Vision has changed since 1987. Back in 1987, Joe Mundy gave a talk about Computer Vision and discussed the key of geometry role in image understanding understanding. Interestingly, he also gave some advice for students wanting to pursue computer vision. A nice quote from the video linked above can be found on the Wikipedia entry on Joseph Mundy, but the punchline is that he believed that (back in 1987) concepts such as optics, transformations, and algebraic surfaces need to be mastered in order to make advances in the field. Interestingly, twenty years later the vision of computer vision has taken a step in a different direction.
Pattern Recognition -- also known as machine learning, or simply put learning. I would say that if a student wants to pursue graduate study in Computer Vision they have a good background in Statistical Machine Learning. I will elaborate on this later.
On another note, I had my Statistical Machine Learning midterm this past week. Quite possibly my last in-class exam ever! I've been taking these things since middle school and it will be a nice change of pace. Only designing/grading midterms from now on.