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I know that we actually see with our brain in a way that eyes only absorb the incident light upon them and they transform some sort of information to the brain and the actual "seeing" is done by the brain.

However, this means that the incident light has to have some "specific properties" such that the transmitted information from eyes to the brain will be different for light coming from different objects.

What are those "specific properties" that light have?

For example, as far as eyes are concerned, the incident light is the same whether was reflected from an object from 5m away or 6m away, or it was a round or a not-so-round object. But there has to be some difference between the light originating from a 5m object and the light originating from a 6m object; otherwise, how could we (our brain) differentiate objects with different depth; we would only see a 2D plane.

Qmechanic
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Despite your intuition, it isn’t a specific property of the light that causes this effect. Instead, it is a statistical relationship between all the different photons stimulating your retina near-simultaneously, and the fact that your brain is very good at drawing conclusions from those patterns.

Computer vision systems are similar, but not (yet) as good. Both computers and our own minds can be fooled by various optical illusions. This is why, when we look at a TV show or a film or play a video game, we perceive the environment displayed as being more than merely a glowing screen with dots on it.

BenRW
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What are those "specific properties" that light have?

It has no any "specific properties".

Perceiving shape is the result that all shape surface reflects light rays and part of them scattered in the direction to your eyes lets brain receive image of that shape. Put some black dye, absorbing light very well, onto part of shape and look at this shape in a dark room with low directional light - now you will trick your brain that object shape has changed.

Perceiving depth of objects or evaluating distance to them is the end result of stereo effect,- the fact that you have a pair of eyes. Each one receives slightly different set of light rays, cause they will be reflected from a different angles of an object. Thus producing different images of a view from the left and right eye. These couple of images are transferred to brain and are "transformed to depth feeling".