Introducing image processing - Should I teach the math
I would tread lightly here for a few reasons:

The math is not strictly necessary.
The students signed up for an image processing workshop in the context of programming.  The core skill that they expect to come out with is the ability to program graphics manipulations.  Spending a substantial portion of this time learning about the underlying math, certainly important in a full semester's undergraduate or graduate coursework, only moves very slowly towards what they (presumably think) they signed up for.

Some kids get turned off by math.
One of the unstated goals of every course is to both show the value of the field, and hope that the student wants to go on with the material and learn further.  That means that we want them to like it.  Using a voluntary summer workshop to emphasize the more abstract parts of the material may turn many of them away from graphical processing entirely.


So, don't do any math then?
Actually, I would not say that.  I would touch on a some of the underlying mathematics, but briefly, and (because it is a summer workshop) with the simple goal of illustrating that there is important material that isn't too difficult to tackle if they eventually want to go further into the topic.