The scale axis picture show

ABSTRACT

We demonstrate how the scale axis transform can be used to compute a parameterized family of shape skeletons. The skeletons gradually represent only the most important features of a shape, in a scale-adaptive manner. Here a shape O is any bounded open subset of the plane R². The scale axis for scale value $s$ is the medial axis of the multiplicatively grown shape O__s, where O_s is the union of medial balls of O with radii scaled by the factor s.

We present a simple algorithm to compute a parameterized family of skeletons for shapes that are finite unions of balls in the plane. The algorithm is based on the scale axis transform. We compare the computed family of skeletons with two medial axis filters, namely the Λ-medial axis, and a filter based on an angle criterion.

REFERENCES

• 1: Nina Amenta , Sunghee Choi , Ravi Krishna Kolluri, The power crust, Proceedings of the sixth ACM symposium on Solid modeling and applications, p.249-266, May 2001, Ann Arbor, Michigan, United States [doi>10.1145/376957.376986]
• 2: N. Amenta, S. Choi, and R. Kolluri. The power crust, unions of balls, and the medial axis transform. Comput. Geom., 19(2-3):127--153, 2001.
• 3: Nina Amenta , Ravi Krishna Kolluri, The Medial axis of a union of balls, Computational Geometry: Theory and Applications, v.20 n.1-2, p.25-37, October 2001 [doi>10.1016/S0925-7721(01)00033-5]
• 4: Frédéric Chazal , André Lieutier, The "λ-medial axis", Graphical Models, v.67 n.4, p.304-331, July 2005 [doi>10.1016/j.gmod.2005.01.002]
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• 6: J. Giesen, B. Miklos, and M. Pauly. The Medial Axis of the Union of Inner Voronoi Balls in the Plane, 2008. Manuscript available at http://www.balintmiklos.com/medial axis union voronoi balls 08.pdf.
• 7: Joachim Giesen , Balint Miklos , Mark Pauly , Camille Wormser, The scale axis transform, Proceedings of the 25th annual symposium on Computational geometry, June 08-10, 2009, Aarhus, Denmark [doi>10.1145/1542362.1542388]
• 8: Balint Miklos , Joachim Giesen , Mark Pauly, Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool, Proceedings of the twenty-third annual symposium on Computational geometry, June 06-08, 2007, Gyeongju, South Korea [doi>10.1145/1247069.1247090]
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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

General Terms:
Algorithms, Theory

Keywords:
medial axis, skeleton, union of balls