GUARNIERI, ALBERTO 
  
2) compute the radial projection of A(k,, Ke» ke) as 
P(K,.K,) = [A(K,,K,.K,)dK, (26) 
0 
3) the angular coordinates of in spherical representation (see Fig. 4) can be found as 
(9,0) -argmin, , P(K,,K,) Q7) 
since, from the inclusion of ® within the locus A(k) = 0, P(k, ,kq) = 0 with P(¢,0) = 0; 
4) define o the versor of the direction (¢,0). 
The use of radial projection (26) simplifies the 3-D search for a line of the locus A(K) = 0 into the minimization of a 2-D 
function which can be solved by standard numerical methods. 
  
  
  
  
  
Fig. 4: Change of coordinate reference systems 
4 ESTIMATION OF THE ROTATIONAL ANGLE vy 
Once the rotational axis has been determined, the estimate of the rotational angle y can be conveniently approached in a 
cartesian coordinate system with an axis along c, as shown in Fig. 4. The determination of this coordinate system and 
the representation in this system of relationship (21) between magnitudes can be obtained as follows. Define the 
cartesian coordinate system 
u k, 
u-[vizc k, (28) 
w k, 
with 
— sing —cos0cosp sin9 cos 
C=| cosp -—cos@sing sin6 sing (29) 
0 sin cos 
In the new cartesian reference system defeined through(28) and (29), equation (21) becomes 
IL, (Cu)| = IL, (R^ Cv) = (co AR Cu) (30) 
Define for convenience| Li(u)| = |L;(Cu)|, i= 1,2, from which(30) can be written as 
  
324 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.