GDV DATA CONVERSION AND COMPRESSION

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GDV DATA CONVERSION AND COMPRESSION ON THE BASIS OF ANALYSIS OF FRACTAL DYNAMICS

K.G. Korotkov, R.I. Polonnikov

Technical University “SPIFMO”, Institute of Cybernetics RAS, St.Petersburg, Russia

Five type classes of GDV images of the fingers (BEO-grams), received with the help of the computer GDV complex, are investigated. Data transformation and compression are carried out using the unique technique and software complex, developed under the supervision of Professor R.I. Polonnikov and adapted to solve the given problem by the authors of this work together.

The authors jointly implement data preparation and structuring. The data – the quantized BEO-grams of fingers containing information on the dynamics of fractals, which describe separate parts of the image – go through the following stages of processing:

  1. Preliminary preparation and structuring, as a result of which two matrixes of numbers sized 1024 × 8 are formed of each image; one of these matrixes -­ F1- bears the information about brightness of the respective pels of the image, and the other one -F2- about the length of a certain radius vector, by means of which geometric position of a pel is described;
  2. Mathematical transformation of matrixes F1 and F2, which is carried out according to the next steps:
  • Transformation of the initial 1024 × 8 matrix into eight matrixes sized 128 × 8 each;
  • Fourier transformation of columns of these eight matrixes and determination of the respective power spectrums;
  • Construction of the mathematical model for each power spectrum enveloping it in terms of:

M(n) = k.n –b ,

where n is a number of harmonic in the power spectrum,

  • Estimation of the model’s parameters k, β by accomplishing the task of curvilinear regression. Thus, two 8 × 8 sized matrixes of numbers are determined:

K =    ,                b = ,

  • For each matrix K and β singular decompositions are assessed and maximum singular figures SNk, SNβ are got; in addition, average and normalized standard deviation are determined for each of these matrixes.

Thus, as a result of these conversions each of the initial matrixes changes to the six figures: SNk, kср, sk/ kср, SNb, bср, sb/bср. This means that essential data compression has taken place. It is worth mentioning that the figures given possess a number of good features: antijamming capability, robustness, recognizability, which were successfully used for solving the problem of recognition of the images of five classes mentioned above (probability of a proper recognition of class from 55 objects on the learning sample ~ 90 %).

For accomplishing the task of recognition the classical procedures of discriminant analysis, in which the six stated above figures were the initial variables, were applied. It is interesting to stress that owing to that comparatively complex and extensional preliminary (i.e. preceding the accomplishment of the recognition task) processing of BEO-grams, the very task of recognition, adding quite a good result reliability, was managed to be accomplished by rather an easy method, which refers to the discriminant analysis. This fact gives an opportunity to hope that the method suggested will be widely practiced in solving such problems. Furthermore, considerable data compression provided by the method makes it suitable for usage in telemedicine. Indeed, through the communication channels instead of graphic images of BEO-grams only six figures corresponding to these can be transmitted.

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