About the Photogrammetry Process
Introduction - A sophisticated technique, called stereophotogrammetry makes it possible
to estimate the three-dimensional coordinates of points on an object seen in photographs. These are determined by measurements made
in two or more photographic images taken from different positions. Common points are identified on each image. A line of sight (or
ray) can be constructed from the camera location to the point on the object. It is the intersection of these rays, by triangulation,
that determines the three-dimensional location of the point.
Photogrammetry is used in different fields, such as topographic
mapping, architecture, engineering, manufacturing, police investigation, and geology, as well as by archaeologists to quickly produce
plans of large or complex sites. It is also used to combine live action film footage with computer generated effects in movies.
Algorithms
for photogrammetry typically express the problem as that of minimizing the sum of the squares of a set of errors.
Explanation
- The Photogrammetry Process requires a lengthy series of experiments, each step reducing the number of options for object position
and camera position for the various camera views used in the analysis (you must have more than one, two is probably minimal, three
is better, and so on. I used seven camera positions.) The recognition of points and objects can be automated by computer algorithms
(such as edge detection and pattern detection processes) or the points and objects can be manually designated by a person performing
the analysis.
Each step makes some determination about either the objects in the image or the camera in relation to the objects.
Each determination reduces the number of options for where an object or camera must be, and if there is enough data in each image,
and enough images from varied camera positions, the reduction of options leads to one reliable conclusion.
For example, if you have two photographs of an object, like a tree, and in the first, the tree is a certain height compared to the
image frame, and in the second photo, the tree is twice as tall as in the first, we can say the camera taking the first image is twice
as far away from the tree than the camera taking the second image, if we are confident the lens focal length has not changed. That
determination specifies something about both camera positions, that however far the second one is from the tree, the first one is
twice as far.
If you have two identifiable objects in that pair of photos, and the one tree changes by being twice as large in
Photo #2 but another tree changes only a small amount, we can confidently conclude that the second tree is much farther away
from camera than the first tree, because the change of camera distance is proportionately less in relation to the overall distance.
So,
in this process, we look to the way objects change, in size, in position, in relation to each other, and each individual determination
reduces some options of where the objects are and the cameras are.
A systematic analysis of this process can, if enough data
is present, reduce the objects to one reliable position in a 3D digital space, in proportion to each other, and can determine the
position of the cameras that were taking the photos, in terms of position.
The methodology I used manually to evaluate the PG
Film images, and the boujou 4.1 software I selected as a corroboration method, use entirely different methods and technology, so that
their shared conclusions can give further reliability to the determination, reducing the question of a flawed method, if only one
were used.
The final results and documentation of the boujou software analysis will be included in the Report, Release Two.
Explanation of Discovery and Subsequent Analysis
Originally, my intention was simply to build a digital site model of Bluff Creek
to assist me in my analysis. I considered several options and decided to explore two. One was to use a 3D visualization software (Bryce)
which I am a very strong, proficient user of, and the second method was to employ a Matchmove software (specifically boujou 4.1 from
2D3 LTD.) because of it's stated capability of analyzing film footage and locating objects, cameras and determining the lens focal
length on the camera at each frame.
Negotiating for the educational license for the boujou software took time, so I proceeded
with my visualization in Bryce in the interim. I stated with the generally assumed report of a 25mm lens on the camera Roger had,
and tried a multitude of methods and techniques, essentially a trial and error experimentation method, to position objects, particularly
the center trees (T - C1 through T - C5, as I have identified them in this report) so they matched the film image frames in size and
position, for multiple camera positions.
For two months, every effort using a 25mm lens specification failed to solve. In analyzing
the failure, I saw some objects which needed to be moved closer for a potential better match or alignment, but if so, then a wider
angle lens would also need to be tested. At that point, I researched lens options for the Kodak K-100 and found the listed 15mm lens
in their inventory.
So I chose to test a 15mm lens as well, in this method of assembling tree objects and trying to align them
in multiple views. The basic model assembled successfully in a matter of hours. So I chose to give my emphasis to refining this model,
using a 15mm lens specification, to see how effectively it can match multiple frames of the PG Film showing distinctively different
camera positions.
The license for the use of the boujou software was finally approved and the software packet sent to me, and
I began learning the software and testing the film footage. I have gotten a preliminary verification of the 15mm lens from their software's
analysis, but that verification is still undergoing further analysis, and the people who actually developed the software have kindly
offered to assist me in running their own analysis of the footage through the software, and their expertise with this software is
unparalleled, since they are the actual developers and designers of it. That is in progress.
So I have continued to build and test the digital site model in the 3D visualization software where I am a generally acknowledged
proficient user, and I have continued to refine the model and methods. But precisely because this is a trial and error methodology,
I have chosen to offer the results, with precise coordinate data for objects and camera positions, as the material for other researchers
to test for reliability and verification. In other words, use the object data to build the 3D model, put your cameras where my position
coordinates say they should be, set the horizontal angle of view as I specified, and use the images provided in the website as backdrop
images to compare, and see if things match up as I have shown. If so, then the 15mm lens is definitely correct.
The issue becomes
a question of whether it is singularly correct, to the exclusion of other lens focal lengths. As there are an infinite number of possibilities
for this alternate idea, I cannot test them all. And my two months of complete failure with the 25mm lens failing to solve, using
the same methods as used for the 15mm lens to succeed splendidly, gives me confidence this is the factual solution. As much as I know
about photography and geometry (which encompasses triangulations and their unique shapes), and the photogrammetry process which essentially
creates traingulated shapes between objects and the camera position for any given image, the more points that match, across more camera
positions, the more likely the determination is the prevailing one to the exclusion of other options. I believe I have met that threshold
with seven different camera positions from the PG Film (plus two from other cameras) and anywhere from 4 to 12 objects aligning well
in these varied camera positions, to confidently say that both the model is correct, and the PG Film camera has a 15mm lens on it.
Here,
on my website, I have provided all the data necessary for others to test this statement, first to verify the data as disclosed is
true and correct, and second, I have provided the tools to assist others who may want to test other model object positions, other
camera positions, and other lens focal lengths, to see if another solution will provide a similarly good alignment of objects to the
film frames.
This will also allow others to test the model in other 3D visualization software programs, which I alone cannot
do, to check for the prospect the software I used may be a mitigating factor in the determination.