Last update: Nov. 6, 2002

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Web-link at Harvard (Post-Doc work, 1995).

Publications by R. L. Ogniewicz et al. on shape symmetry elicitation :

• Hierarchic Voronoi Skeletons, 1995.
• The Skeleton-Space & it Application to Shape Description & Decomposition, 1994.
• Voronoi skeletons: Theory and applications, 1992.
• Skeletons with Euclidean Metric & Correct Topology & their Application in Object Recognition & Document Analysis, 1990.
• Isolation and Identification of Abutting and Overlapping Objects in Binary Images, 1989.

BibTeX references.

Robust and time-efficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noise-sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents. Each component of the VD is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise. The second processing step, a hierarchic clustering of skeleton branches, leads to a multiresolution representation of the skeleton, termed skeleton pyramid.

NB: Extension of the 1992 paper (below).

• Connected skeletons are preserved.
• Applied to both the interior and exterior of shapes; boundaries are known a priori.
• A circularity residual is defined for a branch (defined by a pair of successive vertices: i.e., a link in the graph derived from the V-skeleton) as the difference between the boundary segment represented by a vertex, and the associated circular arc (of the maximal disk centered at that vertex).

Summary: Skeletons with Euclidean metric and correct topology derived from the Voronoi diagram of boundary points.

• The boundary is known, and the skeleton is restricted to be the interior Medial Axis Transform (MAT). The boundary is sampled with points.
• "Any two boundary points must generate a portion of MAT; in the discrete plane this means that the complete MAT is nothing but the inner Voronoi diagram (VD) of the boundary points" [p.342].

NB: An earlier version of this work is reported in a series of manuscripts, in German:

• F. Klein, Vollständige Mittelachsenbeschreibung binärer Bildstrukturen mit Euklidischer Metric une korrekter Topologie, Dissertation ETH Nr. 8411, Zurich, 1987.
• U. Kienholz and R. Ogniewicz, Isolation und Identifikation einander berührender und/oder überlappender Teile in Binärbildern, Diplomarbeit ETH, Zurich 1988.

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