Computing the link center of a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Computing the geodesic center of a simple polygon
Discrete & Computational Geometry
Convergence and continuity criteria for discrete approximations of the continuous planar skeleton
CVGIP: Image Understanding
Computer Vision and Image Understanding
Proceedings of the sixth ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
On the Continuous Fermat-Weber Problem
Operations Research
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Computing Multiscale Curve and Surface Skeletons of Genus 0 Shapes Using a Global Importance Measure
IEEE Transactions on Visualization and Computer Graphics
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Robust reconstruction of 2D curves from scattered noisy point data
Computer-Aided Design
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The medial axis is an important shape descriptor first introduced by Blum (1967) [1] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a ''center point'', is needed in various applications ranging from shape alignment to geography. In this paper, we present a uniform approach to define a global shape measure (called extended distance function, or EDF) along the 2D medial axis as well as the center of a 2D shape (called extended medial axis, or EMA). We reveal a number of properties of the EDF and EMA that resemble those of the boundary distance function and the medial axis, and show that EDF and EMA can be generated using a fire propagation process similar to Blum's grassfire analogy, which we call the extended grassfire transform. The EDF and EMA are demonstrated on many 2D examples, and are related to and compared with existing formulations. Finally, we demonstrate the utility of EDF and EMA in pruning medial axes, aligning shapes, and shape description.