4. Application of the GP Algorithm to Processing of TV Data

[11]  We can consider a sequence of TV images as an experimental data set. However, to calculate the correlation integral from (2) it is necessary to define a distance between vector components. In this case each component is a TV image. In other words, it is necessary to define a "distance'' between TV images. The following variants are possible.

[12]  1. It is possible to characterize each image by "the integrated intensity" and to define the distance between two images as the absolute value of the difference between these integrated intensities. However, in this case information on the spatial distribution of luminosity in the image is completely lost. Besides, the estimation of integrated intensity in a TV image is not correct, as the gradations of half tones in the image are not additive values (because of the absence of exact binding on intensity, mentioned previously).

[13]  2. To use the information about space distribution, it is possible at first to receive the absolute difference of values of appropriate pixels in the images, and then to carry out a summation over all pixels. However, such a summation is also not correct because of the nonlinear recording of the TV system. Therefore in this work we offer the following method for introducing distance (meter) into the space of TV images.

[14]  3. For auroral structure, the dynamics of which we are focusing on, we select the level of intensity on which this structure is conspicuous. In all images the pixels with values less than a selected level are filled with 0 s. The pixels with values not less than this level we fill with 1 s. Following this we consider the distance between two images as simply the number of pixels, having different values in these images. In this way the distance has all the properties of the metric and in this sense is correct. For calculation of the correlation integral from (2) we used the supremum-norm for vectors in the embedded space.