Formal analysis and computer recognition of 2D color images is important branch of modern computer geometry. However, existing algorithms, although they are highly developed, are not quite satisfactory and seem to be much worse than (unknown) algorithms, which our brain uses to analyze eye information. Almost all existing algorithms omit colors and deal with grayscale transformations only. But in many cases color information is important. In this paper fundamentally new method of coding and analyzing color digital images is suggested. The main point of this method is that a full-color digital image is represented, without dropping colors, by special 2D surface in 3D space, after which it is analyzed by methods of differential geometry, rather than traditional gradient-based or Hessian-based methods (like in SIFT, GLOH, SURF, Canny operator, and many other algorithms).