Jacobi's solution involves three consequetive coordinate transformations : 
a) Spatial transformation of object-space control into camera coordinate system (origin at the 
interior perspective center O, and Z azis along the optical axis). 
b) Projective transformation from camera coordinate system into an intermediate image 
coordinate system (plane perpendicular to the optical axis and at a distance from point O equal 
to the principal distance). Correction for radial symmetrical lens distortion is then carried out 
in this plane using appropriate polynomials. 
c) Projective transformation of the corrected intermediate image coordinates into the adopted 
image coordinate system (x, y), by rotationsa and g around point O. 
In the linearization of the error equations, Jacobi uses partial differences rather than 
partial differentials, thereby reducing the computer time necessary for the adjustment. à 
Image 
g y 
P necs s (point of symmetry) 
   
   
  
incipal point) 
  
(interior perspective center) 
Fig. 
3.3. Wolpert's Calibration Method 
  
Woólpert [ 25] designed a portable test object consisting of a number of graduated glass 
scales arranged in a horizontal straight line pattern on a wall. By using multiple exposures and 
rotating the camera around its axis, a second dimension is obtained. The object distance is 
accurately measured, thus enabling complete calibration of the camera. 
3.4. Hallert's Grid Method 
  
This method is well documented in the photogrammetric literature, see for instance 
[14] , [15], [16] and [19] . A two-dimensional test field contains a great number of targets 
arranged in a concentric circles pattern. Photography is taken from a point on the perpendicular 
through the central point of the field, with the negative plane approximately parallel to the plane 
of the test field. The relative location of the targets are determined to a high accuracy by geodetic 
measurements. The radial distortion effects are determined from the scale variation of circular 
combination of test points around the center point, adjusting each circle combination separately. # 
Polynomials (usually of 5th order) can also be used for the determination of radial distortion 
effects, Both methods are frequently used simultaneously for checking purposes, 
To determine the camera constant, either the camera or the object must be translated 
an accurately determined distance along the perpendicular to the grid plane, The resulting 
variation in image scale is used to determine the camera constant, 
3.5. Dóhler's Calibration "Star" e I", 
An interesting device was designed by Dóhler [12] as a test object for close-range camera 
calibration. It consists of a metallic staff of 2.4 m length which can rotate around a mid-point 
  
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