F. Curved Lines

1. General

Not all data relationships are linear. The graph in Figure I-10 are the results of an aerial camera calibration for radial lens distortion. The distortion is caused by lens material and surface curvature. Its effect is measured on the image plane at radial intervals from the principal point. 

Figure I-10 Lens Distortion Data

It's obvious the data doesn't fall on a straight line, but it doesn't follow a simple curve either.  So how do we fit a curve to nonlinear data? Linear regression can't be used to fit a curve because, well, the curve isn't straight.

Actually, linear regression can be used in some cases if the logarithm of the dependent variable or logarithms of both variables are used. But those are exceptions to the rule, we want a universal method.

Let's examine a few surveying applications.