Although it looks difficult, it's actually quite easy to generate a 3D model from a height map. This technique has been used for a long time, most notably in the landmark game Myst.

Blender

We'll use the free and open-source 3D application Blender to generate the 3D model.

The trick is to generate a plane with lots of points, then use the displace modifier to change the position of the points based on the brightness of each pixel.

Resources

For more information, check out the following guides:

• Blender manual
• Simple Terrain Meshes Using The Display Modifier: another video that explains the steps.