It's probably a good idea if you create a separate parallax layer that contain absolute positioned links as a form of navigation. If you strictly want to map certain areas on the image as links, you might want to use a tag as in this example taken from here:
<img src="planets.gif" width="145" height="126" alt="Planets" usemap="#planetmap">
<map name="planetmap">
<area shape="rect" coords="0,0,82,126" href="sun.htm" alt="Sun">
<area shape="circle" coords="90,58,3" href="mercur.htm" alt="Mercury">
<area shape="circle" coords="124,58,8" href="venus.htm" alt="Venus">
</map>
The shape defines the type of area of each clickable area, the coords define the perimeter of said areas; the href attributes define where the page navigates if said area is clicked.
To achieve this with a non-basic shape, you can set the type to "poly" and then set the polygon's each anchor point's coordinates as such:
<area shape="poly" coords="450,25,435,60,400,75,435,90,450,125,465,90,500,75,465,60" href="yellow.html" alt="Yellow star.">