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.
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Notes
- 1.
We are not viewing the space of plane curves as linear, but the integral defined is analogous to Sobolev norms on function spaces and the integrand is analogous to a wavelet decomposition of γ. Additionally, the “norm” gives rise to a metric on curves in the standard way.
References
Alt, H., Efrat, A., Rote, G., Wenk, C.: Matching planar maps. J. Algorithms 49(2), 262–283 (2003)
Aslan, C., Tari, S.: An axis-based representation for recognition. In: ICCV, Beijing, pp. 1339–1346. IEEE Computer Society (2005)
Bai, X., Yang, X., Yu, D., Latecki, L.J.: Skeleton-based shape classification using path similarity. Int. J. Pattern Recognit. Artif. Intell. (IJPRAI) 22(4), 733–746 (2008)
Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)
Belongie, S., Mori, G., Malik, J.: Matching with shape contexts. In: Analysis and Statistics of Shapes, pp. 81–105. Birkhäuser (2005)
Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, pp. 362–380. MIT, Cambridge (1967). http://citeseer.nj.nec.com/context/77000/0
Brakatsoulas, S., Pfoser, D., Salas, R., Wenk, C.: On map-matching vehicle tracking data. In: Proceedings of the 31st International Conference on Very Large Data Bases (VLDB’05), Trondheim, pp. 853–864. VLDB Endowment (2005)
Chen, D., Driemel, A., Guibas, L.J., Nguyen, A., Wenk, C.: Approximate map matching with respect to the Fréchet distance. In: Müller-Hannemann, M., Werneck, R.F.F. (eds.) ALENEX, San Francisco, pp. 75–83. SIAM (2011)
Fei-Fei, L., Fergus, R., Perona, P.: One-shot learning of object categories. IEEE Trans. Pattern Anal. Mach. Intell. 28(4), 594–611 (2006)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 18(4), 377–388 (1996)
Grompone von Gioi, R., Jakubowicz, J., Morel, J.-M., Randall, G.: LSD: a Line Segment Detector. Image Processing On Line (2012)
Gudmundsson, J., Smid, M.: Fréchet queries in geometric trees. In: Bodlaender, H.L., Italiano, G.F. (eds.) Algorithms – ESA 2013, Sophia Antipolis. Lecture Notes in Computer Science, vol. 8125, pp. 565–576. Springer, Berlin/Heidelberg (2013)
Huttenlocher, D.P., Klanderman, G.A., Rucklidge, W.J.: Comparing images using the Hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell. 15(9), 850–863 (1993)
Kushnarev, S.: Teichons: solitonlike geodesics on universal Teichmüller space. Exp. Math. 18, 325–336 (2009)
Leonard, K., Strawbridge, R., Lindsay, D., Barata, R., Dawson, M., Averion, L.: Minimal geometric representation and strawberry stem detection. In: 2013 13th International Conference on Computational Science and Its Applications (ICCSA), Ho Chi Minh City, pp. 144–149 (2013)
Leonard, K., Feiszli, M., Kushnarev, S.: Metric spaces of shapes and applications: compression, curve matching and low-dimensional representation. Geom. Imaging Comput. 1(2), 173–221 (2014)
Leymarie, F.F., Kimia, B.B.: From the infinitely large to the infinitely small: applications of medial symmetry representations of shape. In: Siddiqi, K., Pizer, S.M. (eds.) Medial Representations: Mathematics, Algorithms and Applications. Computational Imaging and Vision, pp. 327–351. Kluwer Academic, Dordrecht (2008). ISBN:978-1-402-08657-1. http://opac.inria.fr/record=b1130467
Lieutier, A.: Any open bounded subset of \(\mathbb{R}^{n}\) has the same homotopy type as its medial axis. Comput.-Aided Des. 36(11), 1029–1046 (2004)
Lin, C.C., Chellappa, R.: Classification of partial 2-D shapes using Fourier descriptors. IEEE Trans. Pattern Anal. Mach. Intell. 5, 686–690 (1987)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Sebastian, T.B., Kimia, B.B.: Curves vs. skeletons in object recognition. Signal Process. 85(2), 247–263 (2005)
Sebastian, T.B., Klein, P.N., Kimia, B.B.: Shock-based indexing into large shape databases. In: Proceedings of the 7th European Conference on Computer Vision-Part III (ECCV’02), Copenhagen, pp. 731–746. Springer, London (2002)
Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing their shock graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 550–571 (2004)
Sharon, E., Mumford, D.: 2D-shape analysis using conformal mapping. Int. J. Comput. Vis. 70, 55–75 (2006)
Trinh, N.H., Kimia, B.B.: Skeleton search: category-specific object recognition and segmentation using a skeletal shape model. Int. J. Comput. Vis. 94(2), 215–240 (2011)
Trouve, A., Miller, M.I., Younes, L.: On metrics and Euler-Lagrange equations of computational anatomy. Ann. Rev. Biomed. Eng. 4, 375–405 (2002)
Wenk, C., Salas, R., Pfoser, D.: Addressing the need for map-matching speed: localizing global curve-matching algorithms. In: Proceedings of the 18th International Conference on Scientific and Statistical Database Management (SSDBM’06), Vienna, pp. 379–388. IEEE Computer Society, Washington, DC (2006)
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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Bal, G. et al. (2015). Skeleton-Based Recognition of Shapes in Images via Longest Path Matching. In: Leonard, K., Tari, S. (eds) Research in Shape Modeling. Association for Women in Mathematics Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-16348-2_6
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DOI: https://doi.org/10.1007/978-3-319-16348-2_6
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