Topographic Mapping



These images show Weaver's Needle in Arizona. The parallax between the top of Weaver's Needle in the top left and right photographs (taken from different points) is noticeably higher than the parallax for the lower-lying ground around it. This is illustrated from a side view in the bottom right image, where  θ1 is the parallax for the top of Weaver's Needle, and the smaller  θ2 is the parallax for a point at a lower elevation. Images from Google Earth.
Photogrammetry is a passive sensing technique, meaning it simply photographs the Earth using light reflected from the sun rather than creating its own EM waves like radar or LIDAR. These images can range in wavelength from visible light to near-infrared. When images of a given object are taken from different positions, there is a change in angle between the two images. The farther away the object is, the smaller this change in angle. When distance to the object is large compared with the camera's change in position, this angle is inversely proportional to the distance between the camera and the object  and directly proportional to the horizontal change in position of the camera between photos. If an airplane or satellite is taking these photographs of the surface of the Earth, this concept, called parallax, can be used to find the distance from the airplane or satellite to the surface, using GPS to determine the change in the camera's horizontal position between photos. Different points in an image will have different elevations and thus display variations in parallax. For example, in the top-view images of Weaver's Needle, the top of the Needle displays a greater change in apparent position between the two images than the surrounding lower-lying features because it is closer to the plane or satellite as it flies over. The top of the needle appears to "swing" south (down in the top-view images) compared to the ground below. A camera is able to determine the parallax angle based on this apparent change in position by identifying the location of similar or identical pixels in two images and applying formulas to determine parallax angles based on their changes in apparent position between the two images. This way, relative elevations can be determined, and absolute elevations can be determined by comparing these relative elevations to ground control points, whose xyz positions have been recorded by GPS.

Photogrammetry is the most widely used topographic mapping technique in the U.S. It is used by the USGS to create 30m resolution digital elevation models (DEMs). As a passive sensing technique it is much cheaper than LIDAR, and older too. The data can be collected by satellites and aircraft that have cameras for other purposes, so it does not require launching or flying technology specifically for topographic mapping purposes, only applying computer algorithms to the imagery. However, it is not as accurate as LIDAR because the images interpret the canopy in forested areas to be the surface, and accuracy is also limited by spatial resolution of the imagery. Photogrammetry also cannot be used when clouds cover the land.