Computer graphics, image processing methods and three-dimensional image construction approaches are widely implemented in various spheres. For example, in medicine, criminology, geology it is necessary to extract a specific region from the image, that will allow the classification of the image. In medicine, in order to diagnose a patient it is necessary to extract only a portion of the image data (pathology zone). In criminology, to identify the image of a person's face often a fragment of the image is needed. That's why image region extraction is such an important task in image processing. In the other hand, 2D image representation is sometimes not enough to classify and analyze these regions. 3D image construction provides greater possibilities for region analysis. In this work, image processing and 3D image construction tasks are analyzed on the medical images example, although methods developed in this work can be used to solve image processing tasks in various spheres. Medical images, acquired with use of computer tomography or magnetic resonance imaging are widely used in medical diagnostics. The analysis and processing of these images is important in both clinical and scientific aspects and allows to ensure high precision of medical diagnosis. In this work, methods of medical image analysis are proposed, that allow extracting any region of interest from medical images, determine the size of the extracted region, estimate the volume of the region, visualize the pathology zone and head of the patient in 3D space, so the physicians could define the placement of pathology zone and plan surgical interventions and also automatically determine the density of pathology zone and its surrounding matters. The proposed methods are combined in one medical image processing system, that is described in the work. Practical results of the research and implementation examples are shown in experimental section. Main results of research were reported on in 14 international conferences as well as published in 15 publications. The work consists of introduction, 4 chapters, conclusions and appendix. It contains 144 pages, 98 figures, 10 tables and 96 references.