This article gives an analysis of the interconnection of the optical properties of incomplete (fragmented) images and the psychophysical recognition thresholds of objects as necessary conditions for the appearance of visual insight. A well-known method of measuring the perception thresholds of fragmented images-the Gollin test-is proposed for the first time for solving the problem of evaluating the characteristics of insight in a person. The architecture of the neural networks that ensure the appearance of insight is considered. (C) 2015 Optical Society of America.