Introduction 
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Much useful information can be extracted from a single photograph of one or more 
man-made objects taken from a station located on or near the ground. In particular, it is 
often possible to obtain from such a terrestrial photograph the dimensions of a building, 
bridge, tower, dam, dock installation, or other engineered structure for the planning of 
future engineering projects or other purposes. Too frequently, however, inaccuracies 
occur due to the limitations of available methods of extracting the mensural data from 
the photograph, and because of the large number of unknown factors associated with the rav 
Very often, the kind of terrestrial photograph used for determining object dimen- 
sions has not been taken for metric purposes in the first place. Indeed, it may only be 
€ | a cropped enlargement of a negative taken with a camera of unknown focal length, thus 
the data. 
be determined. 
The technique of using object 
exterior orientation of a photograph is 
this line in the past, as indicated for 
Merritt [6]. However, these procedures 
limited in application. 
This paper treats the problem 
analytically with as much generality as 
The Projective Equations 
  
expressed collectively by the matrix equation: 
possessing no known interior orientation. Even if the photograph does have known interior 
orientation, it is very unlikely that adequate ground control is available in the object 
space, thus precluding use of any of the established methods of space resection for deter- 
mination of the photograph's exterior orientation. The fact, too, that the information 
is imaged only on one photograph imposes definite restrictions on the interpretation of 
Under the circumstances just cited, it would seem to be an almost impossible task 
to extract any meaningful mensural data from the photograph, and this is often the case. 
However, there are many instances where an effective solution can be cbtained. This occurs 
because most engineered structures possess certain geometrical properties, such as parallel 
: lines, orthogonal lines, and equally segmented lines, which can be used to advantage. Bv 
exploiting these properties, it is often possible to determine the photograph's interior 
orientation and the angular portion of its exterior orientation. This, in turn, along 
with a known dimension in the object space, enables other dimensions and desired data to 
geometry to solve for elements of the interior and 
not new. Procedures have been developed along 
example in the publications of McNeil [5] and 
are either graphical or semi-graphical, and are 
of single photograph mensuration of man-made objects 
possible, 
The basic photogrammetric relationships are given by the projective equations,