Alternative 2D Shape Representations using the Symmetry Set

Research output: Contribution to journalJournal articleResearchpeer-review

Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis $$\mathcal{MA}$$ takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the $$\mathcal{MA}$$ and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set $$\mathcal{SS}$$ . This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane.
In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the $$\mathcal{SS}$$ as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons.
Second, alternative ways to visualize the $$\mathcal{SS}$$ are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure.
Example shapes from a data base are shown and their data structures derived.
Original languageEnglish
JournalJournal of Mathematical Imaging and Vision
Issue number1-2
Pages (from-to)127-147
Publication statusPublished - 2006
Externally publishedYes

ID: 4850735