The standard thing to do in these cases is to make zero be a medium gray, so that you can see negative output as well as positive. If you use one of the edge-detection filters, you'll see what I mean.

In fluid dynamic sims for example. Water level can be positive or negative. Grids of data can represent more than colors in images.

Well yeah. That has use, but when one mentions claiming negative results to black, I assumed that was for pictures. Obviously negative values mean something in other places, but I assumed we were talking about pictures.

No experience with this stuff, but it feels like you could do an abs(kernel) to extract some meaning from the negative value.

Applying this to the "outline" kernel, it seems like white bordered by black would show up just as white as black bordered by white, with homogeneous kernels still showing up black.