# How to draw surface normals from surface normal maps?

Using deep learning to estimate surface normals from monocular RGB images is a common task. The resulting image generally looks like this:

My question is how can I use this map to actually draw a normal vector (arrow) for any given point on the image? For example, I want to draw a line on the countertop that points up.

Most relevant tidbit I found on the topic: "The RGB color channels (red, green, and blue) in a normal map correspond to the respective X, Y, and Z coordinates of surface normals."

But I don't get what this means. The values are standard RGB, i.e., for each coordinate, you get three numbers in range [0, 255]. Just by how color changes between surfaces, it is clearly related to normals (obviously) but when I tried quiver plots using matlab I couldn't get reasonable results.

TLDR: What is the relation between surface normal maps and actual normal vectors? How can I draw a 3d line given a point on the image which represents the normal vector perpendicular to that surface at that point?

$$r = \text{round}((0.5x + 0.5) \cdot 255) \\ g = \text{round}((0.5y + 0.5) \cdot 255) \\ b = \text{round}((0.5z + 0.5) \cdot 255)$$
Decoding is: $$x = (r/255) \cdot 2 - 1 \\ y = (g/255) \cdot 2 - 1 \\ z = (b/255) \cdot 2 - 1$$