Abstract: We propose in this paper a new approach ta segment a discrete :3D object into a stmcturlO of characteristic topological prinùtives with attached qualitative features. This structure can he seen itself as a qua/itatiuf description of the objl~ct, becaU!:i€ * it is intrimic to the 3D object, which rneans it is stable to rigid transformations (rotations and t ra.nslations). * it is locally defined, and therefore stable ta partial occlusions and local modifications of the object structure. * it is rohust to noise and small deformations, as confirmed by our experimental reS1l1ts. Our approach concentrat.es on topological properties of discrete surfaces. These SllrfaCI;S lIlav correspond to the €J.'ternal surface of the objects extracted by a 3D edge detector, or to the .,kdd,J!t surface obtained by a new thinning algorithm. Our labeling algorithm is based un very loc*;d computations, allowing rnassively parallel computations and real time computations. We present a realistic experiment to characterize and locaté spatially a complex 3D [ll'~dical abject using the proposed segmentation of its skeleton.