Bone structure analysis is necessary, when determining the bone strength and measuring the bone micro architecture deterioration, that happens as a result of such a bone disease as osteoporosis. Bone structure analysis on a living person (in vivo) is easier and more effective to perform by using medical images. Traditionally, medical images analysis is performed by a radiologist, who visually looks through all of the two-dimensional images, that were acquired by computed tomography and are divided into slices. Such analysis is subjective and takes a considerable amount of time. To speed up the analysis and acquire reproducible measurements, it is useful to use a computer and automatic medical image processing methods. Bone structure analysis can be further expanded by using bone structure three-dimensional visualization. This dissertation takes a look at several methods of acquiring and processing medical images. The most attention is given to computed tomography, because medical images that are acquired by using this method, are widely used when diagnosing patients. Medical image analysis and processing is useful in both the medical and scientific fields, and it allows for a greater diagnostic precision. In this dissertation, methods of medical image analysis and processing are proposed, which can be used to automatically extract the bone structure from a medical image, and to perform measurements on the extracted bone structure. Three parameters of bone structure are measured: cortical bone average thickness, cortical bone porosity and trabecular bone average density. This work also contains proposed methods that can be used to visualize the bone structure and separately display the cortical bone and the trabecular bone. It is also possible to visually display the cortical bone thickness. Practical results of the research and implementation examples are shown in the fourth chapter. Main results of research were reported on in 11 international conferences as well as published in 11 publications. The work consists of introduction, 4 chapters, conclusions and 4 appendixes. It contains 118 pages, 55 figures, 8 tables and 104 references.