This work concerns with the development of automatic computer methods to detect and measure the state of the retinal branching structures on clinical images by image processing techniques and morphological analysis. Since retinal vessel branching patterns characterise a number of diseases that affect the vascular system, these tools will allow the future development of systems for screening by means of non-invasive techniques. The first stage is the detection and segmentation of the blood vessels to convert the original gray scale image into a binary image. The second stage is to perform the analysis of the morphology of the vascular tree from the binary images by making measurements of the geometrical parameters such as lengths, widths, and branching angles of the blood vessels, from which other important geometrical parameters are defined. Finally, we analysed red-free clinical retinal images from hypertensive patients to study the relationship between vascular patterns and disease. We investigated three main approaches: geometrical, topological and fractal analysis. Preliminary results showed that significant differences could be found between groups in each of these approaches.