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In their paper on Image Pyramids, Burt and Adelson state the following about pyramid generation.

An additional constraint is called equal contribution. This stipulates that all nodes at a particular level must contribute the same total weight($=\frac{1}{4}$) to nodes at the next higher level. Let $\hat{w}(0)=a$,$\hat{w}(-1)=\hat{w}(1)=b$,$\hat{w}(-2)=\hat{w}(2)=c$. In this case, equal contribution requires that $a+2c = 2b$.

How is this weight condition derived and why is the weight $\frac{1}{4}$? For a larger context of the question, the screenshot of the relevant section in the paper can be seen below

enter image description here

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The following picture from this set of lecture slides explains the equal contribution. The contribution from two nodes in the same layer must be equal. With reference to the figure, the sum of weights on green edges must match the sum of weights on the blue edges.

enter image description here

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