Not in any sort of "clean and usable" manner if you want vector and only use Photoshop.
You can create selections in Photoshop, then convert those selections to "Work Paths" (which are vector). And in turn use the work paths to create shape layers.
Based upon that image it would:
Selecting... take a HUGE amount of time to make all the selections considering the type overlays and color variations. Even something like selecting a color range still means you'll need to manually remove the type overlays, either before the selection or from the selection itself.
Work Paths... the resulting paths would most likely not be as accurate as the selections themselves due to the density and size of the lines. Convert to Work Path isn't exactly a precise operation. It's a "best guess" from the app. It often takes manual alteration to get the work path correct. Multiply that by the amount of paths you'll have, and... well...
Shape Layers...creating shape layers could also be very time consuming if you needed different shapes for various areas or, heaven forbid, a different shape for each line.
A better alternative may be to use Photoshop to boost contrast in the image and erase the text overlays. Then use a vector application (Illustrator, Inkscape) that has some tracing capabilities. You still probably won't end up with an exact match, but it would definitely be a lot closer in the end.
Heck, even using the pen tool to manually draw each line, using that photo as a guide would take less time that the 3 steps above for many users.