perhaps the midpoint, as a start. Obviously, if we have been working in 
the image before, we would use the last point computed. Because to a first 
approximation most dynamic camera systems are not significantly different 
in geometric qualities from a frame camera, one would expect that using a 
frame camera solution to solve for image coordinates would produce a result 
which would be closer to the proper answer. Since all differential camera 
systems are essentially one-to-one mappings, we would at least go in the 
proper direction of the solution. In practice, we have found that 
convergence to a solution never fails, and occurs within a few iterations 
for most systems. Convergence after one is within the neighborhood as in 
the case of sequentially processing points, occurs very rapidly. 
In many cases, the inverse problem is solved to derive 
rectification parameters for image processing systems. In this case, one 
is typically moving through a grid of points on the ground, deriving 
coordinates of where to look in the imagery for the grey shade values to 
place at those points. By moving along the grid in the direction most 
closely approximating constant time in the imagery, one can virtually 
insure that the computation of the new framelet for each point will 
converge in a single iteration. When changing rows, there might be a 
necessity for two iterations, but these transitions are rare. 
In any case, these iterations proceed much more rapidly than 
iterations through the rigorous mathematical model for almost all dynamic 
sensors, so that much time is saved in the inverse computation. In fact, 
even if only a single inverse point computation were required, it would be 
more efficient for complex sensors to build the tables and use the 
numerical model than to attempt to iterate to convergence using the 
rigorous model and numerically or analytically derived derivatives to be 
used for the next approximation determination. 
ADVANTAGES OF NUMERICAL MODELS IN APPLICATIONS 
Some of the advantages of these models in applications have 
been discussed briefly above. We will now discuss these applications in 
more detail. 
The most significant advantage of the model is that the 
applications level software becomes generic. The applications programmer 
need not know anything about the sensor, even to use an analytical plotter 
in the applications software. The only place in the entire software 
package where there are differences between sensors is in the software to 
triangulate the imagery, to handle stage to film registration fiducialing, 
and to compute the tables. 
As a parallel advantage, the design of the software system 
becomes identical no matter how many mathematical models will eventually be 
used. While this goal could be accomplished by passing sensor type flags 
into a black box photogrammetric model package, the use of this latter 
philosophy would preclude the applications level programmer from 
customizing or using pieces of the photogrammetric software in different 
places within the software for efficiency. 
New sensors, for this reason, are very easy to implement within 
the applications software. In fact, the use of numerical models permits 
software to be developed in parallel with the development of the 
mathematical model for a new sensor since any existing mathematical model 
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