I was working on a little job today with a 2D temporally variant scalar field.

You know, B&W footage.

I needed to find the parts of the data that were changing the most and compare them to the overall data and the maximum delta.

What I ended up with, once Ben pointed it out to me, was a simple example of calculus laid out in a couple tools.   The simplest case is just taking the frames I have and interpolating the same number of frames, so there’s no missing samples.  It’s silly, really.

But you can try it with other sampling, so there’s also an example of a Sobel filter, with a 1D kernel perpendicular to the normal 2D one.  Cute really.

If you checked out my interactive smoothing comp, you can see how I used a Sobel filter to make the forward facing laser pointer by looking at the differentiation of the R and G channels over time.  Same idea, just different way of expressing the temporal dimension.

I’m tossing in a Laplacian filter too, just for fun, it’s not useful for the calculus part, but it was easy to do, and shows how you can change the kernel to make different effects.  It’s possible to also evaluate 2D or 3D kernels this way, too.  The temporal offsets can be combined with spatial offsets so you could make a 3D blur filter, or a 3D sharpen.  Or a 3D Unsharp Mask, as I’ve also included.