Present paper generally relates to content-aware image resizing and image inscribing into particular predetermined areas. The problem consists in transformation of the image to a new size with or without modification of aspect ratio in a manner that preserves the recognizability and proportions of the important features of the image. Most close solutions presented in prior art cover along with standard image linear scaling, including down-sampling and up-sampling, image cropping, image retargeting, seam carving and some special image manipulations which similar to some kind of image retouching. Present approach provides a method for digital image retargeting by means of erasing or addition of less significant image pixels. The defined above retargeting approach can be easily used for image shrinking easily. However, for image enlargement there are some limitations as a stretching artifact. History map with relaxation is introduced to avoid such drawback and overcome some known limits of retargeting. In proposed approach means for important objects preservation are taken into account. It allows significant improvement of resulting quality of retargeting. Retargeting applications for different devices such as display, copier, facsimile and photo-printer are described as well.