How can perform a distance transform along different directions from a line?

I have grayscale images with rod-shaped particles, and I want to get the intensity as a function of distance across the width of each particle. I have used the particle skeleton and a distance transform to help me find the pixel intensities at increasing distances away from the skeleton, but this doesn't give me any information on the direction of the pixel away from the skeleton i.e. the intensity vs. distance plot I get is an average of both sides of the rod, and I would like to be able to plot intensity in both directions separately.

Is there a way to not only find the distance of each pixel from the nearest 0 pixel, but also its direction relative to that?