Hello all,
I am trying to understand Markov Random Fields and endearing graphs for optimisation with graph cuts. I went to a lecture the other day at a local university and the speaker said something like (from my notes):
"In a an MRF the so-called "cliques" are not ordered. One does not consider two interactions per pairs of pixels say, e.g., (i,j) and (j,i)."
Later when I started thinking about it, it seemed a bit weird to me because if we have a graph, say with nodes x and y where we say consider a simple quadratic potential between them, then there is an edge between x and y with the capacity |x - y|^2 and similarly there is an edge between y and x with the same capacity, correct?
However, according to the speaker it does not make sense to model the two interactions (i, j) and (j, i). I wonder why that is? Is there any physical reason behind it?
Also, what happens when the potential function is not symmetric? i.e. V(i, j) != V(j, i)? Does it still not make sense to model these interactions?
I would be really grateful if someone can shed some light on it. I have been trying to understand this. It is too bad that I did not realise this during the talk as I could have tried to ask the speaker himself!
Many thanks,
Luc
I am trying to understand Markov Random Fields and endearing graphs for optimisation with graph cuts. I went to a lecture the other day at a local university and the speaker said something like (from my notes):
"In a an MRF the so-called "cliques" are not ordered. One does not consider two interactions per pairs of pixels say, e.g., (i,j) and (j,i)."
Later when I started thinking about it, it seemed a bit weird to me because if we have a graph, say with nodes x and y where we say consider a simple quadratic potential between them, then there is an edge between x and y with the capacity |x - y|^2 and similarly there is an edge between y and x with the same capacity, correct?
However, according to the speaker it does not make sense to model the two interactions (i, j) and (j, i). I wonder why that is? Is there any physical reason behind it?
Also, what happens when the potential function is not symmetric? i.e. V(i, j) != V(j, i)? Does it still not make sense to model these interactions?
I would be really grateful if someone can shed some light on it. I have been trying to understand this. It is too bad that I did not realise this during the talk as I could have tried to ask the speaker himself!
Many thanks,
Luc