Before we go any further, you need to read the following text, which is available through the Library Resources tab in Canvas:
This section lays out the five basic steps in overlay analysis, namely:
Steps 1 and 2 are not major concerns from our perspective (although they are, of course, vitally important in real cases). In this section, we focus on step 3, while the remainder of the lesson considers some of the options available for step 4.
Note that affine transformation as discussed on pages 144-145 of the Bolstad text is often used. The affine transformation requires matrix [1] mathematics, particularly multiplication, for a thorough understanding.
The most important aspect to appreciate about this discussion is that, although the mathematics involved in co-registration of map layers is relatively complex, the required computations are almost always performed by a GIS.
In practical GIS applications, a simple linear regression approach, based on a number of ground control points in each layer, is often used to achieve co-registration. This provides estimates of the required parameters for the affine transformation matrix, which are generally sufficient to accurately co-register layers.
Exceptions may occur if the study region is large enough that map projection distortions between layers projected differently are significant. In such cases, first reprojecting layers to the same coordinate system is advisable.