the difference in intensities is often used as the input parameter for MRF potential functions. Let me know if you have any other questions!