Observations on Positions: How High Was that Wire?

A professional painter (PP), showed up for a project on a Saturday. The job was a gasoline station/convenience store in southwestern Louisiana, and his task for the day was to paint the façade of the gas pump canopy. The store was vacant, as it was being refurbished for a new commercial operation. The painter parked his truck, gathered his buckets, rollers, rags, etc. and unloaded his aluminum extension ladder. He extended his ladder and climbed to the top of the metal canopy, and then one-by-one, he pulled up his supplies and tools by ropes.

PP started working; he took out his paint roller and started leaning over the canopy façade and painting. Little by little, he worked all around the perimeter of the roof until he reached his point of beginning, the ladder. He grabbed the metal extension ladder and moved it aside to a portion of the façade that he had already painted. However, the catch hooks came loose and the ladder hung unattached in his hands. PP was faced with a dilemma; either he could reattach the hooks so that he could later descend safely or he would be forced to jump some 17 feet to the ground, surely spraining his ankle or breaking his leg. He repositioned his hands, jiggled the ladder, shook the ladder up and down in an attempt to reattach the hooks, and as he raised the ladder up again and again to set the hooks-the metal ladder touched a high-voltage power line above his head. PP was badly burned and lost consciousness as he crumpled into a heap on top of the canopy.

The sun began to set and PP's family began to wonder where he was. One thing led to another and his truck was discovered at the job site with the aluminum ladder collapsed on the ground under the metal canopy. PP was found on top of the canopy, EMS was dispatched to the site, and he was admitted to the Emergency Room in critical condition. Word spread quickly between friends and family in the small Louisiana community, and PP's best friend rushed to the hospital to learn the details of the tragic accident. The friend had trouble sleeping that night, and he arose the next morning determined to record the accident scene, just in case. He purchased a Polaroid camera and a packet of film and went to the job site.

The power company had crews there when he arrived, and they were already working on repairs to the line. PP's friend started taking pictures. He exposed the entire pack of Polaroid prints, moving from one snapshot to the next. On inspection of the quality of the prints, he was satisfied and drove to the hospital where he put the prints in the hands of PP's mother.

Many months transpired, and PP survived through the heroic efforts of the critical care burn unit. The hospital bill was enormous and the power company denied liability for the catastrophe. PP sued for damages, and a consideration surfaced regarding "how high was that wire?" During a discovery deposition recess, the attorney for the power company asked the plaintiff attorney, "Have you hired a photogrammetrist yet?" The plaintiff attorney replied "No," and then asked where the restroom was. On receiving directions to the location of the restroom, the plaintiff attorney stopped and looked up "photogrammetry" in a dictionary.

Three days later, I received a telephone call. The plaintiff attorney introduced himself, and he asked if it was possible to determine the height of a wire from photographs. I replied that it was pretty difficult unless there were discrete points on the wire that could be identified from photographs that were taken from several different locations. Mr. Attorney said that he had a number of Polaroid prints that showed the wire in question; could he send them to me for an opinion? I replied, "Sure, send them over and I'll take a look for you." The prints arrived shortly thereafter and I was pleased to see that the wire had a number of well-defined photo-identifiable points. The Polaroid prints taken by PP's friend showed a power company's cherry picker truck with workmen in a bucket working on the line in question. The power company's linemen had placed rubber insulation hoses on the wire, and the protection hoses had large "lumps" on one end of each hose that served as female receptacles for another insulating hose. Those "lumps" provided excellent, well-defined discrete points to use for phototriangulation analysis of the points and the power line in question. The multiple images were taken from numerous locations since PP's friend walked from spot-to-spot in between each snapshot. Every photo showed four distinct discrete points on the same wire! There were even photos that matched up to form stereo views.

I telephoned Mr. Attorney and said, "I have good news-the photos can provide the answer of how high the wire was, but I can't guarantee that the answer will be in your favor. The solution is pretty straightforward in analytical photogrammetry, but I will need the services of a local land surveyor to provide the dimensional control for the analysis." I recommended that he retain a local land surveyor of his choice and have him call me for technical instructions. Mr. Surveyor called shortly thereafter, and I explained that photogrammetry is essentially a process of three-dimensional interpolation in between known points with X-Y-Z control coordinates. I said that I would send enlarged copies of the Polaroid prints of the gasoline station with points identified with circles and with explanations of the specific point coordinates required of Mr. Surveyor. Things to consider are that the coordinate system needs to always be positive, and that the traditional (10,000/ 10,000) is not a good thing. What's the difference between Northing/Easting and X/Y? The only way to tell the difference is to have a different number of digits between the coordinate components or a drastic difference in component magnitudes such as (70,000/ 10,000). That way, there is no confusion as to what is Easting or X and Northing or Y, especially in long distance communications between a photogrammetrist in one city and a surveyor in another city.

The Process
The site survey was done and coordinates were transmitted to me. Additional points were discovered in need of control; more work was ordered, and photos and numbers went back and forth between cities. The Polaroid photos were measured, and the imagery and the surveyor's control were put into a least squares bundle block analytical solution with my own software. (Back in the 1990s I used to sell licenses to my photogrammetric software, but after people only wanted Windows software I gave up the enterprise rather than spend the time learning how to be a professional programmer.)

The photogrammetric solution converged, and one of the automatic by-products of a rigorous least squares bundle block adjustment was an analytical resection of the position of each of the camera stations (places where PP's friend was standing when he took each photo). The software computed the (X-Y-Z) position of each of the "lumps" on the wire in question and it also provided the computed geometric dilution of precision (GDOP) of each computed point. That means that for each computed point, there is an accuracy statement on each coordinate component of the point. That is, the X coordinate component is good to so much plus or minus, the Y coordinate component is good to so much plus or minus, and the Z coordinate component is good to so much plus or minus. The catenary was evident and obvious in the Z coordinate components of the four points along the wire, and the computed accuracy of those components was good to a tenth of a foot. In summary, the wire was below code-the power company was at fault, and we had the photos-the physical proof!

I was deposed on my findings. That day was a traumatic experience for the defense attorney representing the power company. After a few hours of explanation of the photogrammetric process and what the analysis showed-the realization of the evidence became apparent to the defense attorney and the deposition was hurriedly concluded. Only a few days transpired before a financial settlement was reached to the satisfaction of the plaintiff attorney and PP.

Reverse Projection
Curiously, the power company had retained the services of their own photogrammetrist, but they never introduced the evidence into the record. Unfortunately for them, the photogrammetrist for the defense chose to use "reverse projection" for the analysis tool.
Reverse projection is a valid method commonly used by the FBI in bank robbery cases because everything in the surveillance photography is controlled. The counters in the bank are bolted to the floor, the camera is bolted to the wall or the ceiling, the furniture is bolted to the floor, and the ONLY variable is the bank robber. It's a pretty easy job in photogrammetry to use reverse projection when everything is known except for the height of the bad guy. However, when attempting to use reverse projection in a situation where practically everything is a variable-the technique is laughable! Guessing as to a camera's focal length with a zoom lens, guessing as to the position of the photographer for a given exposure, guessing as to the height of the photographer for a given exposure, guessing as to the tip, tilt, and swing of the camera for a given exposure, is just that-guess work. The FBI does not guess-they KNOW what those parameters are in a bank robbery photo surveillance scene, and that's why the FBI uses it—everything is bolted down.

Since then, I have worked on a number of non-electric cases for the power company's attorney. Some other power companies have hired me on cases as well. Analytical photogrammetric solutions comprised of a rigorous least squares bundle block with error propagation are the equivalent of a straight royal flush. Know when to hold and know when to fold. Hire a Certified Photogrammetrist-they use land surveyors for their control.


 

Cliff Mugnier is a Board Certified Photogrammetrist and Mapping Scientist (GIS/LIS) and teaches Surveying, Geodesy, and Photogrammetry at Louisiana State University. He is also a Contributing Writer for the magazine.

» Back to our September 2004 Issue