| Summary: | The medial surface of a 3D object is comprised of the locus of centers of its maximal inscribed spheres. Interest in this representation stems from a number of interesting properties: i) it is a thin set, i.e., it contains no interior points, ii) it is nomotopic to the original shape, iii) it is invariant under rigid transformations of the object and iv) given the radius of the maximal inscribed sphere associated which each skeletal point, the object can be reconstructed exactly. Hence, it provides a compact representation while preserving the object's genus and making certain useful properties explicit, such as its local width. These properties have led to its application in a variety of domains, including the analysis and quantification of the shape of volumetric structures in medical images. Despite its popularity, its numerical computation remains non-trivial. Most algorithms are not stable with respect to small perturbations of the boundary, and heuristic measures for simplification are often introduced. The study of the medial surface is the subject of this thesis.
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