Silvia Biasotti

The Laurea degree thesis has been developed in cooperation with the IMA (Institute of Applied Mathematics) of the CNR, Genoa. During this work, a new method for extracting high level characteristics of natural surfaces based on the Reeb Graph has been developed. The Reeb graph allows us to define a high-level representation of a surface, coding only a few level sections and their topological adjacencies. This representation is therefore very useful both in data compression and in shape classification problems. These studies made me confident with computational topology and skeletal representations of polyhedral surfaces. Particular attention has been paid to the coding of an extended Reeb graph representation. The thesis arguments evolved towards the study of the problem of reconstructing triangulations from contours. This research involves the integration of morphological analysis techniques in the surface reconstruction methods from cross sections. At present, the collaboration with the Computer Graphic's and Shape Modelling's groups is keeping on the work already started, with the idea of generalize these applications to 3D objects.