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Notes:


So now we can convert window cost to the cycle cost. Our window cost is roughly as follows. On the top we just have the previously described SSD cost which is to make sure that the pixels in the window have similar colors between the left and the right images. Since we will be comparing windows of different sizes, it is crucial to normalize our cost by window size. So our cost is a ratio of two terms, both of them sum up terms over image window. This nicely corresponds to the MRC formulation, it is also a ratio of 2 terms. Since we can convert from edge cycles to pixels inside the cycles, we can express both the top and the bottom terms of our cost function through the cycles. Now recall that edge weights w can be anything, so we can use this conversion for any graph. However for the bottom weights t we have a restriction that the sum over any cycle is > 0. Thus we cannot work with arbitrary graphs. Recall that to go from area to cycle edges we had to have negative weights. With this weight definition, each clockwise cycle edge weights will add up to + area inside a cycle, and all counterclockwise cycles will add up to –area inside that cycle. We can’t have non positive cycle.s