1356 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975 
views from various angles, can also be easily generated. The digital model may also be used 
for digital simulation to study the behavior of the object under a wide range of environmental 
conditions. Figure 1 illustrates the basic concept of the digital analysis approach. 
Several other factors also strongly encourage the development and adaptation of 
analytical-methods in close-range photogrammetry. The common use of small format cameras 
(such as 35-mm, 4-by-5 inches, and 70-mm), the needs for convergent multi-camera photog- 
raphy, the limited availability as well as the mechanical limitations of universal stereoplot- 
ters, and the large image distortions caused by the camera lens are factors which usually 
dictate the use of analytical methods to determine the spatial positions of points on the object 
being mapped. In addition, analytical methods as well as computer programs are now availa- 
ble for generating contour maps and other graphic products accurately and economically from 
digital data, thus freeing the photogrammetrist from the stereoplotter. 
RECENT DEVELOPMENTS 
The versatility and flexibility of the digital approach have been demonstrated by the works 
of several investigators. In the machining of replicas for limbs and other anatomical parts, 
Duncan et al.!! employed conventional photogrammetric techniques to first obtain a contour 
map ofthe human limb. The contour map was then digitized to provide a digital model, which 
was then used to control the motion of the cutting machine. In a similar application, Kratky2! 
bypassed the photogrammetric compilation of contour maps by the direct computation of 
spatial coordinates using analytical methods. A Zeiss PSK stereocomparator was used to 
measure the photo coordinates of conjugate points in a stereoscopic pair of photos. Relative 
orientation and scaling of each stereo model and linking of overlapping models were all 
performed analytically, and the direct output from the photogrammetric process was a list of 
coordinates which defined the spatial positions of points on the surface of the human limb. 
Mathematical models which describe the shape of the limb were then used to generate data 
points along a regular spatial grid. This final digital model, which consisted of data points in a 
regular pattern, was then used for automatic machining. 
The fully analytical approach was used by Karara!” to derive digital models of aortic heart 
valves. The digital models were used to perform stress analysis by finite element techniques. 
In another biomedical application, Goulet et al.13 employed the digital approach to derive the 
following parametric descriptions of the human body: volume, volume distribution, perime- 
ter distribution, surface area, surface area distribution, center of gravity, and inertia tensor. 
Lippert et al.22:23 used the analytical approach and multi-camera geometry to measure the 
four-dimensional (X, Y, Z, time) motion upon the musculoskeletal system including the knee 
joint. The instantaneous positions ofthe targets which were attached to the knee were defined 
by three-dimensional coordinates. The photo coordinates of these target points were meas- 
ured with a Zeiss 1818 stereocomparator, and the spatial coordinates were computed by 
analytical photogrammetric techniques. The motion of the joint was defined by the change in 
the spatial coordinates of the targets. 
In a further automation of the photogrammetric mapping process, Winteret al.2? employed a 
television camera and a computer to perform dynamic measurements of anatomical volumes, 
area, and position. Television images of the subject in motion were converted directly to 
  
Numerical, 
statistical, 
or graphical 
outputs 
— [Computer| ——= 
  
  
  
  
Digital Model 
object 
     
e. 
Analysis & 
Design 
   
  
Fic. l. The digital approach.