Solving equation (21) for X,> We get: 
xv - x. 
E UTI (22) 
x + 
in which V 9 k ee : 
E "a 
In a like fashion, 
yvy 
a c 
Yn V-1 (23) 
Ne 
in which V = k | —2). 
Ib Ya 
- X. 7 Xp y - % 
If abc is a straight line, as it should be, the ratios -——— and 0B 
Xp T x Yb T Ya 
are identical, and the quantity V can be computed using either ratio with the same result. 
Determination of the Interior Orientation of the Photograph 
The interior orientation, represented by the principal distance, f, and the 
principal point coordinates, x) and Yo? is best provided by camera calibration. Very 
often, however, the only photograph which is available for extracting mensural data is 
one which has been taken with a non-metric camera for which no calibration data are 
provided. In some cases, the principal distance can be approximated by the camera's 
nominal focal length, if it is known, and the principal point can be approximated by the 
center of the photograph format, if the full format is given.. More often, however, 
the object geometry must be used to determine the interior orientation. 
The relationships amongst the image coordinates of the vanishing points of the 
X, Y and Z axes, the elements of the interior orientation, and the elements of the orienta- 
tion matrix [M] are given by equations (7) through (12), previously derived. These 
relationships can be used to solve for the elements of the interior orientation and the 
exterior orientation matrix, given the image coordinates of the vanishing points of the 
X, Y and Z axes. However, a more convenient solution for the interior orientation 
elements only is obtained by exploiting the property of mutual orthogonality of the X, Y 
and Z axes, or more precisely, the mutual orthogonality of lines parallel to the X, Y 
and Z axes and passing through the camera station C. In Figure 2, these three mutually 
orthogonal lines are Coy, On. and en,. 
The directions of lines, On»; Cn and Cn, in the image coordinate system are 
given by the vectors 
3x .Yol' v7 Yoal 228 |y