Abstract Background Computeros tomography and magnetic resonance imaging are usually offered to the clinician in the form of sequences of axial, sagittal and coronal planar cuts. Frequently this does not allow for the full inspection of the morphology of the area of interest, because it is limited by the planarity. Efforts have been made to extract information along curved slices but their planar display is prone to metric deformation. Methods We propose a new visualization alternative of 3 D medical volumes using curved slices adapted to areas of interest. We use surfaces fitted to specific organs as visualization canvasses. We describe the differential geometry techniques used to build the surfaces that may be isometrically flattened. These are referred to as develpable surfaces. Results We show concrete examples deemed useful for the development of clinical and educational tools. Our examples are centered in magnetic resonance data of the rotator cuff muscle complex and computed tomography data of maxillofacial and dental studies. We also look at the extraction and display of information from volumes of aortic aneurysms along transversal surfaces. Discussion We look at extensions of the technique and propose further possible clinical use of texturized surfaces in the context of volume navigation. Conclusions We presented a technique to extract information from computer tomography and magnetic resonance volumes, using two different texturization techniques. In the cases that the fitting surfaces are chosen to be developable, they may be flattened without distortion. We also discuss how tu use the technique in other visualization tasks such as volume navigation and detection of volumetric features.