Exercise : Measuring heights of trees outside the forest (TOF) in digital orthophotos (DOP)

Shadows in orthorectified remote sensing images

Figure A: Shadow length s and object height h

A simple application of the intercept theorem in elementary geometry is to determine the height of a tree by measuring the shadow length. According to Fig. A the shadow length \(s_1\) and the height \(h_1\) of a man-made object such as an overhead line tower were measured on the ground. If the lenght of a tree's shadow \(h_2\) is determined at the same time of the day we are able to compute \(h_2=s_2*\frac{h_1}{s_1}\)

We may also use trigonometry if we know the sun elevation \(\alpha\). The height of a tree is then computed \(h_2=s_2*\tan \alpha\)