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This paper discusses the ways of finding consistency between the well-known statistical statement that "guessing destroys information" and the practically obvious advantage of hierarchical decisions. Certain nonstatistical sources of recognition errors are indicated, the influence of these sources increasing with the size of the image parts on which the first-stage discrete decisions are taken. The rejection criterion is examined from the statistical point of view and the necessity of mathematical models for all images to be rejected is demonstrated. The analysis of the possibilities for developing models of both images to be recognized and to be rejected leads to the conclusion that image recognition should be realized by hierarchical systems. An example of a working hierarchical recognition system for interpretation of handmade drawings is described.