Aaron F. Bobick
MIT Media Laboratory

1. Goals

I see three fundamentally distinct educational goals: It seems best to address these separately. My goal is to consider curriculum choices for each area.

2. Undergraduate education in preparation for graduate study involving images

I think there are two fundamental areas to focus on in undergraduate education. The first is tools --- basic, fundamental tools. Examples from mathematics include probability and linear algebra; one might include some advanced calculus or numerical methods, though those can be acquired in graduate school. The other suite of tools is from computer science, in particular data structures and algorithms. Unfortunately most of those areas tend to be rather application free. On possibility is to incorporate image manipulation tasks into these fundamental courses -- see the opportunities section below. As a side comment, if forced to choose between taking the math or taking the CompSci, I advise students to take the math. Every time.

The second area is exposure to some higher level field that either uses images (such as medical imaging) or considers the vision problem from an inference side (AI or cognitive science). When looking for graduate students (especially PhDs) I find that those with the broader exposure have more passion about what they want to study. As an "educational professional" my efforts here have focused on 1) encouraging broader course selection among Computer Science undergraduates, and 2) making graduate seminars accessible to senior level undergraduates. (Again see opportunities.)

3. Undergraduate education in preparation for industrial image work

First, I include everything I mentioned in the previous section. Perhaps the higher level exposure is not necessary, but it will provide some perspective on just how hard real problems area. To this I would add only one required course plus a choice of some graduate style courses. The requirement I advocate is a "signals and systems" course. At MIT this type of course is taught by at least four different departments, each using examples from their preferred domain. Since all CS students take some EE courses, the EE version focuses on circuits, Laplace and Fourier transforms, and most continuous signals. At the Media Lab we have created a course emphasizing discrete systems. While it is perhaps a matter of taste I wish more students learned about the discrete side from a theoretical perspective, not just as an approximation to the continuous domain. My guess is they would be more prepared for industrial work if they did.

The graduate style electives are image processing and pattern recognition (here is the information about a PR class I just completed). Despite the advances made in computer vision in the past few decades, my experience is that most industrial vision involves IP and PR. A IP course forces students to consider every aspect of the image formation process, to consider color, and basically to recognize the difficulty of extracting information from an image. Also, it reduces theory to practice.

4. Graduate education in CV

Beyond the typical CV curriculum I would like to advocate two distinct areas of study, quite unrelated. The first is geometry and imaging, and in particular a style of geometry that relates normal Euclidean geometry to photogrammetry, and projective geometry to the projective reconstruction now common in Europe. When I talk to a photogrammetrist it is embarrassing what I don't know about the relations between images and geometry. Often they view much of computer vision as naive; perhaps they are a little bit off the mark, but not much.

The second area is "biologically inspired" vision study. One approach is the traditional study of human perception. But perhaps a more engaging approach is a class like the one Ted Adelson, Sandy Pentland, and I teach called "Image Representations for Vision" (information is here). Each of us has a background in perception so we can relate the machine work to human vision. This has been an ideal class for senior undergraduates to take: they not only see the relationships, but also do projects which require the manipulation and interpretation of imagery. My teaching vision mantra: Projects are good!

5. Opportunities

So, what can we do? Here are some possibilities:
  1. Using images in core courses
    Everything from object oriented programming to window manipulation to hierarchical data structure can be taught using images as examples. And students can immediately see the results.

  2. Accessible graduate classes
    The PR and Image Representations classes I teach are listed both as graduate and undergraduate courses. The only difference is the grading pool/procedures. The PR class gives undergrads useful tools for industry; the ImageRep class tries to be broadening (and maybe even inspiring!).

  3. Not teaching "multi-media" courses!
    This is the ultimate "pick it up as you need it" subject matter. Learn about JPEG in IP, not from programming a Netscape plug-in!
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Last modified: Tue Jun 11 13:48:36 EDT 1996