Do we all see the same color?

Here's a trick question. When a group of people all look at the same thing, for example a red tomato, we all agree that it's red, maybe some would say closer to orange, but usually we all agree it's a red tomato.

Now what happens is that our eyes see the object and it's color, and we all agree to call a tomato red, but what if in my mind I see red differently, maybe I'm actually seeing blue but because we all call it red I do as well.

I've often wondered if our eyes actually do some sort of translation of colors so that our brains can make sense of them, which might be why people who have eye transplants still see the same color as they did before.

The scary thing is that in the future when we can get computers to read our minds we might discover that in fact our color charts are unique to each individual, of course that means if computers are ever able to give us information directly into our brains they might have to use a color translator so that our brains see what they're supposed to see.