5.3 Topographic Correction

In previous sections, we attempted to correct the atmospheric effects, i.e. convert image digital numbers DNs to image radiance Ls. After atmospheric correction, we expect to have the spectral reflectivity r.

Assume that atmospheric effects can be completely removed from the image, the spectral reflectivity obtained contains the real target reflectance r and the topographic modification during image acquisition, G.

= r ï G

The G contains information about the viewing and energy incidence geometric relationship.

Moon can be considered approximately as a surface that reflects equal amount of light in all directions.

5.3.1 The role of relief

What effects does the relief have on the image radiometry? To answer this question, a different coordinate system will be used and Figure 5.6 shows this image coordinate system. In this coordinate system, z is the viewing direction and x-y plane is the image plane.

The actual relief for a small area is defined by its normal and the light source defined by

In discrete case these are the differences between elevations between neighbourhood cells and the grid cell under consideration.

5.3.2 Gradient Space

For perfectly white surface, when r = 1

For a grey surface, which is a proportional to a perfectly white surface
We can consideras a function of the slope factor (p, q) of the surface.

If r is the same over the whole study area, we can use two set of (p, q)'s to recover (p, q). Similarly, we can use three sets of
(p, q)s

1(p, q) 2(p, q) 3(p, q) to

recover both "r" and (p, q).

Using (p, q), we can generate a shaded map based on a DEM of an area.

Instead of calculating (p, q) for each grid on a DEM, we can calculate a two dimensional lookup table
-0.2 -0.1 0 0.1 0.2
The entire DEM {p, q} can be mapped using the above table.

in vector form is (-p, -q, 1)

in vector form is (-ps, -qs, 1)

The look direction is (0, 0, 1)

For sensors that look in nadir direction, the image coordinate system is only a shift from the local Cartesian coordinates. Thus, the above formula can be used to correct satellite (Landsat) imagery.

These relationships can be seen from the following diagram.