Skeleton-Based Recognition of Shapes in Images via Longest Path Matching

  • Gulce Bal
  • Julia Diebold
  • Erin Wolf Chambers
  • Ellen Gasparovic
  • Ruizhen Hu
  • Kathryn Leonard
  • Matineh Shaker
  • Carola Wenk
Part of the Association for Women in Mathematics Series book series (AWMS, volume 1)

Abstract

We present a novel image recognition method based on the Blum medial axis that identifies shape information present in unsegmented input images. Inspired by prior work matching from a library using only the longest path in the medial axis, we extract medial axes from shapes with clean contours and seek to recognize these shapes within “no isy” images. Recognition consists of matching longest paths from the segmented images into complicated geometric graphs, which are computed via edge detection on the (unsegmented) input images to obtain Voronoi diagrams associated to the edges. We present two approaches: one based on map-matching techniques using the weak Fréchet distance, and one based on a multiscale curve metric after reducing the Voronoi graphs to their minimum spanning trees. This paper serves as a proof of concept for this approach, using images from three shape databases with known segmentability (whale flukes, strawberries, and dancers). Our preliminary results on these images show promise, with both approaches correctly identifying two out of three shapes.

Notes

Acknowledgements

The authors would like to thank the Institute for Pure and Applied Mathematics, the Association for Women in Mathematics, Microsoft Research, the National Science Foundation, and the National Geospatial Agency for support, financial and otherwise, of this collaboration. Kathryn Leonard thanks Matt Feiszli for providing the initial Matlab code for the H 1∕2 metric for closed curves which was modified for this project.

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Copyright information

© Springer International Publishing Switzerland & The Association for Women in Mathematics 2015

Authors and Affiliations

  • Gulce Bal
    • 1
  • Julia Diebold
    • 2
  • Erin Wolf Chambers
    • 3
    • 4
  • Ellen Gasparovic
    • 5
  • Ruizhen Hu
    • 6
  • Kathryn Leonard
    • 7
    • 8
  • Matineh Shaker
    • 9
  • Carola Wenk
    • 10
    • 11
  1. 1.Department of Computer EngineeringMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of Computer ScienceTechnical University of MunichMunichGermany
  3. 3.Department of Mathematics and Computer ScienceSaint Louis UniversitySaint LouisUSA
  4. 4.Research supported in part by NSF grants CCF-1054779 and IIS-1319573Saint LouisUSA
  5. 5.Department of MathematicsDuke UniversityDurhamUSA
  6. 6.Department of MathematicsZhejiang UniversityZhejiangChina
  7. 7.Department of MathematicsCalifornia State University Channel IslandsCamarilloUSA
  8. 8.Research supported in part by NSF grant IIS-0954256CamarilloUSA
  9. 9.Department of Electrical EngineeringNortheastern UniversityBostonUSA
  10. 10.Department of Computer ScienceTulane UniversityNew OrleansUSA
  11. 11.Research supported in part by NSF grant CCF-0643597New OrleansUSA

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