The work devoted to the problem of analysis and interpretation of multi-dimensional medical data based on the generalized graphic images. The existing methods and approaches, including those proposed by the authors were considered. The main problem of data visualization is the problem of obtaining a visual image that is uniquely relevant to the data set. The authors propose an approach that allows to perform visualization of the major linear structures: segment, polyline, simplex in multidimensional spaces. Presentation of multivariate observations in a two-dimensional image (the curve) ensures that to the close by the values observation will correspond visually similar image-curves; for very different by the values observations its image-curves will be noticeably different. The results of applying this approach to the problems of practical medicine were proposed: analysis of the pregnant women physiological state dynamics, identifying hidden patterns in the structure of the physiological parameters for patients with various forms of asthma.