Several medical imaging techniques are capable of producing tomographic images, corresponding to cross-sections through the body. A stack of adjacent sections contains three dimensional information about the organs of interest, and this can be presented on a two dimensional screen using shaded surface techniques. In order to facilitate the routine use of such images, algorithms and techniques were developed on a conventional medical imaging computer system in a hospital environment. Several object representation schemes were compared, and two new schemes were devised. The 'solid binary object' technique facilitated exploration of the interior of an object, while the 'ordered surface list' technique enabled real time display of object surfaces. Several shading algorithms were compared, and a local polynomial fitting routine was devised. This was found to be superior to other methods using objective evaluation of the accuracy of surface normal estimations, and subjective evaluation of the corresponding image appearance. The techniques developed were applied to a variety of data obtained using xray computed tomography, nuclear magnetic resonance and emission computed tomography. For display of myocardial tomograms, a technique was devised for superposition of colour coded coronary arteries, showing their relationship to observed perfusion defects. For display of time varying images of the heart, a rapid display routine was developed to enable ventricular wall motion to be evaluated from any angle. Colour display techniques were also applied to this data to produce single images which incorporated kinetic as well as morphological information. The results obtained have confirmed that shaded surface images can be produced using computers currently available in hospital imaging departments. Interactive object modification and real time object display can be achieved without requiring special hardware.