MATHEMATICAL FORMULATION & DIGITAL ANALYSIS 1369
photographed using a Polaroid camera. A calibration accuracy of about +1/250 in magnifica-
tion and +0.15 degrees in tilt angle was reported.
Application of stereophotogrammetric mapping techniques in scanning electron micros-
copy is still in the early stage of development. As the demand for accuracy in three-
dimensional measurement continues to increase, the need for advanced instrumentation and
mathematical techniques will undoubtedly follow.
DIGITAL ANALYSIS TECHNIQUES
DATA COLLECTION
Other than the direct measurement of the object, there are three methods by which digital
data can be collected: (1) digitizing an existing map; (2) measurement of photo coordinates,
i.e., the fully analytical approach; and (3) digitizing spatial coordinates from a three-
dimensional optical model which has been set up in a stereoplotting instrument, i.e., the
semi-analytical approach. The mathematical formulation techniques for both the fully- and
semi-analytical approaches have been discussed in the first part of this paper.
There is presently available on the market a wide range of digitizing equipments which may
be used to generate digital data from an existing map. The digitizing tables range in size from
22 inches-by-22 inches to 48 inches-by-60 inches, and the auxillary equipments may include
coordinate display panels, magnetic tape units, minicomputers for performing coordinate
transformations, and data editing facilities. There are basically two modes of operation:
point-by-point modes or line-following modes. In the line-following modes, coordinates can
usually be automatically recorded at a time or distance increment that can be specified by the
operator.
DATA STRUCTURE
Depending on the method and procedure used in the digitization or photogrammetric
mapping process, the digital data which representthe surface ofan object can be distributed in
either a gridded, sectional, or irregular pattern. If the digital data are arranged in the pattern of
a rectangular grid, as shown in Figure 9, the grid spacing in the X and Y directions remains
constant and only the heights (Z-coordinates) ofthe data points need to be recorded. Thus, the
digital data file for a gridded pattern will consist of a string of height data. Knowing the grid
spacing and the number of rows and columns in the grid, the exactX and Y coordinates of each
elevation point can be easily derived. However, since the placement of data points is com-
pletely independent of surface features, this method of data distribution may result in the
omission of critical surface features. The accuracy of surface representation will depend
largely on grid size and surface roughness.
Z
x
X
Data File:
his iere Za nob e Lo e (
Fic. 9. Gridded data pattern.
