Education is what remains after one has forgotten everything one learned in school.

Know the literature If you are working on a problem that you think is important, chances are somebody else has also worked on it. Since the advent of Web searching, it has become easier to search, but don't limit your searches to Google. It's OK if you spend several days looking in the library. Looking at actual paper copies of old journal papers isn't necessarily a bad thing. After all, you plan to spend months or years on this project. Some papers were written before Web searching [13.2]. Often, you can be fortunate enough to find that someone else has done a good literature survey for you. For example, in the topic of the shape from motion, [13.3] and [13.1] thoroughly teach the relevant material.

Form an Objective Function In Chapter 6, we saw one example of finding an image that is the solution to an optimization problem.We found images that resembled the input image but also had some other desirable properties. In Chapter 5 we derived convolution kernels by finding best fits to data. In Chapter 12 objective functions were explicitly used twice.

In some rare instances, it isn't possible to set up a problem in terms of an optimization problem, but it's a good way to start.

Do the Math Correctly Once you have set up an objective function, you need to minimize it. For that, you often need a gradient. Can you find the gradient analytically as in section 6.5.1, or must you use numerical methods to estimate the gradient? In Chapter 12, we solved for a homography by using two images. But even if the math is correct, is it a valid approach?