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Referring to (for example) Visual Thinking for Design, the book discusses various low-level processing channels in the brain. Colour and orientation are two examples.

I wonder if transparency is another such channel; and if it isn't, how exactly transparency manifests itself within the brain.

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'low-level processing' is not a well defined term. Do you mean in V1 (primary visual cortex)? I think transparency is a higher-order feature that requires (object) boundary detection. I doubt you can see a big effect of it in the early visual processing where color and orientation are processed. –  Memming May 23 at 14:48
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That is exactly my thinking, I doubt it is decoded in V1. You could also argue that transparency requires some higher level comparisons, as it involves both colour comparison, and some form of mental subtraction - you can attribute a single colour to two different objects. It kind of follow that you cannot attribute to it the term 'channel' - it's higher level. –  Izhaki May 23 at 16:50
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One interesting way to study transparency is by looking at cases where we perceive transparency even though there isn't any objective transparency.

Take this illusion from Adelson (2000) as an example.

In the both panels the diamonds have the same physical brightness (pixel value on the monitor), but our perception of the diamonds on the right is warped by the seemingly-transparent dark stripe that covers the diamonds on the top. Thus, even low-level image features like brightness are perceptually warped by the way our brain perceives the structure of the image.

There are a large number of papers on mathematical models of illusory transparency perception. A starting point might be Anderson (1997) and the references within. But, the general message from this research is that we sometimes perceive transparency as the result of imposing some kind of higher-order structure to make sense of the image.

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That's a great answer, I only wish it would address the question more directly. The answer offers support to the idea that transparency is a higher-level operation, thus cannot have its own channel. –  Izhaki May 26 at 22:17
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