MATHEMATICAL FORMULATION & DIGITAL ANALYSIS 1357 
digital data in the computer. The digital data were used to measure the volume and shape of 
the left ventricle during the entire cardiac cycle, and to study the kinetics (velocity, accelera- 
tion, and path of movement) of human movements. 
Many of the digital techniques that have been developed for automatic cartography can be 
applied directly for close-range mapping. Both the Ontario Ministry of Transportation and 
Communication in Canada2 and the Texas Highway Department in the U. S.!* have de- 
veloped completely automated drafting systems for topographic mapping. Topographic in- 
formation is digitized and coded directly in the stereoplotter and the output data are recorded 
on magnetic tape. After numerical processing and editing of the raw digital data, the map is 
drawn by an automatic plotter. 
The U. S. Forest Service?? has developed a software package for the collection, manipula- 
tion, and analysis of digital terrain data. Digital data can be generated directly from existing 
topographic maps or from the photogrammetric mapping process. Once the digital data are 
edited and stored in the computer, graphic products such as contour maps, slope maps, view 
maps, and perspective drawing can be generated directly from the data file at the scale 
specified by the user. 
Computer programs for the generation of graphic products from digital data are now readily 
available from both commercial organizations and universities. Of particular interest is the 
Geographic Program Exchange (GPE) at the Michigan State University. The GPE was estab- 
lished to assist universities and non-profit organizations with the exchange of computer 
software which relates to the problems of a geographic nature, such as contouring and 
perspective drawings. The GPE maintains a central file of specialized computer programs 
with associated documentation and test data sets, and makes copies of all or part of this 
material available to users at cost. The operation is directed by Dr. Robert I. Wittick, Compu- 
ter Institute for Social Science Research, Michigan State University, East Lansing, Michigan 
48823, USA. 
There have also been considerable amounts of research activities on the mathematical 
modeling of topographic surfaces such as the studies by Jancaitis and Junkins!5/!6 and 
Maxewell?". At the University of Illinois at Urbana-Champaign an ongoing research project is 
investigating the use of digital terrain data for automatic soil classification based on topo- 
graphical features. 
MATHEMATICAL FORMULATION TECHNIQUES 
SPECIAL CHARACTERISTICS 
The computational problems in close-range photogrammetry are similar in many respects to 
the problems in photogrammetric surveys from aircraft. The problems of camera calibration, 
image refinement, computation of pass point coordinates in single or multiple model config- 
uration, and the determination of exterior orientation parameters involve basically the same 
mathematical formulations and computational algorithm in all areas of application of photo- 
grammetry. It can be expected, therefore, that the many computation techniques that have 
been developed exclusively for application in topographic mapping in general, and analytical 
aerotriangulation in particular, can be used with little or no modification for close-range 
applications. 
Yet, photogrammetric measurements in close-range applications have some basic charac- 
teristics that are distinctively different from aerial applications: measurement objectives, 
control requirements, and geometric configuration of photography. 
In many close-range problems ranging from the measurement of structural deformations to 
the mapping of human body parts, the three-dimensional positions of a large number of points 
must be computed from each stereo pair of photographs. As compared to the standard 6 or 12 
points-per-model pattern that is usually used in aerotriangulation, frequently hundreds of 
points per model must be measured in close-range applications. For example, in the meas- 
urement of aortic heart valve, Kararal” measured thousands of points per model to provide an 
adequate representation of the surface of the heart valve. 
Absolute positioning with respect to a reference coordinate system is not a matter of major 
important in many close-range applications. Of much greater importance is the relative 
positioning accuracy of points on the surface to be mapped. For example, in mapping the body 
surface of a human subject, it is not important to determine precisely the height of the subjects 
shoulder above the floor. But the relative positions of points on the body must be determined 
precisely so that the size, shape, and volume of the body parts can be determined with the 
required accuracy. Therefore, among the traditional parameters of exterior orientation (3