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Photogrammetry 101: Distance From The Camera

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Photogrammetry 101:

 

How do we determine Patty's distance from the camera for a particular frame of the PGF? The only way is with photogrammetry. We need to know the dimensions of the camera's aperture gate and the corresponding frame dimensions on the original film stock, the focal length of the lens, Patty's actual height (body length) and her corresponding image size on the film. Then we can apply the "lens equation" to calculate the distances from the camera. We only need the simple relationship of [height on film / focal length = actual height / distance from the camera], then solve for d:

 

post-337-0-39050400-1435600839.png

 

The assumptions in this case are the aperture gate dimensions = 10.3mm x 7.6mm, the aspect ratio = 1.34, the focal length of the Ektar Cine II lens = 25mm. The following graphic shows how Patty's image height was determined in frame 352:

 

post-337-0-54997700-1435601794.png

 

Patty's height is 578 pixels and the full frame height is 3453 pixels = 16.7% of the  frame height. Since the full frame height = 7.6mm, 16.7% = 1.27mm. This is Patty's actual image height on the film. This gives us the following formula:

 

1.27mm / 25mm = Patty's Height / Patty's distance from the camera. This exercise assumes that Patty's height (body length) was 6' 3" according to the foot ruler. Our equation becomes:

 

Patty's distance from the camera = 75in / (1.27mm / 25mm) = 1476.4in = 123 ft.

 

Now you can play with the numbers to see what it would take for Patty to be 102 ft from the camera at frame 352 (as per Green's measurement):

 

  • If the lens was 20mm and Patty was 6' 6" then d = 102 ft (which is why Bill thinks Roger used a 20mm lens)
  • Patty's standing height needed to be 5' 2" if d = 102 ft for a 25mm lens to work.
  • Glickman needed to measure the gate height on the K-100 to 9.2mm instead of 7.6mm (21% error) for d = 102 ft.

 

If the MK Davis scan of the transparency for frame 352 (which I scaled to 4769 x 3453) was not a full frame then the distances from the camera would increase if we measured the original film. IMO, MK Davis' scan of 352 is the gold standard and shows the best full frame from the PGF. Its borders actually match a full frame from the "casting footage", which means both footages were shot with the same K-100. IMO, the casting footage was shot with a 25mm lens so Roger either used the same lens for the PGF or he changed it between footages. And Green just happened to match the PGF with his own non-standard lens or he used a zoom lens.

 

So how does 123 ft compare with Green's site measurement of 102 ft? Did Green measure from Roger's exact boot print where he thought he stood for frame 352, then measured to Patty's exact footprint for 352? Do you trust that measurement to be accurate within a foot? Not bloody likely. Green didn't shoot McClarin from the same spot as Roger and McClarin did not walk right on top of the trackway. Also, using the same photogrammetric methods McClarin was calculated to be 134 ft from Green's camera at the same point as Patty was in frame 352. This is why Patty looks bigger than McClarin, because he was farther from the camera than Patty. But the main thing to note is that if Green's lens was 1 in (25.4mm) then what was McClarin doing so far from the camera if he was following the trackway? Ans: he was probably walking a few feet beyond the trackway and Green was standing a few feet back from Roger's position. Suddenly, the difference between 123 and 102 shrinks to within the error of uncertainty. We need to investigate the integrity of the site measurements before we try to swap lenses to make the numbers fit.

 

 

 

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Backdoc

Unless I am totally missing something, it seems to me we have an idea of how far Patty was from Roger during the turn back.  We have a good idea where Patty was and a good idea where Roger had planted down.  If what we think of Roger is off by a few feet as well as Patty's position, then the equation could be off by several feet.

 

How confident should we be in this distance number?

 

Backdoc

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Guest

But how could Green have known which boot print/footprint to measure from/to with any degree of accuracy? By far the site measurements are the greatest potential source of error. Otherwise, it is straightforward estimating the range of error for the equation. Just adjust the following numbers to achieve a min and max distance from the camera. Then divide their difference by 2. I'll leave that one up to you. ;)

distance(ft) = h/(hp/hf*hm/fl)/12

d = 75/(578/3453*.0076/.025)/12

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SweatyYeti

But how could Green have known which boot print/footprint to measure from/to with any degree of accuracy? 

 

 

Excellent post, Giganto. :)

 

There's plenty there to consider...and to work with. I'll take some time to look it over, and will get back to you with a few questions.

 

 

Regarding the statement of yours I highlighted....I could see John Green easily making a mistake on precisely where Roger stopped to film the 'look back'...because after Roger had stopped....he moved a couple of steps to his right...and then moved several steps back to his left...and forward, closer to the 'Main Log'.  

 

So, his footprints would have continued around the spot where he had stopped, for the 'look back'. 

Edited by SweatyYeti

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Bigfoothunter

^^

 

I thought I read a letter from Titmus that detailed his findings at the film site. I'll check with John on this as its been a while since I looked through his letters.

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SweatyYeti

One correction to my post above....the situation with Roger's bootprints would have actually applied to the researchers who visited the site shortly after the filming, in 1967. When John Green went there...in June, '68....Roger's prints would have been mostly, if not completely, faded-away....(I would think).  


Unless I am totally missing something, it seems to me we have an idea of how far Patty was from Roger during the turn back.  We have a good idea where Patty was and a good idea where Roger had planted down.  If what we think of Roger is off by a few feet as well as Patty's position, then the equation could be off by several feet.

 

How confident should we be in this distance number?

 

Backdoc

 

 

The figure Giganto has worked-out, Backdoc....varies from the long-reported distance (of 102') by about 20'

 

That's a significant difference....and one that needs to be resolved, if possible. :)

Edited by SweatyYeti

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Backdoc

^^^^

This is why it's my thinking these are estimates but not absolutes. Be prepared to be off by a little or a lot.

It's not my area but I get the overall concept.

It just seems we don't know for certain things about the lens, distance and so on. We have the known height of McClarin as a reference but his position is off to a certain degree, which could be a lot.

Best of luck guys and gals on your efforts to solve this.

Edited by Backdoc

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Bigfoothunter

One correction to my post above....the situation with Roger's bootprints would have actually applied to the researchers who visited the site shortly after the filming, in 1967. When John Green went there...in June, '68....Roger's prints would have been mostly, if not completely, faded-away....(I would think).

 

Roger's prints were not visible when Green was there. Had they of been there, then Green's film would have been shot from where Roger was instead of being too far back and to the right of Roger's location.

 

At the time Titmus was there - one week (give or take) after the film was taken, Bob said he could see where Roger's horse acted up and where Roger was when he filmed the creature once Roger had crossed the stream.

 

As there is little doubt that on-lookers who happened by the site would have walked up to the trackway to view those prints, it's quite possible that this wasn't the case about anyone walking over Roger's film location footprints for who would really care except someone like Titmus who would have a real interest to record where Roger filmed from. One thing that people who knew Titmus have said about him - he was thorough.

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adam2323

Interesting ..... So how does the difference if correct have change the size of Patty? I remember reading that Titmus confirmed the 102' distance when he arrived the following week.

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SweatyYeti

Interesting ..... So how does the difference if correct have change the size of Patty? 

 

 

I'm not sure how that interacts with the photogrammetry equation for the lens size, and for Patty's size, Adam. Giganto could probably answer your question better than I can, at the moment. 

 

Here is a link to an earlier PGF Photogrammetry Analysis, of Giganto's...

 

http://www.readclip.com/crypto/review.htm

 

 

 

 

I remember reading that Titmus confirmed the 102' distance when he arrived the following week.

 

 

Thanks for mentioning that. I didn't know where the 102' figure originally came from. 

 

Regarding the distance from the camera to Patty, I plan on posting some filmsite measurement diagrams, along with pictures of the site...to help verify what the photogrammetry formulas are indicating. :)

Edited by SweatyYeti

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Guest

I didn't think this thread would go far since none of this stuff can be confirmed unless you know photogrammetry.

Here is the follow up error analysis:

Variables:

DFC = Distance from the camera (ft) = 123

HI = Standing Height of Patty (in) = 75

HP = Image Height (pix) = 578

FP = Image Frame Height (pix) = 3453

FM = Frame Height (m) = .0076

FL = Focal Length (m) = 0.025

Now assign a relative % error to each of the variables and calculate the resulting min/max DFC.

HI err = (77 - 73) / 75 / 2 = +/- 2.7%

HP err = (580 - 575) / 578 / 2 = negligible

FP err = (3460 - 3445) / 3453 / 2 = negligible

FM err = same as FP = negligible

FL err = % lens off spec = negligible

DFC Min = (HI * .97) / ((HP * 1.0) * (FP * 1.0) * (FM * 1.0) / (FL * 1.0) / 12 = 120 feet

DFC Max = 123 + (123 - DFC Min) = 126 feet

DFC = 123 +/-3 feet.

This is the convention for calculating the min/max error:

Min=HImn<HImx HPmn>HPmx FPmn<FPmx FMmn>FMmx FLmn<FLmx

Max=HImn>HImx HPmn<HPmx FPmn>FPmx FMmn<FMmx FLmn>FLmx

Assign the error like this:

DFC Min = (HI * .97) / ((HP * 1.1) * (FP * .80) * (FM * 1.1) / (FL * .90) / 12 = 112 feet

DFC Max = 123 + (123 - DFC Min) = 134 feet

DFC = 123 +/-11 feet

=======================================

An error analysis involves assigning the error for each variable and calculating the min/max DFC then dividing the difference by 2. There are only 5 variables and IMO, the greatest source of error is estimating Patty's height.

I will add another installment to the Photogrammetry 101 series showing another method for calc Patty's distances from the camera. Stay tuned.. :)

Edited by Gigantofootecus

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Drew

When you calculated the Foot As A Ruler dimension, did you use a pixel count for that? or did you use the 14.5" cast measurement?

 

Could you do a pixel count, allowing for some foreshortening error by artificially increasing the pixel count, since the foot is in front of the plane of the rest of the body?

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Guest

^I used the foot ruler to establish pixels/inch. Then you can measure the rest of the body with a pixel ruler. When I did that Patty's standing height came to approx. 6' 3". If Patty's foot was actually 12", then the foot ruler would calc her standing height to be approx. 5' 4". So if you want to put Bob H in the suit then Patty's feet were at least 14.5". And if that was true then Patty made the trackway. Otherwise, why would Roger create a fake trackway with 14.5" prints when Bob H already made tracks with 14.5" feet? If anything Roger "enhanced" Patty's prints or added a couple to the existing trackway. Therefore, Patty almost certainly created the tracks with an average step length of 41". Did Bob H ever mention that he was "striding out" in the suit? And how could floppy bedroom slippers create toe prints and leave tracks deeper than a horse?

There are 2 main sources of foreshortening to consider:

1) The angle of the bottom of the foot relative to the camera plane is the foreshortening angle. The f angle reduces the length of the foot ruler by Cos(fa), so that the pixels/inch value is reduced which scales up Patty > 6' 3". When I averaged the foot length (pixels) against all the other views of the foot (in particular frame 72 which was not foreshortened) I found that the foreshortening of the foot in frame 61 was negligible.

2) The foot is overscaled because it is closer to the camera than the body. However, the farther away from the camera the less this is a factor. For example, if Patty was 150' from the camera (frame 61) and the foot was 2' closer to the camera than her body, then the foot would be overscaled by 2/150 = 1.3% or 14.7", which is negligible. This effect would tend to reduce Patty's calc standing height to < 6' 3".

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Guest

To add, IMO the foreshortening angle of the foot in frame 61 is exactly offset by the closeness of the foot to the camera relative to her body. Both are negligible, but they essentially cancel each other out. We are left with a VERY accurate pixel ruler to measure Patty's body parts with. Plus we can transfer the pixel ruler to other frames by measuring the arm with the foot ruler in frames 61 & 72, then using the "arm ruler" to measure the rest of the body in other frames. Then we can derive Patty's body proportions and build our 3D model.

We must credit Bob H for giving us enough images of him to rule him out. A formal photogrammetric study that developed a 3D model of Patty with an error analysis would prove that Bob H (or possibly anyone) couldn't fit in the suit. Unless new evidence comes to light and/or confessions, studying the film itself is the only way to solve the PGF. If a 3D model of Patty can be created according to photogrammetric standards we can animate the whole PGF and view it from any POV. And if we back up the numbers with an analysis to establish the range of error, we can turn some assumptions into facts. Only facts can lead to proof. We must establish them. Then the skeptics must resort to debunking the science as well as the PGF.

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Drew

Why doesn't Bill Munns utilize the foot ruler method?  Does he have a specific reason for not utilizing that?

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