The 9/11 Forum

Observations and comments related to obtaining and analyzing motion data from video.

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Links to Thread Highlights
There are a number of posts I feel have particularly interesting or useful resource content. So they don't get buried forever in the thread, here are links to posts and areas in the thread by topic. This may or may not get updated.

Recent Additions of Note
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The most accurate analysis of WTC7 NW corner vertical displacement to date (01/11/09):

http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-240.html#p1534

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Technique and Methodology

The Definitive Smearogram How-To Video (einsteen)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-30.html#p669
Direct download link: http://www.megaupload.com/?d=JNMLLCLW

Perspective Corrections to Smearograms (Dr. G)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-225.html#p1523

Suggestion to use piecewise fits (Major_Tom)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-60.html#p898

Quick thoughts on David Chandler (Dr. G)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-180.html#p1428


Dynamics

Discussion of Charles M. Beck's paper - WTC7 (Dr. G)
(this leads to an extended discussion of the possibilities of faster than g descent)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-90.html#p944

WTC7 E1 estimate (Dr. G)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-150.html#p1238


Structural Damage Comparisons

References to studies on earthquake-induced building damage and motion, with data (Dr. G)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-75.html#p925

Four controlled demolitions and one structural collapse (einsteen)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-210.html#p1481


CBS video (NIST Camera 3)

NIST fine-resolution horizontal data replicated (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-45.html#p688

NIST horizontal data curve directly visible in smearogram (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-150.html#p1231

North face dark rectangle tracking and data (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55.html#p613
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-30.html#p664

Scene geometry and camera distance (Dr. G)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-30.html#p652

Camera motion tracking (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55.html#p615

Relating NIST time to video time, Part 1 and 2 (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-30.html#p662
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-30.html#p665

Difference images of north upper face early motion (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-30.html#p656

Difference between linear scaling and perspective correction (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-135.html#p1069

Displacement at NW corner vs. midroof, using smear overlays (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-150.html#p1236

Series of smearograms spanning much of building width - several posts (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-180.html#p1438

Animation of NW corner edge deformation (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-195.html#p1460

Smear data (OneWhiteEye)
Column 260 - http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-210.html#p1474
Column 460 - http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-210.html#p1488
Column 516 - http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-240.html#p1527
Column 536 - http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-240.html#p1529
Column 552 - http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-240.html#p1530


Structural Details

Link to floor elevations of WTC 1,2 (Major_Tom)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-15.html#p643


Newly Released (GldBr) WTC7 Video

Location, scene geometry and camera distance (Dr. G)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-135.html#p1087


Miscellaneous

Very helpful advice on Windows crash recovery (chek)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-180.html#p1429

Clone partition to .gho file (einsteen)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-180.html#p1434

Basic software tools (OneWhiteEye)
http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55-195.html#p1451

This post is in reply to a comment by Dr. G in another thread, from this page (http://the911forum.freeforums.org/withering-critique-of-the-new-wtc7-report-t44-75.html) where he writes:

Dr. G wrote:This is with his selection of t(zero). Even looking at the velocity plot he displays in his video I would move his t(zero) cursor a tad to the left which would slow his acceleration significantly ......

This has prompted me to do some sensitivity tests on some of my own collapse plots. I have taken one of my "best efforts", which generates a very smooth curve, and looked at the effect of shifting t(zero) by just 0.1 seconds. When I do this I get these two curves:

The original plot fits to:

Drop = -0.077t^3 + 4.8433t^2 -0.2123 t + 0.0669

And the plot shifted by 0.1 seconds gives:

Drop = -0.0176t^3 + 4.4721t^2 - 0.5854t + 0.0034

Hence for the acceleration, by double differentiation, we have:

Original plot:

Accel = 9.6866 - 0.462t

Plot shifted by 0.1 seconds:

Accel = 8.9442 - 0.1056t

Thus we see a marked change in the calculated acceleration for just a 0.1 second shift. This is why I have argued that the measured acceleration is about 9.2 +/- 0.6 m/s^2.

This is very interesting to me. I raised this issue once (http://www.physforum.com/index.php?showtopic=12383&st=8925&#entry302106) when asking David B. Benson at physorg about choice of t0 ; it seemed the choice would have an impact in his process of choosing a hypothesis and I wanted to get his take on it, particularly as the low grade hypotheses were not afforded the luxury of adjusting the initial time as were the high grades. I think his final word on it was here: http://www.physforum.com/index.php?showtopic=12383&st=9015&#entry304291.

In an attempt to gain some understanding about this situation, I played with polynomial curve fits agianst known polynomials which were offset by a varying delta T, which would represent a constant error stemming from poor choice of t0. Unfortunately I couldn't find the previous work so here's today's run.

Executive Summary: Proper choice of t0 can be very important and not too easy.

I created four datasets from the function x(t) = t^2 evaluated over a 1 unit range with +/- offsets in t from 0. The increment, which represents frames, is 0.01 so the normal frame times are 0.00, 0.01, 0.02,... 1.00. The offset frame times are just those +/- some small constant; I chose 0.01 and 0.03, representing one and three frames of error in t0. Then, the resulting datasets of x(t) calculated from the offset times were fitted against the unadjusted frame times. I did polynomial fitting as follows: 2nd and 3rd degree, with and without linear term (A1), constant term A0 always fixed to zero.

Here are fits for an offset of +/- 1 frame:

Minus offset
2nd degree, A1 zero: http://i38.tinypic.com/2cz3ioi.png
2nd degree, A1 free: http://i36.tinypic.com/2zs68hf.png
3rd degree, A1 zero: http://i35.tinypic.com/35izxcp.png
3rd degree, A1 free: http://i34.tinypic.com/fc41f9.png

Plus offset
2nd degree, A1 zero: http://i38.tinypic.com/i1fyiw.png
2nd degree, A1 free: http://i33.tinypic.com/2u7vvoj.png
3rd degree, A1 zero: http://i34.tinypic.com/260y1rq.png
3rd degree, A1 free: http://i33.tinypic.com/1z2m8ba.png

No explanation required, all point to the form x(t) = t^2 being the best fit. The worst error in the calculation of the squared term in each of these is 6%. These errors represent the best case scenario where there is infinite spatial resolution and accuracy, no noise, and jackhammer precision in the sample intervals. All error comes from uncertainty in the coincidence of the sample times and t0. The parameter t should be an adjustable parameter and participate in the fitting process. But real video is noisy and the measurements imprecise, there is no clear line between stationary and first motion, choosing the best two frames and interpolating between is not really possible.

Carrying on with an offset akin to what you considered, Dr. G, the fits for three frames of error are:

Minus offset
2nd degree, A1 zero*: http://i35.tinypic.com/2ngcxfs.png
2nd degree, A1 free: http://i34.tinypic.com/dng4ut.png
3rd degree, A1 zero: http://i36.tinypic.com/2428sb9.png
3rd degree, A1 free: http://i36.tinypic.com/2lt1p1h.png

Plus offset
2nd degree, A1 zero*: http://i37.tinypic.com/2je5ks8.png
2nd degree, A1 free: http://i38.tinypic.com/1jw1zr.png
3rd degree, A1 zero: http://i35.tinypic.com/vys4sz.png
3rd degree, A1 free: http://i35.tinypic.com/546d6t.png

* for the case of testing the actual relation, t^2, it's still only a little over 7% in either direction.

All fits are reported as 100% confidence, though some are pretty far off in calculation of A2. An interesting result is that better accuracy in A2 is obtained by not insisting that the A1 be identically zero, even though there is no linear term in the underlying relation. Thus, the wrong hypothesis gives a better value for the square term but, in tradeoff, introduces a small erroneous linear coefficient. This is also true for the 3rd degree fit with respect to both A1 and A3. The small magnitude of these coefficients might suggest that they are really only corrective terms, but that's subjective and maybe I only think that way because I know they should be zero.

Obviously, this is just the scenario for a simple function, x(t) = t^2. When you don't know the real relation, things get much more complicated. One measurement per frame helps. It's tempting to skimp on pre-initiation data points, but when is initiation?

OneWhiteEye:

Thanks for this very detailed analysis of the "t(zero) problem". And thanks for reminding me, ..... I forgot about that old PhysOrg thread on WTC 1 & 2. I guess there is nothing new under the sun! Especially since you, David Benson and others have been over this issue in some detail for WTC 1 & 2.

However, whether we like it or not, we now have to add the WTC 7 collapse to the list of buildings needing a collapse initiation mechanism!

The curve fitting exercise we are discussing is fascinating but I also like to think about it in physical terms. What puzzles me is the start of free fall, or of "near free fall if you prefer", which must involve a finite time interval. For WTC 7 I think we are talking about the first second or so of collapse. Whatever its magnitude, the "collapse induction" time is simply the time needed to get to a constant acceleration ~ g starting from rest, ...... and as this time interval gets smaller and smaller, the movement gets less and less and we seem to be getting into the old "Zeno's paradox" type of problem.

With WTC 1 & 2 I believe the collapse mechanism involves a tipping motion. This is a lot like the falling pencil problem and is an example of exponential growth, or thinking in reverse, exponential decay.

For WTC 7 there is no significant tipping but, so NIST says at least, we have a case of building failure by pure column buckling with some connector failure thrown in for good measure. So we have to ask: How fast can steel beams buckle? How fast can bolts fracture?

Whatever the answer, OWE, you are correct, a study of the first moments of a collapse should tell us a lot about what causes collapse initiation, .... but we have to first ask if the measurements are good enough to reveal the collapse mechanism and, for example, distinguish between a "natural" collapse and a controlled demolition.

This deserves a reply after taking time for consideration.

Dr. G,

Given the sensitivity of acceleration calculations to t(0), it seems fair to ask: What can one really know about t(0)? What if the outer structure had been slowly moving downward for seconds - minutes - or even hours - before the more popular t(0)s?

Dr. G:

I'm going to take one piece at a time, starting at the end.

Dr. G wrote:...but we have to first ask if the measurements are good enough to reveal the collapse mechanism and, for example, distinguish between a "natural" collapse and a controlled demolition.

The first thing that came to my mind was probably not, given the quality of the videos. The Sauret video is so good it spoils a person, I wish there were comparable quality for WTC7. I need to look at what einsteen and Dictator Cheney are posting.

As I thought about it, though, the outlook improved. In the one frame einsteen posted in the other thread, there are about 150 horizontal pixels of roofline. Are you with me? That's 150 smearograms right there, each pixel of the camera is an individual transducer! True, the building's structure is not rigid and did kink but adjacent pixel columns will have minimal differences. In this case, getting per-frame data is essential but leads to thousands of measurements for just a couple of seconds of one video. This is where automation becomes very handy.

As for time resolution, taking data from more than one video not only gives more sample points, it is also probable that the samples from each video will be out of phase, i.e. absolute sample times differ even if rates are the same, as depicted below where the horizontal scale is time (one frame interval) and X is the point in time where the image is taken in three different cameras:

Code: Select all

|-X--------|
|----X-----|
|-----X----|


While posing a problem for correlation of t0 between videos, I think there could be a slight effective increase in the time resolution. How to take advantage of that without knowing the precise relative offsets of the sample intervals, I do not know at this time. Nevertheless, from a purely infomation-theoretic standpoint, the additional information is there, I don't see why it would be totally lost by not knowing the offsets. I'm only talking about long baseline followed by a few frames of motion. Correlated sets may then automatically inherit some benefit over merely averaging frames which are recorded at exactly the same time, something you'd think would be ideal (and may happen by chance anyway). Think of how numerical methods sometimes stress irregularity in sampling, like a Monte Carlo method.

I would propose that each data series be partitioned into known stationary baseline, known motion, and those few frames in between that represent collapse induction with fuzzy boundaries. The baseline interval, easily chosen, hopefully will consist of many points and firmly establish the initial position of each pixel column and also deal with constant offsets between them. Begin examination at the first frame of the induction zone - which will still be stationary at first, and go forward in time frame by frame. The point at which the deflection first rises above the noise by some epsilon and does not fall below a threshold in the next frame becomes the frame of first motion and redefines the beginning of the known motion set. From the other direction, the known motion sets can be fitted and extrapolated back to t0, which should lie interstitially in the last frame of the induction zone or, in extreme, the prior frame. The values of all 150 or so pixel columns can then be composed to a single value of t0.

Subpixel resolution in each column is possible, too, even with fairly blurry video. How is a subject for another post. It does confer a distinct advantage over starting with integral position values.

All in all, it's a fair bit of work, but I'm up to it - in spirit anyway. It may not be necessary, but I think the important thing is to realize that, yes, the potential is there to get a very accurate characterization of the early motion.

Max Photon and OneWhiteEye:

I like the idea of using many vertical slices from a given video to construct a whole bunch of smearograms and then averaging the result. After all, there's a lot of collapse information in each video -why throw most of it away!?!

Perhaps an initial motion of less than 0.5 meters could never be detected, but a 0.5 meter resolution might still be good enough to distinguish between different collapse initiation scenarios. Certainly NIST's simulation suggest there was a protracted "turning off" of the reaction force supporting the building so that the gravitational force built up over about 2 seconds. This should be revealed in the first two seconds of motion but, as far as I can tell right now, was not seen!

OneWhiteEye wrote:This post is in reply to a comment by Dr. G in another thread, from this page (http://the911forum.freeforums.org/withering-critique-of-the-new-wtc7-report-t44-75.html) where he writes....

I'm sorry to say the fits in this post were all wrong. The curves were not offset to start at x=0 so constraining the A0 term to be zero was wrong; one or the other but not both. Oh well, it was playing around anyway so I'm not going to bother redoing it.

Dr. G wrote:The curve fitting exercise we are discussing is fascinating but I also like to think about it in physical terms. What puzzles me is the start of free fall, or of "near free fall if you prefer", which must involve a finite time interval. For WTC 7 I think we are talking about the first second or so of collapse. Whatever its magnitude, the "collapse induction" time is simply the time needed to get to a constant acceleration ~ g starting from rest, ...... and as this time interval gets smaller and smaller, the movement gets less and less and we seem to be getting into the old "Zeno's paradox" type of problem.

With WTC 1 & 2 I believe the collapse mechanism involves a tipping motion. This is a lot like the falling pencil problem and is an example of exponential growth, or thinking in reverse, exponential decay.

For WTC 7 there is no significant tipping but, so NIST says at least, we have a case of building failure by pure column buckling with some connector failure thrown in for good measure. So we have to ask: How fast can steel beams buckle? How fast can bolts fracture?

I don't know. After several days pondering this, that's the best I could come up with.

You posted this at physorg: http://www.physforum.com/index.php?show ... ntry277670.

A few years ago I had a cheap set of glass cookware. One day, I removed a piece from the dishwasher and placed it in a cupboard, at which time it exploded in my face, sending shards all over the kitchen. When did it start to break? Maybe from the time it was manufactured?

Gearing up to take massive amounts of data.

Quick look at some new WTC7 motion data. This comes from one of the videos einsteen posted in the Dr. G WTC7 thread, the one labeled as an NIST video (29.97 fps, more details and reference back to source to follow). The target is a large dark rectangle at the top center of the north face. The units are time and pixels.

I'll follow up with some inline pictures in a few; the new board format, while pleasing to the eye, clips images horizontally (this is a big downer, admin, other aspects seem nice).

Frames 0-335, about 11.2 sec of data: http://i36.tinypic.com/2dv5yq8.jpg
The first 6 seconds of above, zoomed: http://i37.tinypic.com/2vsf3gm.jpg
5 to 9 seconds (1 second overlap with above): http://i37.tinypic.com/23wuusw.jpg

The interesting thing is the almost linear decline followed by a rebound upward, seen in the second graph. As best as I can tell so far, the tracking is accurate, whether the motion is real or not I still need to verify. Could be camera motion.

The video (WTC7 NIST Clip with east penthouse.avi) was posted on this page by einsteen - http://the911forum.freeforums.org/withering-critique-of-the-new-wtc7-report-t44-105.html

The target is the dark rectangle seen here:



When viewed with (inverted) pixel intensity in the 3rd dimension, it is the magenta section:





Rather large feature for this sort of procedure but the results appear to be good.

These are the same graphs posted above but reduced to fit within the page.

Frames 0-335, about 11.2 sec of data:


The first 6 seconds of above, zoomed:


5 to 9 seconds (1 second overlap with above):

One potential measure of camera motion is data obtained from a stationary feature. The feature chosen here was a group of windows on a foreground building. The graph's vertical axis is 1 pixel deflection, the 'stationary' windows drift a total of about 0.3 pixels over the course of frames 0-335.


http://i33.tinypic.com/11khwes.png

OneWhite Eye:

So now we have yet another collapse curve to look at!

First of all, very nice data presentation!

I have tried a quick height calibration by subtracting 90 pixels from your pixel number so that the collapse data starts from ~ 0.2 pixels and ends at ~ 88 pixels. I have multiplied the resultant pixel count by 0.5 and called that the drop distance in meters. I have also subtracted 7 seconds from your time axis to define some sort of t(0).

Now, OWE, the interesting thing about the resulting data is that it will not fit to a 2nd or 3rd order polynomial at all! The curve is simply too slow at short times and too fast at long times. So I tried an exponential curve and got an excellent fit with:

Drop = 0.0509 exp^{1.6462t)

The "goodness of fit" parameter R^2 = 0.9981 shows just how good the fit is!

However, the problem now is that this curve is quite unlike all the other curves I have seen, .....

P.S. Edited to add that my drop height scaling may be off and you don't need the 0.5 factor. This simply changes the pre-exponential factor to 0.1018 ..... but the goodness of fit remains the same.

Thanks for looking it over.

There are only a few things I can say right now, I will try to shed more light on this in a short bit.
- the big dark rectangle doesn't undergo exactly the same motion as the upper corner
- there is some deformation along the face, it's near the kink
- it's not the same video as the Naudet video that einsteen posted data for; different perspective
- I'm trying now to do the same rectangle in the Naudet video

and:

13 floors = 300 pixels (toward right side corner)
=> 0.0433 fl/px
if 3.7m/fl => 0.16m/px

Let me examine this more closely.