Missing Nix frames

[Frank Agbat]

More tracking of the Nix frames:

Explanation of Graph:

I went back through and attempted to more precisely locate BOTH the center of wheel AND the front of the limo. Instead of drawing a 0.1cm line to indicate the point, I used a single pixel. Each point (pixel) recorded was then changed to a vertical line. Thus, each vertical line you see represents the location of either the wheel center or the front of the limo.

The brown lines (top grid) track the center of the wheel.

The blue lines (lower grid) track the front of the limo. (This grid has fewer points because the front of the limo is obscured by J. Altgens before the tire is.)

As you can see, both the top and bottom grids show some variations in the spacing of the frame marker points. To determine if these irregularities appear when tracking both the front of the limo and the wheel center, the grids are aligned at the headshot frame (and slightly overlapped). The spacing is consistent to within a few pixels in even the worst case.

This seems to indicate that observed variations are likely to be legitimate, and not merely a by-product of image distortion, blur, or perspective for the tracking points chosen. In other words, the method used seems to be internally consistent and able to be replicated.

Of course, many things can lead to variations in frame spacing. The movie camera itself can (and does) introduce some minor variations. The limo speed changed, etc, etc. The next thing I'm going to look into is whether any of the variations seem out of line (i.e. statistically unlikely). Any variations that fall into that category would have to be deemed unusual.

[Thomas H. Purvis]

http://i27.photobucket.com/albums/c168/yanndee/b.gif

is a 3 meg Z sequence overlapping with the end of the Nix posted above

(small version)

Thanks for that LARGE gif John.

I watch it replay over and over again. !

Mezmerizing.

Robin;

Excellent enlargements.

Could you, John, or Frank assign frame numbers to these three enlargments of the Nix film, in order that they may be further discussed.

Thanks,

Tom

[John Dolva]

Frank, I've selected a smaller group and redone the set you sent using the center of the front chrome emblem. The reason is that the first few are more blurred and this group has a particular spot on the road that occurs on all these frames so It's probably as accurate as I can get it. However as it diverges from yours in one section I'll redo it a few times again.

Tom, I'll check on that and let you know.

[John Dolva]

Tom : 15, 24, 37

The rest up to the standing man. It looks to me that within an acceptable error margin we have the same for that set of frames.

So. The clip initially used has frames missing in an odd pattern.

The WC numbering is correct according to both sets of frames.

The WC has wrongly identified the headshot frame, perhaps by two, definitely by one.

Movements sync with the zfilm and muchmore needs looking at.

J. O'Hagan indicates that frames have been doctored with.

James, could you pass on if you know where on which frames the doctoring occured?

[Frank Agbat]

Tom : 15, 24, 37

The rest up to the standing man. It looks to me that within an acceptable error margin we have the same for that set of frames.

So. The clip initially used has frames missing in an odd pattern.

The WC numbering is correct according to both sets of frames.

The WC has wrongly identified the headshot frame, perhaps by two, definitely by one.

Movements sync with the zfilm and muchmore needs looking at.

J. O'Hagan indicates that frames have been doctored with.

James, could you pass on if you know where on which frames the doctoring occured?

John,

I concur.

I'm still a bit confused by the frame pattern in the original clip, although I am now inclined to believe that the missing frames were the result of improper IVTC.

I suspect that the original clip was de-interlaced *AND* inverse-telecined. This could *possibly* explain an odd clustering of 'extra' frames. If a few frames that should have been eliminated survived (but appeared merely as blurry frames due to the method used to de-interlace), this could explain it.

As such, I'm inclined to say that anomalies that showed on the original clip were created (probably accidentally) in the digital domain.

[Thomas H. Purvis]

Tom : 15, 24, 37

The rest up to the standing man. It looks to me that within an acceptable error margin we have the same for that set of frames.

So. The clip initially used has frames missing in an odd pattern.

The WC numbering is correct according to both sets of frames.

The WC has wrongly identified the headshot frame, perhaps by two, definitely by one.

Movements sync with the zfilm and muchmore needs looking at.

J. O'Hagan indicates that frames have been doctored with.

James, could you pass on if you know where on which frames the doctoring occured?

John,

I concur.

I'm still a bit confused by the frame pattern in the original clip, although I am now inclined to believe that the missing frames were the result of improper IVTC.

I suspect that the original clip was de-interlaced *AND* inverse-telecined. This could *possibly* explain an odd clustering of 'extra' frames. If a few frames that should have been eliminated survived (but appeared merely as blurry frames due to the method used to de-interlace), this could explain it.

As such, I'm inclined to say that anomalies that showed on the original clip were created (probably accidentally) in the digital domain.

Nix 15 = Z-307

[Thomas H. Purvis]

Tom : 15, 24, 37

The rest up to the standing man. It looks to me that within an acceptable error margin we have the same for that set of frames.

So. The clip initially used has frames missing in an odd pattern.

The WC numbering is correct according to both sets of frames.

The WC has wrongly identified the headshot frame, perhaps by two, definitely by one.

Movements sync with the zfilm and muchmore needs looking at.

J. O'Hagan indicates that frames have been doctored with.

James, could you pass on if you know where on which frames the doctoring occured?

John,

I concur.

I'm still a bit confused by the frame pattern in the original clip, although I am now inclined to believe that the missing frames were the result of improper IVTC.

I suspect that the original clip was de-interlaced *AND* inverse-telecined. This could *possibly* explain an odd clustering of 'extra' frames. If a few frames that should have been eliminated survived (but appeared merely as blurry frames due to the method used to de-interlace), this could explain it.

As such, I'm inclined to say that anomalies that showed on the original clip were created (probably accidentally) in the digital domain.

Nix 15 = Z-307

Nix 24 = Z-317

[Thomas H. Purvis]

OK. WC frame 24 is my frame 25. Their frame 10 is 11. So the frames missing from the clip are indeed 4 and they must have left out frame 1 counting it as too blurry and the true headshot frame is two or three before the one they say is the headshot.

Now assuming that you mean their frame 10 and 24 I get the distance travelled during 14 frame transitions as ten feet. (see image) limo is 21.34 feet

Ten feet during 14/18.5 is average speed 9.0 mph. (please check) and for the four frames before the first missing frame the average speed is 8.4 mph

and for the eight frames after the wc 24 the average speed is 7.6 mph

Vehicle speed at Z-308 to Z-312 was approximately 8.73 mph, if that is of any help.

[Frank Agbat]

I took some time out tonight to analyze the Nix frame spacing a bit more. What I did was create a table of values representing the lines from the two grids that I charted (limo wheel, and limo front). I used the "pixel" as a unit of measure. I believe this is a reasonably valid approach since I am only looking at relative differences, not absolute values.

Additionally, because of blurring and the possibility of human error in placing the markers, I averaged the data between the two different methods (aligned on the headshot frame) to create a third data set. This, too, should be valid, as it will have the effect of softening (averaging-out) error on any particular frame.

Using the center wheel, I discovered the following (all units are in pixels on a 720x480 image):

Intervals Measured: 48

Smallest Gap: 9

Largest Gap: 16

Mean (Avg): 12.479

Std Deviation: 1.646

Mode: 14

Percentage of gaps within +/- 1 Standard Deviation: 87.50%

Percentage of gaps within +/- 2 Standard Deviations: 93.75%

Percentage of gaps outside +/- 2 Standard Deviations: 6.25% (3 gaps, 2 are greater than +2 Std devs, 1 less than -2 std devs)

-------------------------------------------------------------------------

Using the front of limo, I discovered the following (all units are in pixels on a 720x480 image):

Intervals Measured: 44

Smallest Gap: 9

Largest Gap: 20

Mean (Avg): 12.477

Std Deviation: 2.148

Mode: 14

Percentage of gaps within +/- 1 Standard Deviation: 70.45%

Percentage of gaps within +/- 2 Standard Deviations: 95.45%

Percentage of gaps outside +/- 2 Standard Deviations: 4.55% (2 gaps)

-------------------------------------------------------------------------

Using the average of the two previous measurements, I discovered the following (all units are in pixels on a 720x480 image):

Intervals Measured: 48 (for the final 4 points, only 1 data set, the center wheel, was available)

Smallest Gap: 9.5

Largest Gap: 18

Mean (Avg): 12.490

Std Deviation:1.775

Mode: 14

Percentage of gaps within +/- 1 Standard Deviation: 72.92%

Percentage of gaps within +/- 2 Standard Deviations: 95.83%

Percentage of gaps outside +/- 2 Standard Deviations: 4.17% (2 gaps)

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

Preliminary interpretation:

Using the limo front and the averaged data set produced a distribution that could be considered normal -- 95% of the distribution falls within 2 standard deviations.

Using the center of the front tire produced a distribution that is exceedingly close to being a normal -- 93.75% of the distribution falls within 2 standard deviations.

All three data sets (center tire, limo front, and average) had in excess of 70% of the gaps fall within 1 standard deviation. (Center tire had the largest population within 1 Standard Deviation at 87.5%).

What this tells me is that the spacing between N-frames using both the center tire and the front of the limo exhibit variations that are statistically consistent when the headshot frame is used as the reference point. In fact, the values appear to fall within a distribution that is exceedingly close to what is called a "normal distribution" in statistics.

The gaps that fall outside the 2 standard distribution range all fall quite easily within +/- 3 standard deviations. The frames exhibiting the aforementioned gaps are N2-N3 and N3-N4. Both gaps are greater than +2 std. devs. (farther apart than 95% of the frames) When using the wheel center, N39-40 exhibits a gap outside -2 standard deviations (closer together than 95% of the frames).

If anyone wants the actual data in a CSV file, let me know and I'll make it available. I also want to look at this with different reference points (i.e. using N1 instead of the headshot frame).

[John Dolva]

Interesting approach, Frank. I wonder if the results can be used as a kind of reference to compare the other films. Would a similar pattern, say of the Z-film, mean a sync? Conversely would a different pattern indicate frames missing? I wonder what other data can be derived or inferred?

Some of the frames are more blurred than others. Particularly the first few. For those frames one would expect a larger error.

Also the frames at either end only compare to those on one side, so a change may, if movement on the 'unknown' side was included, lessen discrepansies there?

If so, could one tentatively conclude that the data indicates that there are no frames missing?

[Ashton Gray]

Interesting approach, Frank. I wonder if the results can be used as a kind of reference to compare the other films. Would a similar pattern, say of the Z-film, mean a sync?

Whatever the result on Nix and possible application to the Zapruder film, I think the approach that you and Frank have taken is the most practical, rational, and disinterested analysis that I've seen to date, and I just wanted to voice my appreciation for what I think will stand as landmark work.

Ashton

[Frank Agbat]

Interesting approach, Frank. I wonder if the results can be used as a kind of reference to compare the other films. Would a similar pattern, say of the Z-film, mean a sync? Conversely would a different pattern indicate frames missing? I wonder what other data can be derived or inferred?

Some of the frames are more blurred than others. Particularly the first few. For those frames one would expect a larger error.

Also the frames at either end only compare to those on one side, so a change may, if movement on the 'unknown' side was included, lessen discrepansies there?

If so, could one tentatively conclude that the data indicates that there are no frames missing?

John,

I think it is a very interesting idea to apply our approach to other films individually, and then comparing films against each other. I believe this to be a logical next step.

Blur certainly introduces some degree of error, and one thing that might be good to consider is the relative amount of blur (could be measured in Pixels) and how the extremes and the mean value of the blur impact the overall analysis. By averaging the values of two reference points, I attempted to reduce some of the effects of blurring. However, one could argue that I merely showed that my own personal "best point" selection process was consistent. Your "unknown side" point is quite valid and probably would lessen discrepancies.

I believe that it is fair to reach a tentative conclusion that there are no missing frames, yes. However, I'd like to to a couple more experiments before calling it a "final" conclusion. I need to verify that the method is sound and that missing frames or inserted frames would be detected.

[John Dolva]

Ashton, thank you. I think you recognise it's the method that is responsible and staying disinterested is essential. It's possibly one of the hardest things but a slow methodical, critically reviewed method leads to results that one can confidently build on.

Frank another thing that comes to mind is the location of the reference point in relation to lens centre. ie. the closer to the edges various lens distortion introduces shifts.

I'll go on and create an image/measurement for the Z-film over the sequence we have looked at here.

[Frank Agbat]

I took a look at what an N-film clip with removed frames might look like in terms of spacing, and the associated math.

The first question I had to consider was how many frames to remove. In our tracking sample, I had 48 measurable gaps. I wanted to remove a number that would seem fairly unnoticeable to the eye. After debating this for a while, I decided on 3 frames. At 18.5 frames per second, this would cause a loss of 0.162 seconds of total run length.

The next question was, "which frames to remove?" For this exercise, I decided to remove three frames at random, with the qualifier that they had to be at least 9 frames (~.5 second) apart. I then used a random number generator and had it pick three frames...

Here is the resulting gap analysis:

I then ran the same analysis on the "new" gaps and produced a distribution chart showing both the original source and the altered source:

Some items of note:

1) I have used colored boxes to show standard deviations around the mean value. The height of the boxes corresponds to expected values in a normal distribution (except for the green box, which would extend beyond the graph).

2) The standard deviation of the "missing frames" version is 3.43 (vs 1.65 for the normal version). This leads to a massive difference in the variance as well.

3) The "missing frames" version has two very anomalous gaps (25 and 28). The expected value for this area in a normal distribution is very close to zero (0.052 frames for the +4SD group, and even lower for the +5SD group).

4) The "normal" version has only one frame that is even slightly unexpected (the +2SD group has 2 frames, where 1 is expected). This could easily be blur, measurement error, etc.

5) Interestingly, one of the "altered" frames (gap = 20) might be able to escape attention, as some frames are expected to be in the yellow region. I'll post more about this observation separately.

[Frank Agbat]

Proof of concept animation:

Zapruder frames Z-298 through Z324

Nix frames aligned so that bloodsplatter frame (NS-23) = Z313.

120x200 clips, aligned/stabilized on T. Foster.

Running slightly fast (actually makes the sync a bit easier to see)

(Edit - replaced with higher quality version)

Edited December 11, 2006 by Frank Agbat