The human brain will do its best to make the pieces (visual images) fit the puzzle it is working on.
...That my friend is the "scientific" explanation of a person seeing what they want to see. I'm not trying to say they are making stuff up. They want to see what they believe, and the brain accommodates their desire.
All quite true. Our brains naturally look for patterns in things. That's why there are so many images of the Virgin Mary or Jesus found on burnt tortillas.
It's not just with visual images either. Think about some of the conspiracy theorists. They regularly put very plausible (on the surface) sounding scenarios together from bits and pieces of data that really aren't connected at all. However, they interpret data to make it fit into whatever mould they've committed themselves to. "When you've got a hammer in your hand, everything looks like a nail."
Combine the above with a few faked pieces of "evidence" (certain footprints come to mind), questionable eyewitness accounts and some nebulous visual images we see with our own eyes. It's not hard to see how serious self-deception can happen, and most people are too proud to admit that what they firmly believe could be dead wrong.
Magicians, mentalists, faith healers, etc. all manipulate their audiences by toying with the same basic properties of the human brain. We often don't need someone else to fool us though; we can do a pretty good job of it on our own.