How to combine the information of two probabilities? I have a segmentation problem that using two different models I can assign a probability to each pixel of the image to be a background part. Two models produce slightly different results. Some pixel may have zero probability using one model, but have some value using the other model. But the idea is try to combine the outputs of two models.
The question is how to combine these two probabilities for each pixel? For example, using mutual information? I think the two probabilities I got are two marginal probabilities, then how to get the joint probability in order to calculate the mutual information?
Or you have a better idea to combine the two probabilities please tell me. Thanks very much.
A.
 A: It sounds like a mixture of the model probabilities is likely to be related to what you want. The question is how to weight. There are a variety of ways to produce approximate model weights.
Some examples of methods: 
i) use approximate Bayesian inference via BIC to derive model weights (Bayesian model averaging); 
ii) use the information-theoretic approach discussed in the book Model Selection and Multimodel Inference by Burnham and Anderson (same approach as before, but using AIC);
iii) there's also frequentist approaches (e.g.). 
iv) Outside likelihood-based methods (but not unrelated to them), there's approaches like cross-validation to choose the model-weights.
There's probably an approach based on entropy too, I just haven't seen one.
A: One possible way to use mutual information in the context of your problem is to use an approach similar to image registration. For each pixel, take a box region (say 11x11 box centered around the pixel). Next, calculate the histogram of probabilities from each model over the box. Now that you have two histograms, calculate the mutual information between the two (or other metrics more related to your problem). After looping over all pixels, you have a new image where each pixel contains a measure of "agreement" between your two models. 
