The development of numerical methods of mathematical morphology and topology gives us opportunity to analyze various structures on the plane and in space. In particular they can be used to analyze the complexity of the image by estimating the variation of the number of connected structures and holes depending on the brightness level. Alternate sum of this numbers gives topological invariant Euler characteristic. The other approach to estimation this characteristic is persistent homology calculation at the different sub level sets. It turned out that the application of these ideas to the active regions of the Sun magnetograms allowed diagnostic changes in different dynamic regimes connected with sun flares.