ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
  
  
  
  
  
  
  
  
  
  
  
  
Z'X 7 nJn, I' 2 nni 
For simplification, the following denotations are Z', = n/n, l'y 7 nyng 
introduced: 
ik Ay, Bly 4X o Zu dY, dA 
R-R,4- R,, Q) ] 
. OR , OR, OR ; 
D LIRE TZ. A +7 Y m I dr + 
R-R,4 Ris | Tr T gr or ; 
Laser scanning is now regarded as a technique to model terrain 2 
surface. Assume that we want to derive a TIN surface of / : (5) 
elevations. | OR. OR. OR 
+|Z, tZ, A PU gpe 
Z fq (3) p pepe) 
The gradient in Z in the X and Y direction is finite and exists l | 
for all Z. ON „OR... OR x 
+| Zr — +Z, — || 7, j-dh 
oh oh oh ; 
ie =, , 
Ze = Zt 
0X where Az, = discrepancy between measured and 
of approximate value 
— 12 PP 
Y OY (dX. s dY, 4 y = updates to the unknown 
(4) datum shift 
(r, p, h) 7 roll, pitch, heading 
(dr, dp, dh) = updates to the unknown misalignment 
Some laser scanner systems register the intensity of each | 
angles 
reflected laser shot. Equivalent to elevation the intensity is 
continuos in at least some parts of the laser scanned area and 
the I (intensity value) can be expressed as function of X and Y 
(horizontal co-ordinates). The gradient in a point (X, Y) can be 
found in the normal vector of the triangle plane (figure 1). 
Also differences in intensity values serve as observations 
(Maas 2001) and their observation equation will be: 
  
  
  
Figure 1. Gradients can be derived from the TIN surface. À, eJ dX ot I,: dY ot 
Li 
| BRI" Bp 
A laser shot, (X, Y, Z); can be related to the TIN surface through +l, —+1, d > | dr+ 
interpolation of the three surrounding nodes. In this way, *sgr or ; 
original laser point can be used avoiding error contribution [ 7 
from regular grid interpolation (Maas 2000).. 
: ; ; oR oR bs (6) 
Equivalent interpolation can be done for intensity. + Tr A + H : E » ‚dp + 
The observation equation for elevation measurements l j 
(combining equation 1 and 4) will after linearisation be: 
l 
: OR; "OR, N 
[a ap sir = > ; : dh 
F 
  
  
Further information about the underlying theory can be found 
in (Burman 2000b).