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Technical notes on video motion analysis

Other 9/11 topics of a technical nature.

Re: Technical notes on video motion analysis

Postby OneWhiteEye » Fri Jan 09, 2009 10:13 pm

Dr. G wrote:Perspective Corrections to Smearograms

Thank you Dr. G, this is an excellent contribution. More than ever, I feel the need to construct a list of links to posts like these. Thankfully, the board has been set up to allow long term editing. A table of contents, of sorts, could be placed into the first post to try to keep great references like this from getting buried.

OWE, I guess (in theory) you could set up a variable pixel-to-vertical height correction factor that could automatically be applied to each smearogram as it was being generated. Alternatively, the necessary correction factors could be applied to the data as required when drop vs. time plots were being created.


Absolutely. No problem to throw that into the mix*. For my own uses, I've sometimes included a value that represents the best conversion available at the time. Only recently has this occasionally gone into posts. We've discussed this a bit on physorg, you may recall.

*ah, but we probably need to discuss the mix. Buzzwords like 'process pipeline' and 'supervised learning' are no longer abstract. The required data reduction isn't cooking of the sort practiced by social scientists, so relax if that's a concern. There is mapping and correction to be applied, some best done while in the pixel domain.

----

My read_me post will have to wait. It's even better now just to get the data, so here's the summary:
1) be very, very careful; there are many pitfalls, many more than the thread has touched
2) there is very little in a smear that directly translates to physical rectilinear motion, except in "approximation"
3) the closer you look, the bigger the warts
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

 

CBS (Camera 3) pixel column 516

Postby OneWhiteEye » Fri Jan 09, 2009 11:59 pm

On the roofline between the end of the west penthouse and the NW corner, closer to the penthouse. Good quality signal. Sixteen thresholds used at 5 unit intervals, 125-200. Average in last column. Lower threshold numbers are closer to building, higher numbers closer to sky, in terms of placement in the edge.

All individual threshold levels on one graph:

Image


The average over entire interval:

Image


A close-up of the average over the first 10 seconds. The vertical axis spans only 3 pixels:

Image


And the data. Two more smears (536 and probably 552), closer to the corner, will follow soon. This will allow either averaging, or fitting a line which points back to the NW corner vertex.

Code: Select all
Frame,Row125,Row130,Row135,Row140,Row145,Row150,Row155,Row160,Row165,Row170,Row175,Row180,Row185,Row190,Row195,Row200,Avg
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186,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21.75
187,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5625
188,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5625
189,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,20,21.625
190,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5625
191,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,20,21.6875
192,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5625
193,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5
194,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5
195,23,22,22,22,22,22,22,22,21,21,21,21,21,21,20,20,21.4375
196,23,23,22,22,22,22,22,22,21,21,21,21,21,21,20,20,21.5
197,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
198,23,22,22,22,22,22,22,22,21,21,21,21,21,21,20,20,21.4375
199,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
200,23,23,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.375
201,23,22,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.3125
202,23,22,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.3125
203,23,22,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.3125
204,23,22,22,22,22,22,21,21,21,21,21,21,21,20,20,20,21.25
205,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
206,23,22,22,22,22,22,21,21,21,21,21,21,21,20,20,20,21.25
207,23,22,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.3125
208,23,22,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.3125
209,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
210,23,22,22,22,22,22,21,21,21,21,21,21,21,20,20,20,21.25
211,23,23,22,22,22,22,21,21,21,21,21,21,21,20,20,20,21.3125
212,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,20,21.1875
213,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,20,21.1875
214,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,20,21.25
215,22,22,22,22,22,22,22,21,21,21,21,21,21,20,20,20,21.25
216,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,20,21.25
217,23,23,23,22,22,22,22,21,21,21,21,21,21,21,20,20,21.5
218,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
219,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5625
220,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5
221,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5
222,23,22,22,22,22,22,22,22,21,21,21,21,21,21,20,20,21.4375
223,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
224,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
225,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,20,21.5
226,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
227,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
228,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
229,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
230,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
231,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
232,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
233,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.375
234,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
235,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,20,21.4375
236,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
237,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.5625
238,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.5625
239,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
240,23,22,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21.625
241,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.5625
242,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,20,21.625
243,23,23,22,22,22,22,22,21,21,21,21,21,21,21,21,21,21.5625
244,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
245,23,23,22,22,22,22,22,21,21,21,21,21,21,21,21,21,21.5625
246,23,23,22,22,22,22,22,21,21,21,21,21,21,21,21,21,21.5625
247,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.5625
248,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
249,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.5625
250,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
251,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
252,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
253,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
254,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
255,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
256,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21.6875
257,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
258,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21.6875
259,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21.6875
260,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21.6875
261,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21.75
262,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21.75
263,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21,21,21.6875
264,23,23,22,22,22,22,22,22,22,22,21,21,21,21,21,21,21.75
265,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21,21.625
266,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21.75
267,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21,21.75
268,23,23,23,23,22,22,22,22,22,22,22,21,21,21,21,21,21.9375
269,23,23,23,23,23,22,22,22,22,22,21,21,21,21,21,21,21.9375
270,23,23,23,23,22,22,22,22,22,22,21,21,21,21,21,21,21.875
271,23,23,23,23,23,23,22,22,22,22,22,22,21,21,21,21,22.125
272,23,23,23,23,23,22,22,22,22,22,22,22,22,21,21,21,22.125
273,23,23,23,23,23,23,22,22,22,22,22,22,21,21,21,21,22.125
274,24,23,23,23,23,23,23,22,22,22,22,22,22,22,21,21,22.375
275,24,23,23,23,23,23,23,22,22,22,22,22,22,22,21,21,22.375
276,24,23,23,23,23,23,23,22,22,22,22,22,22,22,21,21,22.375
277,24,23,23,23,23,23,23,23,22,22,22,22,22,21,21,21,22.375
278,24,23,23,23,23,23,23,22,22,22,22,22,22,21,21,21,22.3125
279,24,24,23,23,23,23,23,23,22,22,22,22,22,22,22,21,22.5625
280,24,24,23,23,23,23,23,23,23,22,22,22,22,22,21,21,22.5625
281,24,24,24,24,23,23,23,23,23,23,22,22,22,22,22,22,22.875
282,24,24,24,23,23,23,23,23,23,23,22,22,22,22,22,21,22.75
283,24,24,24,24,23,23,23,23,23,23,22,22,22,22,22,22,22.875
284,24,24,24,24,24,24,23,23,23,23,23,23,23,22,22,22,23.1875
285,24,24,24,24,24,24,23,23,23,23,23,23,23,23,22,22,23.25
286,25,24,24,24,24,24,24,24,23,23,23,23,23,23,23,22,23.5
287,25,25,24,24,24,24,24,24,24,23,23,23,23,23,23,23,23.6875
288,25,25,24,24,24,24,24,24,24,23,23,23,23,23,23,23,23.6875
289,25,25,25,25,25,24,24,24,24,24,24,24,24,23,23,23,24.125
290,25,25,25,25,25,24,24,24,24,24,24,24,24,23,23,23,24.125
291,25,25,25,25,25,24,24,24,24,24,24,24,24,23,23,23,24.125
292,25,25,25,25,25,25,25,24,24,24,24,24,24,24,24,23,24.375
293,26,26,26,25,25,25,25,25,25,25,24,24,24,24,24,24,24.8125
294,27,27,26,26,26,26,26,26,25,25,25,25,25,25,25,24,25.5625
295,27,27,27,27,27,26,26,26,26,26,26,25,25,25,25,25,26
296,28,27,27,27,27,27,27,27,27,26,26,26,26,26,26,26,26.625
297,28,28,28,28,28,27,27,27,27,27,27,27,27,27,26,26,27.1875
298,29,29,29,29,29,29,29,28,28,28,28,28,28,28,28,27,28.375
299,31,31,31,31,30,30,30,30,30,30,29,29,29,29,29,29,29.875
300,32,31,31,31,31,31,31,31,31,30,30,30,30,30,30,30,30.625
301,32,32,32,32,31,31,31,31,31,31,31,31,31,31,30,30,31.125
302,33,33,33,33,32,32,32,32,32,32,32,31,31,31,31,31,31.9375
303,35,35,35,34,34,34,34,34,34,33,33,33,33,33,33,32,33.6875
304,35,35,35,35,35,35,35,35,35,34,34,34,34,34,34,34,34.5625
305,35,35,35,35,35,35,35,35,35,34,34,34,34,34,34,34,34.5625
306,36,36,36,36,36,35,35,35,35,35,35,35,35,35,35,34,35.25
307,38,38,38,38,37,37,37,37,37,37,37,36,36,36,36,36,36.9375
308,39,39,38,38,38,38,38,38,38,38,38,37,37,37,37,37,37.8125
309,40,40,40,39,39,39,39,39,39,39,39,38,38,38,38,38,38.875
310,42,42,42,42,42,42,42,42,41,41,41,41,41,41,41,40,41.4375
311,43,43,42,42,42,42,42,42,42,42,42,42,42,41,41,41,41.9375
312,45,45,45,45,45,45,45,45,44,44,44,44,44,44,44,43,44.4375
313,46,46,46,46,45,45,45,45,45,45,45,45,45,45,45,45,45.25
314,49,49,49,48,48,48,48,48,48,47,47,47,47,47,47,46,47.6875
315,49,49,49,49,49,49,49,49,49,49,48,48,48,48,48,48,48.625
316,52,52,52,52,52,52,52,52,52,51,51,51,51,51,51,51,51.5625
317,54,53,53,53,53,53,53,53,53,53,52,52,52,52,52,52,52.6875
318,56,56,56,55,55,55,55,55,55,55,55,55,54,54,54,54,54.9375
319,58,58,58,58,58,58,57,57,57,57,57,56,56,56,56,56,57.0625
320,60,60,60,60,60,60,59,59,59,59,59,59,59,59,59,58,59.3125
321,63,63,63,62,62,62,62,62,62,62,62,62,62,62,61,61,62.0625
322,65,65,65,65,65,64,64,64,64,64,64,64,64,64,64,63,64.25
323,67,67,67,67,66,66,66,66,66,66,66,66,65,65,65,65,66
324,70,70,70,70,70,69,69,69,69,69,69,69,69,68,68,68,69.125
325,73,73,73,73,73,73,73,73,72,72,72,72,72,72,72,71,72.4375
326,76,76,76,76,75,75,75,75,75,74,74,74,74,74,74,74,74.8125
327,77,77,77,77,77,77,76,76,76,76,76,76,76,76,75,75,76.25
328,84,84,84,84,84,83,83,83,83,83,83,83,83,83,83,82,83.25
329,87,87,87,87,86,86,86,86,86,86,85,85,85,85,85,85,85.875
330,91,90,90,90,89,89,89,89,89,89,88,88,88,88,88,87,88.875
331,93,93,92,92,92,92,92,92,91,91,91,91,91,91,91,90,91.5625
332,95,95,95,95,94,94,94,94,94,94,94,93,93,93,93,93,93.9375
333,98,98,98,98,98,98,98,98,98,97,97,97,97,97,97,97,97.5625
334,102,102,102,102,101,101,101,101,101,101,101,101,100,100,100,100,101
335,102,102,102,102,101,101,101,101,101,101,101,101,100,100,100,100,101
336,105,105,105,105,104,104,104,104,104,104,104,104,104,103,103,103,104.0625
337,109,109,108,108,108,108,108,108,108,108,107,107,107,107,107,107,107.75
338,112,112,112,112,112,112,112,111,111,111,111,111,111,111,111,111,111.4375
339,116,115,115,115,115,115,115,115,115,114,114,114,114,114,114,114,114.625
340,119,119,119,119,119,119,119,119,119,118,118,118,118,118,118,118,118.5625
341,123,122,122,122,122,122,122,122,122,122,122,122,121,121,121,121,121.8125
342,126,126,126,126,126,126,125,125,125,125,125,125,125,125,124,124,125.25
343,130,130,130,129,129,129,129,129,129,129,129,129,128,128,128,128,128.9375
344,134,133,133,133,133,133,133,133,133,132,132,132,132,132,132,132,132.625
345,138,137,137,137,137,137,137,137,136,136,136,136,136,136,136,136,136.5625
346,143,143,142,142,142,141,141,141,141,141,141,140,140,140,140,140,141.125
347,147,147,147,147,146,146,146,146,146,146,146,145,145,145,145,145,145.9375
348,151,151,151,150,150,150,150,150,150,150,150,150,149,149,149,149,149.9375
349,154,154,154,154,153,153,153,153,153,153,153,153,152,152,152,152,153
350,158,158,158,158,158,158,158,157,157,157,157,157,157,157,156,156,157.3125
351,163,163,163,162,162,162,162,162,161,161,161,161,161,160,160,160,161.5
352,168,168,168,168,167,167,167,167,167,167,166,166,166,166,166,165,166.8125
353,172,171,171,171,171,171,171,171,171,170,170,170,170,170,170,169,170.5625
354,176,175,175,175,175,175,175,175,175,174,174,174,174,174,174,174,174.625
355,181,181,180,180,180,180,180,180,180,179,179,179,179,179,179,179,179.6875
356,185,185,185,185,185,185,185,185,184,184,184,184,184,184,184,184,184.5
357,189,189,189,189,189,189,189,189,188,188,188,188,188,188,188,188,188.5
358,195,194,194,194,194,193,193,193,193,193,193,192,192,192,192,191,193
359,204,204,204,203,203,203,203,203,203,202,202,202,202,202,202,201,202.6875
360,209,209,209,208,208,208,208,208,208,208,207,207,207,207,207,207,207.8125
361,214,214,213,213,213,213,213,213,213,213,213,213,213,212,212,212,212.9375
362,219,218,218,218,218,218,217,217,217,217,217,217,216,216,216,216,217.1875
363,224,224,224,223,223,223,223,223,223,223,222,222,222,222,222,222,222.8125
364,229,229,228,228,228,228,228,228,227,227,227,227,227,227,226,226,227.5
365,235,234,234,234,234,234,233,233,233,233,233,233,233,233,232,232,233.3125
366,239,238,238,238,238,238,238,237,237,237,237,237,237,237,237,236,237.4375
367,244,244,244,244,244,244,244,243,243,243,243,243,243,243,242,242,243.3125
368,249,249,249,249,249,249,248,248,248,248,248,248,248,248,247,247,248.25
369,255,254,254,254,254,254,254,254,253,253,253,253,253,253,253,253,253.5625
370,260,260,260,260,259,259,259,259,259,259,259,259,258,258,258,258,259
371,265,265,265,265,265,264,264,264,264,264,264,264,264,263,263,263,264.125
372,271,271,270,270,270,270,270,270,270,269,269,269,269,269,269,268,269.625
373,276,276,276,276,275,275,275,275,275,275,275,275,274,274,274,274,275
374,282,282,282,281,281,281,281,281,281,280,280,280,280,280,280,279,280.6875
375,287,287,287,287,287,287,286,286,286,286,286,286,286,285,285,285,286.1875
376,293,292,292,292,292,292,292,292,292,292,291,291,291,291,291,291,291.6875
377,298,298,297,297,297,297,297,297,297,297,297,296,296,296,296,296,296.8125
378,304,304,303,303,303,303,303,303,303,302,302,302,302,302,302,301,302.625
379,310,310,310,309,309,309,309,309,309,308,308,308,308,308,307,307,308.625
380,315,315,315,315,315,314,314,314,314,314,314,314,314,313,313,313,314.125
381,327,327,326,326,326,326,326,325,325,325,325,325,325,324,324,324,325.375
382,333,332,332,332,332,332,332,331,331,331,331,331,331,331,331,330,331.4375
383,339,339,339,339,338,338,338,338,338,338,338,337,337,337,337,337,337.9375
384,344,344,344,344,344,343,343,343,343,343,343,343,342,342,342,342,343.0625
385,350,350,350,350,350,350,350,349,349,349,349,349,349,349,349,349,349.4375
386,357,357,357,356,356,356,356,356,356,355,355,355,355,355,354,354,355.625
387,363,363,363,363,362,362,362,361,361,361,361,361,361,361,360,360,361.5625
388,369,369,369,368,368,368,368,368,368,367,367,367,367,367,367,366,367.6875
389,375,375,375,375,374,374,374,374,374,374,374,374,373,373,373,373,374
390,382,382,381,381,381,381,381,381,380,380,380,380,380,380,379,379,380.5
391,388,388,388,388,387,387,387,387,387,387,386,386,386,386,386,385,386.8125
392,388,388,388,388,387,387,387,387,387,387,386,386,386,386,386,386,386.875
393,395,394,394,394,394,393,393,393,393,392,392,392,392,391,391,391,392.75
394,400,400,400,400,399,399,399,399,399,399,399,398,398,398,398,398,398.9375
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

Comparison of C260 and C516

Postby OneWhiteEye » Sat Jan 10, 2009 12:42 am

The average values for pixel columns 260 and 516 are compared. The crude method of zeroing was not entirely accurate, as can be seen, but it's within a pixel. C260 is blue.

Entire interval:

Image


Closeup of first 10 seconds:

Image
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

CBS (Camera 3) pixel column 536

Postby OneWhiteEye » Sat Jan 10, 2009 1:36 am

For C536, everything the same as the last time, except threshold range is 130-205.


All individual threshold levels on one graph:

Image


The average over entire interval:

Image


A close-up of the average over the first 10 seconds.

Image

Code: Select all
Frame,Row130,Row135,Row140,Row145,Row150,Row155,Row160,Row165,Row170,Row175,Row180,Row185,Row190,Row195,Row200,Row205,Avg
0,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
1,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
2,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
3,20,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17.9375
4,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
5,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17.875
6,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
7,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
8,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
9,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
10,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,16,18
11,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
12,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
13,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
14,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
15,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17.875
16,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
17,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17.875
18,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
20,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
21,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
22,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
23,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
24,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
25,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
26,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
27,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
28,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,16,17.625
29,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
30,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
31,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,16,17.625
32,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
33,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
34,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,16,17.625
35,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
36,19,19,18,18,18,18,18,18,18,18,17,17,17,17,17,16,17.6875
37,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
38,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
39,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
40,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
41,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
42,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
43,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
44,19,19,19,18,18,18,18,18,18,18,18,17,17,17,17,16,17.8125
45,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
46,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
47,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
48,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
49,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
50,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
51,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
52,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
53,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
54,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
55,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
56,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
57,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
58,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
59,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
60,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
61,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
62,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
63,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
64,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
65,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
66,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
67,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,18
68,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
69,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
70,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,16,17.625
71,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
72,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
73,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
74,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
75,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
76,19,19,19,19,19,18,18,18,18,17,17,17,17,17,17,17,17.875
77,19,19,19,19,19,18,18,18,18,17,17,17,17,17,17,16,17.8125
78,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
79,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
80,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
81,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
82,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
83,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
84,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
85,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
86,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
87,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
88,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
89,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
90,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
91,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
92,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
93,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
94,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,16,17.625
95,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
96,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
97,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
98,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
99,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
100,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
101,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
102,19,19,19,18,18,18,18,17,17,17,17,17,17,17,16,16,17.5
103,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5625
104,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.8125
105,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
106,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
107,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
108,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
109,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
110,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
111,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
112,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
113,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.125
114,20,19,19,19,19,19,18,18,18,18,17,17,17,17,17,17,18.0625
115,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18.0625
116,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18.0625
117,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18.0625
118,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.0625
119,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18.0625
120,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
121,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
122,20,20,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.25
123,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
124,20,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.1875
125,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
126,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.1875
127,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.1875
128,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.125
129,20,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.1875
130,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.1875
131,20,20,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.25
132,20,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.25
133,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.1875
134,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.1875
135,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
136,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.1875
137,20,20,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.25
138,20,20,19,19,19,19,19,18,18,18,18,17,17,17,17,17,18.25
139,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
140,20,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,18.4375
141,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
142,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
143,20,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.25
144,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
145,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
146,20,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.25
147,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
148,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
149,20,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,18.375
150,20,19,19,19,19,19,19,18,18,18,18,18,18,17,17,17,18.3125
151,20,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,18.375
152,20,20,19,19,19,19,19,19,18,18,18,18,17,17,17,17,18.375
153,20,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,18.4375
154,20,20,20,19,19,19,19,18,18,18,18,18,18,17,17,17,18.4375
155,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
156,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
157,20,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,18.4375
158,20,20,20,19,19,19,19,18,18,18,18,18,18,17,17,17,18.4375
159,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
160,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
161,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.3125
162,20,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,18.25
163,20,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.1875
164,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.125
165,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
166,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.1875
167,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.1875
168,20,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,18.25
169,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.1875
170,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.1875
171,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,16,18.0625
172,20,20,19,19,19,19,18,18,18,18,17,17,17,17,17,17,18.125
173,20,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.125
174,20,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,17.875
175,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
176,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
177,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
178,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
179,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
180,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
181,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
182,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
183,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,16,18
184,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
185,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,18
186,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
187,19,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.0625
188,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
189,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
190,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
191,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
192,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
193,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
194,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
195,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
196,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
197,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
198,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
199,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
200,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
201,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
202,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
203,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,17.75
204,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
205,19,19,18,18,18,18,18,18,18,18,17,17,17,17,17,16,17.6875
206,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5625
207,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
208,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,16,17.5625
209,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
210,19,19,18,18,18,18,18,18,18,18,17,17,17,17,16,16,17.625
211,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,16,17.5625
212,19,19,18,18,18,18,18,17,17,17,17,17,17,17,16,16,17.4375
213,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
214,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
215,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
216,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,16,17.625
217,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,16,17.625
218,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
219,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,16,17.625
220,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5
221,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5
222,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5625
223,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5625
224,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17,16,17.5625
225,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5625
226,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,16,17.625
227,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
228,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,16,17.625
229,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5625
230,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,16,17.5625
231,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5
232,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,16,17.5
233,19,19,19,18,18,18,18,18,18,17,17,17,17,17,16,16,17.625
234,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,16,17.5625
235,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
236,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
237,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
238,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
239,19,19,19,18,18,18,18,18,18,18,17,17,17,17,16,16,17.6875
240,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
241,19,19,19,18,18,18,18,18,18,18,17,17,17,17,16,16,17.6875
242,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
243,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,16,17.6875
244,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17,17.8125
245,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,16,17.75
246,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
247,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
248,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17,17.8125
249,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,16,17.75
250,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
251,19,19,19,19,18,18,18,18,18,18,18,18,17,17,17,17,18
252,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
253,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,17,17.875
254,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
255,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
256,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
257,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,16,17.875
258,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
259,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
260,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
261,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
262,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,16,17.875
263,19,19,19,19,18,18,18,18,18,18,18,17,17,17,17,17,17.9375
264,20,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,18
265,19,19,19,19,19,18,18,18,18,18,17,17,17,17,17,17,17.9375
266,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,16,17.9375
267,19,19,19,19,19,18,18,18,18,18,18,17,17,17,17,17,18
268,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
269,20,20,20,19,19,19,19,18,18,18,18,17,17,17,17,17,18.3125
270,20,20,19,19,19,19,19,18,18,18,18,18,17,17,17,16,18.25
271,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
272,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,17,18.1875
273,20,20,19,19,19,19,19,18,18,18,17,17,17,17,17,17,18.1875
274,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
275,20,20,20,19,19,19,19,19,18,18,18,18,17,17,17,17,18.4375
276,20,20,20,20,19,19,19,18,18,18,18,18,17,17,17,17,18.4375
277,20,20,20,19,19,19,19,18,18,18,18,18,17,17,17,17,18.375
278,20,20,20,19,19,19,19,19,18,18,18,18,17,17,17,17,18.4375
279,20,20,20,20,19,19,19,19,18,18,18,18,18,18,17,17,18.625
280,20,20,20,20,19,19,19,19,19,18,18,18,18,17,17,17,18.625
281,20,20,20,20,20,19,19,19,19,19,19,18,18,17,17,17,18.8125
282,20,20,20,20,19,19,19,19,19,18,18,18,18,18,18,17,18.75
283,21,20,20,20,20,19,19,19,19,19,18,18,18,18,18,17,18.9375
284,21,20,20,20,20,20,20,20,19,19,19,19,18,18,18,18,19.3125
285,21,21,20,20,20,20,20,19,19,19,19,19,18,18,18,18,19.3125
286,21,20,20,20,20,20,20,19,19,19,19,19,18,18,18,18,19.25
287,21,21,21,20,20,20,20,20,20,19,19,19,19,19,18,18,19.625
288,21,21,21,20,20,20,20,20,20,19,19,19,19,19,18,18,19.625
289,21,21,21,21,21,20,20,20,20,20,20,19,19,19,19,19,20
290,21,21,21,21,21,21,20,20,20,20,20,20,20,19,19,19,20.1875
291,21,21,21,21,21,21,21,20,20,20,20,20,20,20,20,19,20.375
292,22,22,21,21,21,21,21,21,21,21,20,20,20,20,20,20,20.75
293,22,22,22,21,21,21,21,21,21,21,21,20,20,20,20,20,20.875
294,23,22,22,22,22,22,22,21,21,21,21,21,21,21,20,20,21.375
295,23,23,23,23,22,22,22,22,22,22,21,21,21,21,21,20,21.8125
296,25,24,24,23,23,23,23,23,23,22,22,22,22,22,22,21,22.75
297,25,25,24,24,24,24,24,23,23,23,23,23,23,22,22,22,23.375
298,26,26,25,25,25,25,25,25,24,24,24,24,24,24,24,23,24.5625
299,26,26,26,26,26,25,25,25,25,25,25,25,25,24,24,24,25.125
300,27,27,27,27,27,26,26,26,26,26,26,26,25,25,25,25,26.0625
301,28,28,28,28,28,27,27,27,27,27,27,27,26,26,26,26,27.0625
302,28,28,28,28,28,28,28,28,28,27,27,27,27,27,27,27,27.5625
303,30,30,30,30,29,29,29,29,29,28,28,28,28,28,28,28,28.8125
304,32,31,31,31,31,31,31,31,31,30,30,30,30,30,30,30,30.625
305,32,31,31,31,31,31,31,31,31,30,30,30,30,30,30,30,30.625
306,32,32,32,32,32,31,31,31,31,31,31,31,31,31,30,30,31.1875
307,34,34,33,33,33,33,33,33,32,32,32,32,32,31,31,31,32.4375
308,35,35,35,35,35,35,35,34,34,34,34,34,34,34,33,33,34.3125
309,36,36,36,36,35,35,35,35,35,35,35,35,35,35,34,34,35.125
310,38,38,38,38,37,37,37,37,37,36,36,36,36,36,36,35,36.75
311,39,39,39,38,38,38,38,38,38,38,38,38,38,38,37,37,38.0625
312,41,41,41,41,41,40,40,40,40,40,39,39,39,39,39,38,39.875
313,43,43,43,42,42,42,42,42,42,42,42,41,41,41,41,41,41.875
314,45,45,45,44,44,44,44,43,43,43,43,43,43,43,42,42,43.5
315,46,46,45,45,45,45,45,45,45,45,45,45,45,45,44,44,45
316,49,48,48,48,47,47,47,47,47,46,46,46,46,46,46,45,46.8125
317,49,49,49,49,49,49,49,48,48,48,48,48,48,48,48,48,48.4375
318,53,53,53,52,52,52,52,52,52,52,51,51,51,51,51,51,51.8125
319,54,54,54,53,53,53,53,53,53,52,52,52,52,52,52,52,52.75
320,56,56,56,56,56,55,55,55,55,55,55,55,55,54,54,54,55.125
321,59,59,59,59,59,58,58,58,58,58,58,58,58,57,57,57,58.125
322,61,61,61,60,60,60,60,60,60,60,59,59,59,59,59,59,59.8125
323,64,64,63,63,63,63,63,63,63,62,62,62,62,62,62,61,62.625
324,67,67,66,66,66,66,66,66,65,65,65,65,65,65,64,64,65.5
325,69,69,69,68,68,68,68,68,68,67,67,67,67,67,66,66,67.625
326,71,71,71,71,70,70,70,70,70,70,70,69,69,69,69,69,69.9375
327,74,74,74,74,74,73,73,73,73,73,73,73,73,73,72,72,73.1875
328,80,80,80,80,79,79,79,79,78,78,78,78,78,78,77,77,78.625
329,83,83,83,82,82,82,82,82,82,81,81,81,81,81,81,80,81.6875
330,85,85,85,84,84,84,84,84,84,84,84,84,83,83,83,83,83.9375
331,88,88,88,88,88,87,87,87,87,87,87,86,86,86,86,86,87
332,92,91,91,91,91,91,91,91,91,90,90,90,90,90,90,90,90.625
333,95,95,95,94,94,94,94,94,94,93,93,93,93,93,93,93,93.75
334,98,98,98,98,98,98,98,97,97,97,97,97,97,97,97,97,97.4375
335,98,98,98,98,98,98,98,97,97,97,97,97,97,97,97,97,97.4375
336,102,102,102,102,101,101,101,101,101,101,101,101,100,100,100,100,101
337,105,105,105,104,104,104,104,104,104,104,103,103,103,103,103,103,103.8125
338,109,109,108,108,108,108,108,108,108,107,107,107,107,107,107,107,107.6875
339,113,112,112,112,112,112,112,112,111,111,111,111,111,111,111,110,111.5
340,116,116,116,115,115,115,115,115,115,115,114,114,114,114,114,114,114.8125
341,119,119,119,119,119,119,119,119,118,118,118,118,118,118,118,117,118.4375
342,123,122,122,122,122,122,122,122,122,122,122,121,121,121,121,121,121.75
343,126,126,126,126,126,126,126,125,125,125,125,125,125,125,124,124,125.3125
344,130,130,130,130,130,130,130,129,129,129,129,129,129,129,129,128,129.375
345,134,133,133,133,133,133,133,132,132,132,132,132,132,131,131,131,132.3125
346,138,138,138,138,137,137,137,137,137,137,137,136,136,136,136,136,136.9375
347,144,144,144,143,143,143,143,142,142,142,141,141,141,141,140,140,142.125
348,148,148,148,147,147,147,147,147,146,146,146,146,146,145,145,145,146.5
349,151,151,151,151,151,151,150,150,150,150,150,150,150,149,149,149,150.1875
350,155,155,154,154,154,154,154,154,154,153,153,153,153,153,153,152,153.625
351,159,159,159,158,158,158,158,158,158,158,158,157,157,157,157,157,157.875
352,165,164,164,164,163,163,163,163,162,162,162,162,161,161,161,161,162.5625
353,169,168,168,168,168,168,168,167,167,167,167,167,167,167,167,166,167.4375
354,172,172,172,171,171,171,171,171,171,170,170,170,170,170,170,170,170.75
355,177,177,177,177,177,176,176,176,176,176,176,175,175,175,175,175,176
356,182,182,182,182,181,181,181,181,181,181,180,180,180,180,180,180,180.875
357,186,186,185,185,185,185,185,185,185,185,185,184,184,184,184,184,184.8125
358,191,191,190,190,190,190,189,189,189,189,189,189,188,188,188,188,189.25
359,199,199,199,199,199,199,199,199,198,198,198,198,198,198,198,198,198.5
360,206,205,205,205,205,204,204,204,204,204,204,204,203,203,203,203,204.125
361,210,210,210,210,210,209,209,209,209,209,209,209,208,208,208,208,209.0625
362,216,215,215,215,214,214,214,214,214,214,213,213,213,213,213,213,213.9375
363,221,221,220,220,220,220,220,220,219,219,219,219,218,218,218,218,219.375
364,225,225,225,225,225,224,224,224,224,224,224,224,223,223,223,223,224.0625
365,232,231,231,231,231,230,230,230,230,229,229,229,229,229,229,228,229.875
366,236,235,235,235,235,235,235,235,235,234,234,234,234,234,234,234,234.625
367,242,242,241,241,241,241,241,240,240,240,240,240,240,239,239,239,240.375
368,246,246,245,245,245,245,245,245,245,245,244,244,244,244,244,244,244.75
369,252,252,252,252,251,251,251,251,251,251,251,250,250,250,250,250,250.9375
370,257,257,256,256,256,256,256,255,255,255,255,255,255,254,254,254,255.375
371,263,262,262,262,262,262,262,261,261,261,261,261,261,260,260,260,261.3125
372,267,267,267,267,267,266,266,266,266,266,266,266,265,265,265,265,266.0625
373,273,273,273,273,273,273,273,273,272,272,272,272,272,272,272,271,272.4375
374,279,279,279,278,278,278,278,277,277,277,277,277,276,276,276,276,277.375
375,284,283,283,283,283,283,283,283,283,283,282,282,282,282,282,282,282.6875
376,290,290,290,290,289,289,289,289,289,289,289,288,288,288,288,287,288.875
377,295,295,294,294,294,294,293,293,293,293,293,293,292,292,292,292,293.25
378,301,301,301,301,300,300,300,300,300,300,299,299,299,299,299,299,299.875
379,307,307,307,306,306,306,306,305,305,305,305,305,305,305,304,304,305.5
380,312,312,312,312,312,311,311,311,311,311,311,311,311,311,310,310,311.1875
381,324,323,323,323,323,323,322,322,322,322,322,321,321,321,321,321,322.125
382,330,329,329,329,329,329,329,329,328,328,328,328,328,328,328,327,328.5
383,336,336,336,336,336,335,335,335,335,335,335,335,334,334,334,334,335.0625
384,343,342,342,342,342,342,341,341,341,340,340,340,340,339,339,338,340.75
385,348,348,347,347,347,347,346,346,346,346,346,345,345,345,345,345,346.1875
386,354,354,354,353,353,353,353,353,353,353,352,352,352,352,352,352,352.8125
387,360,360,360,359,359,359,359,359,359,359,358,358,358,358,358,357,358.75
388,367,366,366,366,366,366,365,365,365,365,365,365,365,364,364,364,365.25
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

CBS (Camera 3) pixel column 552

Postby OneWhiteEye » Sat Jan 10, 2009 3:54 am

Threshold range for this one is 140-215. I won't bother showing all thresholds over the entire interval, just the close up for the first 10 seconds. Note the bottommost curve (peach) which is for threshold 215. I almost did not include it. Pure judgement call.


A close-up of all individual threshold levels over the first 10 seconds:

Image


The average over entire interval:

Image


A close-up of the average over the first 10 seconds:

Image


Almost forgot the data:

Code: Select all
Frame,Row140,Row145,Row150,Row155,Row160,Row165,Row170,Row175,Row180,Row185,Row190,Row195,Row200,Row205,Row210,Row215,Avg
0,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,13,15
1,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,13,14.875
2,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,13,14.875
3,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,13,14.875
4,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,13,14.875
5,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,13,14.9375
6,16,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.1875
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212,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15
213,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,15.0625
214,17,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,15.125
215,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,15.0625
216,17,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,15.125
217,17,16,16,16,16,15,15,15,15,15,14,14,14,14,14,14,15
218,17,16,16,16,16,16,15,15,15,15,14,14,14,14,14,14,15.0625
219,16,16,16,16,16,16,15,15,15,15,14,14,14,14,14,13,14.9375
220,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15.0625
221,17,16,16,16,16,16,15,15,15,15,14,14,14,14,14,14,15.0625
222,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,13,15
223,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15.0625
224,16,16,16,16,16,16,15,15,15,15,14,14,14,14,14,13,14.9375
225,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,13,15
226,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,13,15
227,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,14,14.9375
228,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15
229,16,16,16,16,16,15,15,15,15,14,14,14,14,14,14,14,14.875
230,16,16,16,16,16,16,15,15,15,15,14,14,14,14,14,14,15
231,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15
232,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15
233,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,14,15
234,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,14,14.9375
235,17,16,16,16,16,15,15,15,15,15,14,14,14,14,14,13,14.9375
236,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,14,14.9375
237,17,16,16,16,16,16,15,15,15,15,15,14,14,14,14,14,15.125
238,17,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,15.1875
239,17,17,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.3125
240,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
241,17,16,16,16,16,16,16,15,15,15,15,15,15,14,14,14,15.3125
242,17,16,16,16,16,16,16,15,15,15,15,15,15,14,14,14,15.3125
243,16,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,15.125
244,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
245,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
246,17,16,16,16,16,16,15,15,15,15,15,15,15,14,14,14,15.25
247,17,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,15.25
248,16,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.1875
249,17,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,15.1875
250,16,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.1875
251,17,17,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.3125
252,17,17,16,16,16,16,16,15,15,15,15,15,15,14,14,14,15.375
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254,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
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256,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
257,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
258,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
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260,17,16,16,16,16,16,16,16,15,15,15,15,14,14,14,14,15.3125
261,17,17,16,16,16,16,15,15,15,15,15,15,14,14,14,14,15.25
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263,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
264,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
265,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
266,17,16,16,16,16,16,16,15,15,15,15,15,14,14,14,14,15.25
267,17,16,16,16,16,16,15,15,15,15,15,15,14,14,14,14,15.1875
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273,17,17,16,16,16,16,16,16,15,15,15,15,14,14,14,14,15.375
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275,17,17,17,16,16,16,16,16,15,15,15,15,15,14,14,14,15.5
276,17,17,17,17,16,16,16,16,15,15,15,15,15,15,14,14,15.625
277,17,17,17,17,16,16,16,16,16,15,15,15,15,15,14,14,15.6875
278,17,17,17,16,16,16,16,16,16,15,15,15,15,15,14,14,15.625
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280,17,17,17,17,16,16,16,16,16,15,15,15,15,15,14,14,15.6875
281,18,17,17,17,17,16,16,16,16,16,15,15,15,15,15,14,15.9375
282,17,17,17,17,17,17,16,16,16,16,15,15,15,15,15,14,15.9375
283,18,17,17,17,17,17,17,16,16,16,16,16,15,15,15,15,16.25
284,18,17,17,17,17,17,16,16,16,16,16,16,16,15,15,15,16.25
285,18,17,17,17,17,17,17,16,16,16,16,16,16,16,15,15,16.375
286,18,17,17,17,17,17,17,16,16,16,16,16,16,16,15,15,16.375
287,18,17,17,17,17,17,17,16,16,16,16,16,16,16,15,15,16.375
288,18,18,17,17,17,17,17,17,16,16,16,16,16,16,16,16,16.625
289,18,18,17,17,17,17,17,17,16,16,16,16,16,16,16,16,16.625
290,18,18,18,17,17,17,17,17,17,16,16,16,16,16,16,15,16.6875
291,18,18,18,17,17,17,17,17,17,16,16,16,16,16,16,16,16.75
292,19,19,18,18,18,18,18,17,17,17,17,17,17,16,16,16,17.375
293,19,19,18,18,18,18,18,17,17,17,17,17,16,16,16,16,17.3125
294,19,19,19,18,18,18,18,17,17,17,17,17,17,17,16,16,17.5
295,20,20,20,20,19,19,19,18,18,18,18,18,18,17,17,17,18.5
296,21,20,20,20,20,19,19,19,19,19,18,18,18,17,17,17,18.8125
297,22,21,21,21,21,20,20,20,20,20,20,19,19,19,19,18,20
298,23,22,22,22,21,21,21,21,21,21,20,20,20,20,20,19,20.875
299,24,23,23,23,22,22,22,22,22,22,21,21,21,21,21,20,21.875
300,24,24,24,23,23,23,23,22,22,22,22,22,22,21,21,21,22.4375
301,26,26,25,25,25,25,24,24,24,24,23,23,23,22,22,22,23.9375
302,26,26,25,25,25,25,25,25,24,24,24,24,23,23,23,23,24.375
303,28,27,27,27,26,26,26,26,26,26,26,25,25,25,24,24,25.875
304,29,28,28,28,28,28,27,27,27,27,26,26,26,26,26,26,27.0625
305,29,28,28,28,28,28,27,27,27,27,27,26,26,26,26,26,27.125
306,29,29,29,28,28,28,28,28,28,27,27,27,27,27,26,26,27.625
307,31,31,30,30,30,30,29,29,29,29,29,28,28,28,28,28,29.1875
308,33,32,32,32,32,32,31,31,31,31,31,31,30,30,30,30,31.1875
309,33,33,33,33,32,32,32,32,32,32,31,31,31,31,31,30,31.8125
310,36,35,35,35,35,35,34,34,34,34,34,34,33,33,33,33,34.1875
311,36,36,36,36,36,35,35,35,35,35,35,35,34,34,34,34,35.0625
312,38,38,38,38,38,37,37,37,37,37,37,36,36,36,36,36,37
313,40,39,39,39,39,38,38,38,38,38,38,38,37,37,37,37,38.125
314,42,42,42,42,41,41,41,41,41,40,40,40,40,39,39,39,40.625
315,43,43,43,43,43,42,42,42,42,42,42,42,41,41,41,41,42.0625
316,46,46,46,45,45,45,45,45,45,44,44,44,44,44,44,43,44.6875
317,46,46,46,46,46,45,45,45,45,45,45,44,44,44,44,44,45
318,50,50,50,49,49,49,49,49,48,48,48,48,48,48,47,47,48.5625
319,52,51,51,51,51,50,50,50,50,50,49,49,49,49,48,48,49.875
320,54,53,53,53,53,53,52,52,52,52,52,52,52,51,51,51,52.25
321,56,56,56,56,55,55,55,55,55,55,55,54,54,54,54,54,54.9375
322,57,57,57,57,57,56,56,56,56,56,56,55,55,55,55,54,55.9375
323,60,60,60,60,60,59,59,59,59,59,59,59,58,58,58,58,59.0625
324,64,64,64,63,63,63,63,63,63,62,62,62,62,62,62,61,62.6875
325,66,66,66,66,65,65,65,65,65,64,64,64,64,64,64,63,64.75
326,68,68,68,67,67,67,67,67,66,66,66,66,66,66,65,65,66.5625
327,70,70,70,70,70,69,69,69,69,69,69,69,68,68,68,68,69.0625
328,77,77,76,76,76,76,76,76,75,75,75,75,74,74,74,74,75.375
329,80,80,80,79,79,79,79,79,79,79,78,78,78,77,77,77,78.625
330,83,82,82,82,82,81,81,81,81,81,81,80,80,80,80,79,81
331,84,84,84,84,84,84,84,83,83,83,83,83,83,83,82,82,83.3125
332,88,88,88,87,87,87,87,87,86,86,86,86,86,86,85,85,86.5625
333,91,91,91,91,91,91,90,90,90,90,90,90,90,90,89,89,90.25
334,94,94,94,94,93,93,93,93,93,93,93,93,92,92,92,92,93
335,94,94,94,94,93,93,93,93,93,93,93,93,92,92,92,92,93
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338,105,105,105,104,104,104,104,104,104,104,104,103,103,103,103,103,103.875
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340,112,112,112,112,112,111,111,111,111,111,111,111,111,110,110,110,111.125
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342,119,119,119,119,119,119,119,119,118,118,118,118,118,118,118,117,118.4375
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344,126,126,126,126,126,126,125,125,125,125,125,125,124,124,124,124,125.125
345,131,131,131,130,130,130,130,130,130,130,129,129,129,129,128,128,129.6875
346,135,135,135,134,134,134,134,133,133,133,133,132,132,132,132,132,133.3125
347,140,140,139,139,139,139,139,138,138,138,138,138,137,137,137,136,138.25
348,143,143,143,143,143,143,142,142,142,142,142,142,141,141,141,141,142.125
349,147,147,147,147,146,146,146,146,146,146,146,146,145,145,145,145,146
350,151,151,151,151,150,150,150,150,150,150,150,149,149,149,149,149,149.9375
351,156,156,156,156,155,155,155,155,155,155,155,154,154,154,154,153,154.875
352,161,161,161,160,160,160,160,160,160,160,160,160,159,159,159,159,159.9375
353,165,164,164,164,164,164,164,164,163,163,163,163,163,163,162,162,163.4375
354,169,169,169,169,169,169,169,168,168,168,168,168,168,167,167,167,168.25
355,175,175,174,174,174,174,174,173,173,173,173,173,172,172,172,172,173.3125
356,179,179,179,179,179,178,178,178,178,178,178,178,177,177,177,177,178.0625
357,183,183,183,182,182,182,182,181,181,181,181,181,180,180,180,180,181.375
358,189,189,189,189,188,188,188,187,187,187,187,187,186,186,186,185,187.375
359,198,197,197,197,197,196,196,196,196,196,196,196,195,195,195,195,196.125
360,204,204,203,203,203,202,202,202,202,202,202,201,201,201,201,200,202.0625
361,207,207,207,207,207,206,206,206,206,206,206,206,206,205,205,205,206.125
362,215,214,214,213,213,213,213,212,212,212,212,211,211,211,211,211,212.375
363,217,217,217,217,216,216,216,216,216,216,215,215,215,215,215,215,215.875
364,223,223,223,223,223,223,222,222,222,222,221,221,221,221,220,220,221.875
365,228,228,227,227,227,227,227,226,226,226,226,226,226,225,225,225,226.375
366,235,234,234,233,233,233,233,232,232,232,232,231,231,231,230,230,232.25
367,238,238,238,238,238,237,237,237,237,237,237,237,236,236,236,236,237.0625
368,245,244,244,244,244,244,243,243,243,243,242,242,242,242,242,241,243
369,249,249,249,249,248,248,248,248,248,247,247,247,247,247,246,246,247.6875
370,255,255,255,255,255,254,254,254,254,253,253,253,253,253,253,252,253.8125
371,259,259,259,259,259,259,259,258,258,258,258,258,258,257,257,257,258.25
372,266,265,265,265,265,265,265,264,264,264,264,263,263,263,263,263,264.1875
373,270,270,270,270,270,269,269,269,269,269,269,268,268,268,268,267,268.9375
374,276,276,276,275,275,275,275,275,275,274,274,274,274,274,273,273,274.625
375,283,282,282,281,281,281,281,281,280,280,280,280,279,279,279,278,280.4375
376,287,287,287,287,286,286,286,286,286,286,285,285,285,285,285,284,285.8125
377,294,294,293,293,293,292,292,292,292,292,291,291,291,291,291,290,292
378,298,298,298,298,298,297,297,297,297,297,297,297,296,296,296,296,297.0625
379,305,305,304,304,304,304,304,303,303,303,303,303,303,303,302,302,303.4375
380,311,311,311,311,310,310,310,310,309,309,309,309,308,308,307,307,309.375
381,322,322,322,321,321,321,321,321,321,321,321,320,320,320,320,320,320.875
382,329,329,328,328,328,327,327,327,327,326,326,326,326,325,325,324,326.75
383,334,334,333,333,333,332,332,332,332,331,331,331,331,330,330,330,331.8125
384,340,340,340,339,339,339,339,339,339,339,338,338,338,338,338,330,338.3125
385,346,346,346,346,346,345,345,345,345,345,344,344,344,344,343,343,344.8125
386,355,352,351,351,351,351,351,350,350,350,350,350,349,349,349,349,350.5
387,358,357,357,357,357,357,357,357,357,356,356,356,356,356,355,355,356.5
388,365,365,365,364,364,364,364,364,363,363,363,363,363,362,362,362,363.5
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

Averages of C516, C536, C552

Postby OneWhiteEye » Sat Jan 10, 2009 4:21 am

Plot of ~ first 10 seconds (300 frames) of average curves for C516, C536, and C552:

Image


Zooming in on first 280 frames:

Image


Finally an average of all three averages, first 280 frames:

Image


I'm not claiming this is (noisy) real vertical motion of the NW corner. In fact, at this resolution, it becomes necessary to correct for camera motion at the very least. It's just interesting.
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

Table of Contents Especial

Postby OneWhiteEye » Sat Jan 10, 2009 6:51 am

I've edited the first post of this thread to include links to posts I felt shouldn't get lost in the shuffle. Now, to make a Klein bottle of this thread, I give you a link back:

http://the911forum.freeforums.org/technical-notes-on-video-motion-analysis-t55.html
OneWhiteEye
 
Posts: 4977
Joined: Sat Jul 05, 2008 9:40 pm

Re: Technical notes on video motion analysis

Postby Dr. G » Sun Jan 11, 2009 8:31 pm

OWE:

Well, I've been busy with some of your recently posted smearograms and I have some interesting results to report!

I have worked with the column 536 data set because it appears to provide a good smearogram for the NW corner of WTC 7.

Below I have tabulated three sets of drop distances vs. drop time data. The first set of drop distances I call "raw data" since these are simply calculated from the raw smearogram data with a constant calibration factor of 1 pixel = 0.16 meters

The second set of drop distances I call "persp corr" because I have applied a perspective correction factor to the raw data to allow for the foreshortening of vertical distances as you look higher and higher up the north face of the building.

The third set of drop distances I call "tilt corr" because I have applied an additional correction factor to allow for the tilting of the building as it fell. For this correction you cannot use the Camera 3 video because the tilting is more or less in line with the angle of view. For this reason I worked with a number of alternative collapse videos, especially the one that came out in early November 2008, which show that the NW edge of WTC7 tilted to the south-east as it fell. I won't go into the gory details of the math required for the tilt correction factor just now, but the table of data shows it becomes quite significant after about 3.5 seconds ......

Time (s) Drop (m) Drop (m) Drop (m)
raw data persp corr tilt corr
0 0.004678 0.00517 0.00517
0.1 0.009357 0.009892 0.009892
0.2 0.02807 0.028842 0.028842
0.3 0.046784 0.047802 0.047802
0.4 0.065497 0.066762 0.066762
0.5 0.084211 0.085722 0.085722
0.6 0.093567 0.095202 0.095202
0.7 0.140351 0.142602 0.142602
0.8 0.224561 0.227916 0.227916
0.9 0.271345 0.27531 0.27531
1 0.364912 0.370091 0.370091
1.1 0.477193 0.483816 0.483816
1.2 0.776608 0.787021 0.787021
1.3 1.160234 1.175368 1.175368
1.4 1.54386 1.563566 1.563566
1.5 2.039766 2.065159 2.065159
1.6 2.62924 2.661066 2.661066
1.7 3.22807 3.266068 3.266068
1.8 4.098246 4.14456 4.14456
1.9 4.884211 4.937372 4.937372
2 5.960234 6.021747 6.021746
2.1 7.157895 7.227313 7.227312
2.2 8.327485 8.40321 8.403209
2.3 10.20819 10.29112 10.29112
2.4 11.63977 11.72577 11.72577
2.5 12.72515 12.81209 12.81208
2.6 14.36257 14.44864 14.44864
2.7 16.08421 16.16642 16.1664
2.8 17.83392 17.90909 17.90906
2.9 19.87368 19.93672 19.93666
3 21.71696 21.76537 21.76525
3.1 23.92515 23.95147 23.95122
3.2 26.07719 26.0772 26.07668
3.3 28.89357 28.852 28.85093
3.4 31.36374 31.27904 31.27684
3.5 33.91813 33.78226 33.77776
3.6 36.29474 36.10529 36.09604
3.7 38.94269 38.68675 38.66774
3.8 41.51579 41.18839 41.14933
3.9 44.05146 43.64702 43.56679
4 46.92398 46.42433 46.25951
4.1 50.74152 50.10231 49.76376

I have mentioned before that you cannot get a simple (2nd or 3rd-order) polynomial to fit WTC 7 drop data over the entire time range from 0 - 4.1 seconds. However, you can get very good fits if you use two time intervals, one from 0 - 1.3 seconds and the other from 1.3 - 4.1 seconds. Now if you try a 2nd order fit in the 1-3 - 4.1 s interval on the drop vs. time data described above you get a very interesting result:

The raw data fits:

drop = 4.8926t^2 - 8.7105t + 4.017

This means the acceleration for this set is 9.785 m/s^2 - thus we could say it indicates a descent at almost precisely free fall.

HOWEVER, here's the rub!

If we try to fit the fully corrected (perspective + tilting) data we find an excellent fit with the function:

drop = 4.6374t^2 - 7.5427t + 2.8283

Thus we can see, that for the fully corrected data, the acceleration is reduced to a value of 9.275 m/s^2 or 5.5 % less than free fall.

This suggests that we need to be very careful in analyzing smearograms to derive meaningful collapse accelerations. You will note that the corrections I have applied change the drop distances by only about 1 meter at the 4.1 second mark, (from 50.7 to 49.7 meters) which is 1 part in 50 or 2 %. However, this changes the calculated acceleration by 5.5 %.
Dr. G
 
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Re: Technical notes on video motion analysis

Postby OneWhiteEye » Mon Jan 12, 2009 1:00 am

Dr. G wrote:OWE:

Well, I've been busy with some of your recently posted smearograms and I have some interesting results to report!

Interesting is an understatement. I think you've advanced the characterization of the collapse to a new level, no exaggeration. This work (need I disclaim with in my opinion?) supersedes all previous on the subject.

The second set of drop distances I call "persp corr" because I have applied a perspective correction factor to the raw data to allow for the foreshortening of vertical distances as you look higher and higher up the north face of the building.

That would be the first time such correction has been applied, at least as I'm aware. A major step forward.

The third set of drop distances I call "tilt corr" because I have applied an additional correction factor to allow for the tilting of the building as it fell.

Another first!

I have mentioned before that you cannot get a simple (2nd or 3rd-order) polynomial to fit WTC 7 drop data over the entire time range from 0 - 4.1 seconds. However, you can get very good fits if you use two time intervals, one from 0 - 1.3 seconds and the other from 1.3 - 4.1 seconds. Now if you try a 2nd order fit in the 1-3 - 4.1 s interval on the drop vs. time data described above you get a very interesting result:

The raw data fits:

drop = 4.8926t^2 - 8.7105t + 4.017

This means the acceleration for this set is 9.785 m/s^2 - thus we could say it indicates a descent at almost precisely free fall.

I'm right there with you...

HOWEVER, here's the rub!

I knew the best was last!

If we try to fit the fully corrected (perspective + tilting) data we find an excellent fit with the function:

drop = 4.6374t^2 - 7.5427t + 2.8283

Thus we can see, that for the fully corrected data, the acceleration is reduced to a value of 9.275 m/s^2 or 5.5 % less than free fall.

In my humble opinion, this is the number that should be quoted by anyone striving for accuracy in their claims. Great work!

This suggests that we need to be very careful in analyzing smearograms to derive meaningful collapse accelerations. You will note that the corrections I have applied change the drop distances by only about 1 meter at the 4.1 second mark, (from 50.7 to 49.7 meters) which is 1 part in 50 or 2 %. However, this changes the calculated acceleration by 5.5 %.

This is a very important result. It shows the sensitivity to correction, particularly if acceleration is the end result. By extension, it demonstrates the importance of doing all necessary and possible corrections. For this video, a good estimate of the effects of perspective and tilt are now available. The consequent impact is the difference between no resistance and quite a lot.

Part of the problem with g and faster-than-g results is it opens up a can of worms - no longer is something like simple 1D crush-up capable of explaining even the most basic of observations. Researchers are forced towards possible but improbable attributes in order to try to explain a spectre... what an incredible waste. This is a legitimate instance in which Occam's razor can be be invoked: there is better data, better analysis, and the results say there's no need to go there - at least not at the present.

Congratulations, Dr. G.
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Re: Technical notes on video motion analysis

Postby einsteen » Mon Jan 12, 2009 3:58 pm

Great I didn't read the "gore" math and details but am sure that it wil be correct, but that is great work, is this the t0 situation or is it the after t1 situation ? Friggin' fast!
einsteen
 
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Re: Technical notes on video motion analysis

Postby einsteen » Mon Jan 12, 2009 3:58 pm

Great I didn't read the "gore" math and details but am sure that it wil be correct, but that is great work, is this the t0 situation or is it the after t1 situation ? Friggin' fast!
einsteen
 
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Re: Technical notes on video motion analysis

Postby Dr. G » Mon Jan 12, 2009 6:57 pm

OWE & Einsteen:

Thanks for all the kind words, ....... but anything I have found, I OWE it all to both of you!

The curve fits are all well after t(0), 1.3 seconds to 4.1 seconds to be precise, so I believe we are looking at the true post-initiation collapse phase - what NIST calls "stage 2". Interestingly NIST do not appear to have applied perspective or tilting corrections. If you take my result without these corrections you will see I estimate an acceleration of 9.79 m/s^2, while NIST reported 9.81 m/s^2. That's pretty darn close I would say!
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Re: Technical notes on video motion analysis

Postby einsteen » Mon Jan 12, 2009 8:09 pm

So NIST in fact agrees with the near free fall after 1.3 seconds, didn't expect that..

An other thing to mention is the height, you used 186 meter for your correction, but were OWE's smearograms also based on that height ?
einsteen
 
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Re: Technical notes on video motion analysis

Postby Dr. G » Mon Jan 12, 2009 8:53 pm

Einsteen:

I am doing all my calculations with a WTC 7 building height of 186 m which is, I believe, also the value used by NIST (See NCSTAR 1-9 page 98 for example). The key, as you know, is the vertical pixel-to-height conversion factor which is about 0.16 to 0.18 meters per pixel, in agreement with OWE (I think!) - the precise value depending on the location on the building's face (this is the perspective effect!).
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Re: Technical notes on video motion analysis

Postby chek » Tue Jan 13, 2009 10:36 pm

Just a quick note say that I'm d/l'ing a torrent of allegedly hi-res news feeds from 911 which I'm expecting to contain TV res footage of WTC1, 2 & 7.

Once the torrent completes (stuck at 93% for the past few days) I'll post a short description of significant events together with the resolution, and I'll upload any requests for worthwhile clips in avi format to a download site such as Rapidshare.
chek
 
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