For calculation of the statistical proximity one can suggest the following scheme:

1.We should calculate a set of the initial parameters {Pr} (r=1,2,…,R), which characterize the initial sequence considered.

2.Then these parameters should be normalized.

3.After normalization it is necessary to calculate the GPCFp(s1, s2) for each pair (s1, s2), with s1 and s2 = 1, 2, …, R. Doing the same with all pairs we obtain the symmetric correlation matrix CC(s1, s2) having the size R R.

4.Then this matrix is clusterized in accordance with the chosen partitioning of the total clusterization interval [cfmin, 1,0] on the given number of subintervals.

Comparison of 17 sequences based on the calculated values of the complete CCF. This factor can be located in the wide correlation limits. For the given case this interval is equaled to [0. 0.68]. In the right corner we show the number of correlations that are located in the given interval equaled 5.

(9+3+1+2+2)=17.

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The system of equations for calculation of the exponential parameters.

Expression for calculation of the weight factors.

The unknown value of k can be found by considering all positive statistical weights and by minimizing the percentage relative fitting error.

To synthesize, the reduction procedure is realized to determine the reduced set of parameters {(ws, s), s = 1, 2,…, k}, with k << N.

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Integration and differentiation pre-processing

To stress the power of the proposed approach, we add a further processing of the originally available data. Namely, we apply an integration and a differentiation to the sequence of frames, so that we obtain two additional and different random sequences of frames that are characterized by totally different statistical properties. By processing the information in this way, we expect that differentiation creates high-frequency fluctuations. On the contrary, integration is particularly suitable for restoring the long- term trend of video sequences, and analyzing their fluctuations on longer time scales. The very simple numerical integration by the trapezoidal rule is of great help in filtering the high-frequency components of the video data sets under analysis.

The normalized function of the moments N(x) of the 3-D video

stream.

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Initial curve ( 1 = –2.6865, 2 = –

0.2168) and exponential separated

curve ( sep1 = –1.7865, sep2 = 0.6832).

The final fit of the initial functionN(x): 8 fingerprint significant

parameters are shown.

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Mean values and​ confidence intervals of the parameters for the original data of the three considered videos, with (a-left ) SBS format and (b-right) FS formats

Mean values ​and confidence intervals of the parameters for the differentiated

data of the three considered videos, with (a) SBS format and (b) FS format

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Mean values and​ confidence intervals of the parameters for the integrated data of the three considered videos, with (a) SBS format and (b) FS format

How the original data do look? The Film - Alice in Wonderland. SBS-format. From the left to the right: original data, differentiated data, integrated data.

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