ANALYTICAL
PHOTOGRAMMETRY
Everett L. Merritt
PHOTOGRAMMETRY, Inc.
Silver Spring, Maryland
The purpose of this paper is to define the scope and establish the require-
ment for a general mathematical treatment of photogrammetry embraced in a book
entitled Analytical Photogrammetry.
If photogrammetrists are going to be burdened with a mathematical treatment
of photogrammetry, there ought to be a demand or a requirement for such a book.
A random survey of photogrammetrists at home and abroad shows there is little
demand for a comprehensive mathematical treatment of photogrammetry, while
an extensive survey of photogrammetric writings at home and abroad shows there
is an urgent requirement for a comprehensive mathematical treatment of photo-
grammetry in the light of a multitude of recent non-topographic uses of photo-
grammetry, and with the advent of electronic and mechanical computing machines.
The reason for the small demand is due largely to the purposes. and concepts
embodied in existing writings on photogrammetry.
Most writings on photogrammetry are devoted to the photogrammetric proce-
dures and instrumentation required for making a map in the geographic area of the
writers. The limited photogrammetric equations given in these writings are spe-
cial case equations subordinated to the topographic uses in the geographic area
of the writers.
For this reason photogrammetry is generally given a dimensional topographic
definition, the fundamental concept of interior orientation is treated scantily, and
the universal concept of total orientation in a scientific sense is omitted entirely.
There are scattered writings approaching a generalized concept that, without ex-
ception, employ obscure non-photogrammetric notation and omit mathematical de-
velopment and derivation entirely. Still other rather voluminous works devóte
endless pages to a single method of exterior orientation arrived at by the writers
as if the photogrammetric science were wholly embraced in a single method of
exterior orientation for cartographic delineation.
Thus photogrammetrists are groping clumsily like each of n blind men in an
attempt to evaluate the photogrammetric elephant. Since each photogrammetric
school has a local viewpoint, endless controversy arises out of the attempt to de-
fine the whole with the part. Furthermore, we have competent mechanical engi-
neers designing cameras and plotting instruments, and equally competent optical
men calibrating cameras--who occasionally for economic reasons are not able to
share photogrammetrists' comprehensive viewpoint. This is, indeed, a logical
consequence of the photogrammetrist himself placing camera design and camera
calibration outside of his responsibility.
Thus there is an urgent requirement for a mathematical treatment of photo-
grammetry that proceeds from the general to the particula:. Proceeding mathe-
matically from the general to the particular, we arrive at a universal definition of
photogrammetry that embraces the fundamental concepts of interior orientation,
exterior orientation, and reciprocal orientation as simplifications of the general
concept of total orientation. We arrive, moreover, not at a definition restricted to
a partial concept and existing solely as a cartographic tool, but rather at a defin-
ition embodying a general concept and existing as a means of defining the di-
