ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision‘, Graz, 2002 
  
4. REFINEMENT OF THE RECONSTRUCTION 
In order to remove the projection errors and its 
negative influences on the 2D and 3D reconstruction, 
we use the height information to project raw data on a 
local plane through the 3D object line. As one can see 
in section 2 the projection errors become zero when 
Ah (hobj-Rpiane) 1S Zero. 
When an object line is recorded, high grey value 
gradients occur in the image data, due to the 
reflectance properties of (the surrounding of) the edge 
of the object. This physical property is now used in 
order to refine the reconstructed object line. Raw 
image pixels whose rays cross the approximated object 
line within a certain distance, are expected to have 
recorded (the surrounding of) the 3D object line. (A 
ray is the line starting from the CCD element through 
the projection centre, see figure 3.) The refinement 
consist of an adjustment of the 3D line such that the 
line is determined by high gradient pixels, in nadir, 
forward and backward configuration. "This 
optimisation criterion can be established by least 
squares minimisation of the perpendicular distances 
between rays of high gradient pixels and the 3D line. 
This has been done by weighting the distance with the 
Ray (Ox, Oy, Oz, Tx, Ty, Iz) 
\ 
Approx. 3D line(vx, Vy, Vz, Ux, Uy, Uz) 
Figure 3: Geometric configuration of 
observation (d). 
grey value gradient, perpendicular to the 3D line. The 
effect of the weights is that the estimation of the 3D 
line is dominated by rays through edges of the 
reconstructed object. 
The perpendicular distance d between a ray and the 3D 
line can be written as: 
de Ay) SO) [8] 
luxr| 
| s 
with s’= —,and s =u Xr. 
Is 
  
  
For all rays within some distance of the approximate 
3D line the observation equations are introduced. The 
meaning of using observation equations is that it 
expresses the distance d in terms of the unknown 
changes to the parameters of the 3D object line Ap;. 
e od dg \ 
Bd) - Ap. Wid} = = . [9] 
i=l i 
Where E{d} denotes that d is expected to be equal to 
the linear expression at the right-hand side of the 
equation, and W{d} is the weight of the observed 
distance. The elements Od/Op; are the partial 
derivatives of distance d to the object line parameters 
and can be written in terms of the approximate 3D 
object line and the ray elements. 
  
  
  
Dr nm 
dd 
—— = Yi 11 
ay | Thi 
od 
ez 12 
9z: P$ Li 
os = DL 
dd. 0X, ox, 
= (v—0), 
x, M i 
: 0 
with — =|-Z, 
dX, 
x 
epe 
ad oy JY, 
aY = ( z O), 
ae t 
z 
with — -|0 
u - X, 
0s nis uos 
N) 
od oZ oZ 
u u ; (v Le 0), 
oZ, ls] 
[15] 
T RR e 
oZ 
u 0 
For each 3D line, the observation equations are put in 
a model of observation equations. For m observed 
distances d, the model can be represented as follows: 
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