Vol 73, No 1 (2018)

Formal analysis and computer recognition of 2D color images is an important branch of modern computer geometry. However, the present methods, in spite of their longstanding high development, are not quite satisfactory and seem to be much worse than (unknown) algorithms used by our brain to analyze visual information. Almost all existing algorithms omit colors and deal with gray scale transformations only. However, in many cases color information is important and has to be proceeded. In this paper a fundamentally new method of encoding and analyzing color digital images is proposed. The main idea of this method is that a full-color digital image is encoded by a special two-dimensional surface in the three-dimensional space. After that the surface is analyzed by methods of differential geometry rather than traditional gradient-based or Hessian-based methods (like SIFT, GLOH, SURF, Canny operator, and many other well-known algorithms).

For the Euclidean plane ℂ the Steiner mapping associating any three points a, b, c with their median s, and the corresponding operator P_D of metric projection of the space l₁³(ℂ) onto its diagonal subspace D = {(x,x,x): x ∈ ℂ}, P_D(a,b,c) = (s,s,s): s are considered. The exact value of the linearity coefficient of P_D is calculated.

The natural deduction systems for the three-valued nonsense logics Z and E are presented in the paper.

It is proved that the almost contact metric structures on a hypersurface with type number 1 and on a hypersurface with type number 0 are identical in a W₄-manifold.