In general case the transformation of image it is possible to present as transformation of contour, 
and transformations of regions bounded by contour. 
For the complex contours the transformation of contours of images 
in affine space results in the significant error. 
With the purpose of decreasing of error of transformation 
the adoption of topological space is offered. 
The method and algorithms of transformation of regions 
are based on the construction of skeletons of images 
and next transformations a "region to region". 
The theorem, which states that in the case when an region 
is bounded by a piecewise-linear border then a skeleton is piecewise-linear, is proven.  
Transformation for the cases of isomorphic and not isomorphic skeletons is considered. 
For software realization of the offered algorithms 
the integrated development environment Borland Delphi 7.0 and 
libraries of classes, procedures and functions for work with the graphs GTL and AGraph is used.