DEVELOPING ORTHOGRAPHIC VIEWS FROM FISHEYE PHOTOGRAPHS
Graham T. Richardson
Central Intelligence Agency
Washington, D.C.
ABSTRACT:
20505
In close-range photogrammetry, the exploitation of fisheye photographs for dimensional infor-
mation has been overlooked due to an apparent lack of techniques for correcting the curvilinear
perspective.
This paper presents a new procedure for transforming the distorted perspective of the
fisheye view into corrected standard perspective views that then may be rectified into orthographic
views by standard graphical techniques.
point perspective are described.
Corrections resulting in standard one-, two-, and three-
Computer-aided design was used in addition to graphical and
mathematical checks to ensure the accuracy of the work--presented here as a proof-of-concept only.
The routines needed for analytical photogrammetric analysis of fisheye photographs have yet to be
compiled.
KEY WORDS: Close-range photogrammetry,
INTRODUCTION
A fisheye lens (8 mm focal length) on a standard
commercial, or non-metric, 35 mm camera body
yields a circular image with a field of view
that extends 180 degrees (Fig. 1). This paper
contains a description of a new technique to
transform the circular or spherical perspective
of prismatic objects in such a photograph into
standard perspective views. These corrected
views may then be rectified into standard or-
thographic presentations of the top, bottom, or
sides of the prismatic object in question.
Conventional wisdom has held these circular im-
ages to be unworkable by either graphical
methods (because the lines were curved, not
straight) or analytical techniques (because the
circular view did not conform to the colinear-
ity concept). Although a fisheye lens is quite
a bit more expensive than "normal" camera lens-
es, its ability to record more visual informa-
tion in one view, or very few views, ought to
allow it to produce more work at the same ac-
curacy as the other lenses.
UNDERSTANDING THE FISHEYE VIEW
Experimental photographs using an Olympus 8 mm
fisheye lens have shown that straight lines
within the original field of view are distorted
in one of three ways. When the film plane is
parallel to the straight lines, the photograph
produces arcs that extend to vanishing points
along the perimeter of the circular image.
When the film plane is perpendicular to straight
lines within the field of view, the photograph
produces straight lines that converge toward
one vanishing point at the center of the cir-
cular image. When the film plane is at any
angle other than 0 or 90 degrees to the straight
lines in the field of view, the photograph
yields complex curves (also referred to as
transcendental curves) that still look arc-like
but are not.
fisheye images,
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corrective procedures.
Figure 1. A circular fisheye photograph dis-
playing 180 degrees of coverage in its field of
view.
The sequence of grids that corresponds to these
different views is displayed in Fig. 2. The
grids were developed from the hemispheric
Azimuthal-Equidistant map projection (suggest-
ed to this author) and range from the so-called
"equatorial" view, with its nested arcs and
perimeter vanishing points, through as many as
88 intermediate or oblique grids (using only
one-degree intervals) finishing at the "polar"
view (Snyder, 1987; Flocon and Barre, 1987).
Computer-aided design methods compared observed
lines in the test photographs with predicted
grid lines from the suggested map projection,
and produced an almost exact fit.
CORRECTING THE FISHEYE VIEW
The correction of the curvilinear perspective
in two simplified fisheye views will be de-
scribed here. Each view was an "arranged"
photograph, taken so that the geometry in the
