I am trying to implement the "Interactive Graphcut" algorithm for color (3 channel) images. So the user is asked to pick a series of pixels(voxels) as forground and a series of seies of pixels ad background.
So When the user picks "N" pixels as foreground and "M" pixels for background, I will have:
(N x 3) values for fg
(M x 3) values for bg
where 3 is the number of channels. when I use EM to get my probability distributions, I must apply it to each channel (right?) and so for each segment (fg/bg) I will have 3 GMMs.
Now to compute the likelihood of being foreground or background for each pixels I should compute the likelihood of each of the 3 channel values given the corresponding probability distribution Meaning that for each of the 2 segments I will have 3 likelihoods(one for red channel, one for green channel and one for blue channel). Now what should I do?
Should I sum the 3 likelihoods up for each pixel? or should I average them?
I need "The Likelihood of being forground p(I|F)" and "The Likelihood of being Background p(I|B)" for each pixel.
thanks!
Why you use separate likelihoods for each channel?
Just treat each pixel (voxel) as a multi-dimensional data and use two Multivariate Gaussians as the likelihoods; one for the foreground and the other for the background.
Regards!
I was having the same problem months ago. When we use GMM, we have a set of parameters for each distribution. So, you should compute two likelihoods. One for foreground and the other for background.
I will send a paper that describes how to calculate the parameters from GMM.
Best Regards!
http://vislab.isr.ist.utl.pt/wp-content/uploads/2012/12/11-mva-greggio.pdf
I hope i can help you in this link
http://www.mathworks.com/matlabcentral/fileexchange/26184-em-algorithm-for-gaussian-mixture-model--em-gmm-
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