94 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
X 
X far rs fis S 0 0 -Xx. Y 
y |= O51 O59 93 0-s O -yY, Z 
= Guy Wan fan 0 0 S -—Z S 
It may be necessary in certain photogrammetric operations to consider the origin o(x,, y;) of 
the image coordinates as unknown: 
1 
X 1.0 -F, a, G0, Qu S. 0 6 —X, X 
y = 0 1 dan Cz 04 0 Ss 0o —Y, Y 
= 0 0 5 031. 432 433 0.0 S. —Z. Z 
S 
Anamorphic lenses can be considered to have two projection distances: one applies for all 
measurements to be taken in the direction of film transport in the camera, the other for all 
measurements taken perpendicular to this direction. These two projection distances are here 
introduced indirectly as the scale factors c, and c,. Hence 
x 1 0 —F, ce, 0 0 dis  di2 dis S 0 0 -X, X 
y 1-101 0 c, Q azn daz das 0.S 0 —Y, Y 
z 0.0 zZ 050: 431  d32 dass 00 S-Z, Z 
S 
Non-photogrammetric cameras are not equipped with reference marks defining the image 
coordinate system. It is therefore not possible to orient the photograph in the measuring 
instrument. If an amorphic lens is used, a rotation between the image coordinate system and 
the amorphic coordinate system of the measuring instrument will be included into the 
orthogonal matrix A. However, because ofthe scale differences in an anamorphic photograph, 
it is also necessary to define for these photographs the angle of rotation a between the 
anamorphic photograph and the amorphic measuring system. Hence 
X 1 0 + cosa —sina 0 cx 0° 0 0 G2 dis 
7414219. 1 - sina cosa 0 0o sc, 0 93 939 dogg 
= 0 0 = 0 0 1 0 0 1 Gyn Usa as 
Ss 0 0 =X ‘IX 
0 s à rl; } 
0 0 $ 2,212 
Ifz = 1, this equation contains the following twelve unknowns: the coordinates ofthe origin of 
the image coordinate system x, and y,, the rotation a between the anamorphic and amorphic 
coordinate systems, the anamorphic scale factors c, andc,, the rotational elements a12, a15, and 
d23 (for x, 6 and o respectively), the scale factor S, and the coordinates of the position of the 
projection center X,, Y, and Z,. The matrices in the above equation can all be multiplied. The 
resulting matrix 
10 -x;] [cose -sina O €; 0 0 
0 1. -U. sina : cosa 0 0 c, 0 
0.1 0 0 1 0 0 1 
11 12 13 S.0.0 -X, by, bi, bis b, 
dar fan Qos 0 S 0 —Y | = 1 ba Pan Pas Pa 
d3; 035 035. ] LO O S -Z, bs, Das Das Das