The tricky part is that people don't necessarily report what they see as what they see, and you can't really look inside their brains to get at what they meaningfully perceive.

A good example of this was the inauguration crowd size photos where people who were unfamiliar with the topic reported a unified perception on which crowd was bigger based purely on the photos. People who knew what the photos were of varied their conclusion based upon their political stance.

One conclusion you could draw from this is that their beliefs were altering their perception, but how would you distinguish that from people altering their expression of what they saw based upon their beliefs?