Using a grayscale image to sculpt detail

I have a grayscale topographical image showing the surface of Mars. I would like to take the height information from the grayscale values and use them to sculpt the features onto a sphere. I don’t want to use the image as a texture for the normals. I want a true 3D representation of the terrain. I’m fairly new to Blender but I can manage to get around easily in the program. I’ve tried looking in the program to where I can accomplish this. Thanks.

UV unwrap the sphere to match the layout of the greyscale image.
Subdivide the sphere with subsurf modifier
Add adisplacement modifier set to UVs and using the greyscale image

Example: