Principle  of  organization  of  functional base  for  fast,  interference-resistant  selection  of  contour  boundaries  (edges  of  brightness)  on  the  half-tone  images.

Shulga V.I.

https://shulga.tripod.com/mixt_2/funcbasis/E.htm

An analysis of frequency component is one of the most universal methods of interpretation of actual signals. In the basis, this method demands to solve a rather toilful computing problem - convolution of the researched signal with reference frequency functions. For this reason when one of determinatives is analysis time, it is necessary to be satisfied with much more primitive algorithms.

The widely known, effective, mathematically elegant Hueckel's operator, intended for selection of graduated overfalls of brightness, gives an example of such situation [1], [2],

To realize all its virtues in practice it is offered to use the following reasons.

2D basic functions "are easily gathered" from the simplest bell-shaped ones. In turn, convolution with bell-shaped function is a more simple problem in the essence. Eventually, it is no more than diffusion-defocusing that can be realized by any optic-electronic converter "for one step"... Thus the value of convolution with basis functions will be defined as the simplest algebraic sum of values from several "diffusion strata".

Thus, it will be possible to apply the frequency analysis in all its power, even there where it could not be made owing to rigid temporal restrictions (for example, in a practical robotics).

2. Hueckel M. A local visual operator wich recognizes edges and lines / JACM. 1973. Vol.20. No.4. P.634-647.