Numerical Photogrammetric Models for High Speed Solutions 
Dr. Clifford W. Greve, Craig W. Molander, Dewey Houck 
Autometric, Incorporated 
Falls Church, Virginia 
ABSTRACT 
Rigorous evaluation of photogrammetric math models associated 
with dynamic sensors is time consuming and computationally intensive. A 
numerical model developed by Autometric provides an alternative evaluation 
of projective geometry without sacrificing accuracy. Software 
implementation of numerical model allows rapid computation of space 
intersections and inverses. It also allows "generic" sensor modelling 
which minimizes the impact of adding sensors to the system. 
INTRODUCTION 
Autometric, Inc. has developed a photogrammetric model which 
permits the very rapid computation of general photogrammetric projection 
equations for any camera system which is at least differentially perspec- 
tive. Although originally developed for use in the real-time computation 
of servo control parameters within analytical stereoplotters, these 
algorithms have proven to be beneficial in general software applications. 
Because the same basic implementation of the mathematical model suffices 
for all systems, it is possible to build applications software systems in 
which all the processing is independent of camera type, once the 
appropriate information for the images have been computed and loaded. This 
philosophy greatly simplifies the development of software systems, while 
yielding accuracies identical to those which would have been rigorously 
computed using the theoretical models for the various sensors. 
WHAT IS A NUMERICAL MODEL? 
A numerical model, as used by Autometric, refers to a 
formulation which permits all differentially perspective camera systems to 
be processed using the same set of mathematical equations. We define 
differentially perspective to mean any camera system wherein a strip of 
film or a sensor array is exposed by a lens System, such that all points 
along the strip are exposed at a given instant of time. This strip then 
becomes a projective framelet of narrow (differential) width, but having 
the full projective properties along its width (see Figure 1). In fact, 
these projective properties are identical to those of the simple frame 
camera system. Since all camera systems strive to present the ground with 
some equality of scale between the in-scan and cross-scan directions, the 
width of the differential framelet can frequently be expanded to some 
finite size without generating any serious errors in geometry. This 
approach yields an efficient method for computing the parameters of the 
differential framelet and the results obtained by using the framelet are 
virtually identical to those obtained with the theoretical model. In fact, 
as the width of the framelet becomes differentially narrow, the error 
contributed by the frame approximation approaches zero, yielding results 
identical to the rigorous model. Autometric has developed an innovative 
way to store the data to compute these instantaneous framelet parameters 
for any dynamic camera system which is differentially perspective. 
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