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Supporting exact indexing of arbitrarily rotated shapes and periodic time series under Euclidean and warping distance measures

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Abstract

Shape matching and indexing is important topic in its own right, and is a fundamental subroutine in most shape data mining algorithms. Given the ubiquity of shape, shape matching is an important problem with applications in domains as diverse as biometrics, industry, medicine, zoology and anthropology. The distance/similarity measure for used for shape matching must be invariant to many distortions, including scale, offset, noise, articulation, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However, rotation invariance is noted in the literature as being an especially difficult challenge. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of discrimination ability, or in the distance measure, at the expense of efficiency. In this work, we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems our technique can take current approaches and make them four orders of magnitude faster without false dismissals. Moreover, our technique can be used with any of the dozens of existing shape representations and with all the most popular distance measures including Euclidean distance, dynamic time warping and Longest Common Subsequence. We further show that our indexing technique can be used to index star light curves, an important type of astronomical data, without modification.

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References

  1. Adamek T., O’Connor N.E.: A multiscale representation method for nonrigid shapes with a single closed contour. IEEE Circuits Syst. Video Technol. 14(5), 742–753 (2004)

    Article  Google Scholar 

  2. Adamek, T., O’Connor, N.E.: Efficient contour-based shape representation and matching. Multimedia Information Retrieval, pp. 138–143 (2003)

  3. Attalla E., Siy P.: Robust shape similarity retrieval based on contour segmentation polygonal multiresolution and elastic matching. Pattern Recognit. 38(12), 2229–2241 (2005)

    Article  Google Scholar 

  4. Bartolini B., Ciaccia P., Patella P.: WARP: accurate retrieval of shapes using phase of fourier descriptors and time warping distance. IEEE Trans. Pattern Anal. Mach. Intell. 27(1), 142–147 (2005)

    Article  Google Scholar 

  5. Bhanu, B., Zhou, X.: Face recognition from face profile using dynamic time warping. In: Proceedings of International Conference on Pattern Recognition (ICPN’04), pp. 499–502, (2004)

  6. Borgefors G.: Hierarchical chamfer matching: a parametric edge matching algorithm. IEEE Trans. Pattern Anal. Mach. Intell. 10(6), 849–865 (1988)

    Article  Google Scholar 

  7. Cardone A., Gupta S.K., Karnik M.: A survey of shape similarity assessment algorithms for product design and manufacturing applications. ASME J. Comput. Inform. Sci. Eng. 3(2), 109–118 (2003)

    Article  Google Scholar 

  8. Ciaccia P., Patella M.: Searching in metric spaces with user-defined and approximate distances. ACM Trans. Database Syst. 27(4), 398–437 (2002)

    Article  Google Scholar 

  9. Gdalyahu Y., Weinshall D.: Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes. IEEE Trans. Pattern Anal. Mach. Intell. 21(12), 1312–1328 (1999)

    Article  Google Scholar 

  10. Hodges W., Zamudio K.: Horned lizard (phrynosoma) phylogeny inferred from mitochondrial genes and morphological characters: understanding conflicts using multiple approaches. Mol. Phylogenet. Evol. 31, 961–971 (2004)

    Article  Google Scholar 

  11. Iwabe N.: Sister group relationship of turtles to the bird-crocodilian clade revealed by nuclear DNA-coded proteins. Mol. Biol. Evol. 22, 810–813 (2004)

    Article  Google Scholar 

  12. Jalba A.C., Wilkinson M.H.F., Roerdink J.B.T.M., Bayer M.M., Juggins S.: Automatic diatom identification using contour analysis by morphological curvature scale spaces. Mach. Vis. Appl. 16(4), 217–228 (2005)

    Article  Google Scholar 

  13. Karydis Y., Nanopoulos A., Papadopoulos A.N., Manolopoulos Y.: Evaluation of similarity searching methods for music data in peer-to-peer networks. Int. J. Bus. Intell. Data Mining 1(2), 210–228 (2005)

    Article  Google Scholar 

  14. Keogh, E.: www.cs.ucr.edu/~eamonn/shape/shape.htm (2006)

  15. Keogh, E.: http://www.cs.ucr.edu/~eamonn/time_series_data/

  16. Keogh, E.: Exact indexing of dynamic time warping. In: Proceedings of the 28th International Conference on Very Large Data Bases, Hong Kong, pp. 406–417 (2002)

  17. Keogh, E., Kasetty, S.: On the need for time series data mining benchmarks: a survey and empirical demonstration. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, Canada, pp. 102–111 (2002)

  18. Keogh, E., Palpanas, T., Zordan, V., Gunopulos, D., Cardle, M.: Indexing large human-motion databases. In: Proceedings of the 30th International Conference on Very Large Data Bases, Toronto, Canada, pp. 780–791 (2004)

  19. Lee, D.J., Schoenberger, R.B., Shiozawa, D.K., Xu, X., Zhan, P.: Contour matching for a fish recognition and migration monitoring system. In: SPIE Optics East, Two and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, vol. 5606–05, pp. 37–48, Philadelphia, PA, USA, October 25–28 (2004)

  20. Li, D., Simske, S.: Shape retrieval based on distance ratio distribution. HP Tech Report. HPL-2002–251 (2002)

  21. Li Q., Lopez I., Moon B.: Skyline index for time series data. IEEE Trans. Knowl. Data Eng. 16(6), 669–684 (2004)

    Article  Google Scholar 

  22. Ling, H., Jacobs, D.W.: Using the inner-distance for classification of articulated shapes. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. II, pp. 719–726 (2005)

  23. Marzal A., Palazón V.: Dynamic time warping of cyclic strings for shape matching. ICAPR 2, 644–652 (2005)

    Google Scholar 

  24. Mollineda R.A., Vidal E., Casacuberta F.: Cyclic sequence alignments: approximate versus optimal techniques. Int. J. Pattern Recognit. Artif. Intell. (IJPRAI) 16(3), 291–299 (2002)

    Article  Google Scholar 

  25. Niennattrakul V., Wanichsan D., Ratanamahatana C.: Hand geometry verification using time series representation. KES 2, 824–831 (2007)

    Google Scholar 

  26. O’Brien, M.J., Lyman, R.L.: Resolving phylogeny: evolutionary archaeology’s fundamental issue. In: VanPool, T.L., VanPool, C.S. (eds.) Essential Tensions in Archaeological Method and Theory, pp. 115–135. University of Utah Press, Salt Lake City (2003)

  27. Olson C.F., Huttenlocher D.P.: Automatic target recognition by matching oriented edge pixels. IEEE Trans. Image Process. 6(1), 103–113 (1997)

    Article  Google Scholar 

  28. Osada R., Funkhouser T., Chazelle B., Dobkin D.: Shape distributions. ACM Trans. Graphics 21(4), 807–832 (2002)

    Article  Google Scholar 

  29. Protopapas P., Giammarco J.M., Faccioli L., Struble M.F., Dave R., Alcock C.: Finding outlier light curves in catalogues of periodic variable stars. Mon. Not. R. Astron. Soc. 369(2), 677–696 (2006)

    Article  Google Scholar 

  30. Ratanamahatana, C.A., Keogh, E.: Three myths about dynamic time warping. In: Proceedings of SIAM International Conference on Data Mining (SDM ’05), Newport Beach, CA, April 21–23, pp. 506–510 (2005)

  31. Rath, T., Manmatha, R.: Lower-bounding of dynamic time warping distances for multivariate time series. Tech Report MM-40, University of Massachusetts Amherst (2002)

  32. Seba, A.: Locupletissimi rerum naturalium thesauri accurata descriptio Naaukeurige beschryving van het schatryke kabinet der voornaamste seldzaamheden der natuur. Amsterdam, 1734–1765, 4 vols. 2o, 394 B 26–29, vol. 3, plate XXXV (1734)

  33. Sebastian T., Kimia B.: Curves vs. skeletons in object recognition. Signal Process. 85(2), 247–263 (2005)

    Article  MATH  Google Scholar 

  34. Sakoe H., Chiba S.: Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoust. Speech Signal Proc. 26, 43–49 (1978)

    Article  MATH  Google Scholar 

  35. Thakoor, N., Gao, J.: Shape classifier based on generalized probabilistic descent method with hidden Markov descriptor. In: Computer Vision, 2005, ICCV 2005, Tenth IEEE International Conference, vol. 1, pp. 495–502 (2005)

  36. Veltkamp, R.C., Latecki, L.J.: Properties and performance of shape similarity measures. In: Proceedings of IFCS 2006 Conference: Data Science and Classification, July (2006)

  37. Vlachos, M., Hadjieleftheriou, M., Gunopulos, D., Keogh, E.: Indexing multi-dimensional time-series with support for multiple distance measures. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, pp. 216–225, August 24–27 (2003)

  38. Vlachos, M., Vagena, Z., Yu, P.S., Athitsos, V.: Rotation invariant indexing of shapes and line drawings. In: Proceedings of ACM Conference on Information and Knowledge Management (CIKM), pp. 131–138 (2005)

  39. Wang, Z., Chi, Z., Feng, D., Wang, Q.: Leaf image retrieval with shape features. In: Proceedings of the 4th International Conference on Advances in Visual Information Systems, pp. 477–487 (2000)

  40. Wei, L., Keogh, E., Van Herle, H., Mafra-Neto, A.: Atomic wedgie: efficient query filtering for streaming time series. In: Proceedings of the 5th IEEE International Conference on Data Mining (ICDM 2005), pp. 490–497 (2005)

  41. White T.D.: Human Osteology, 2nd edn. Academic Press, San Diego (2000)

    Google Scholar 

  42. Woodford, B.J., Kasabov, N.K., Wearing, C.H.: Fruit image analysis using wavelets. In: Ko, K., Kasabov, N. (eds.) Proceedings of the ICONIP/ANZIIS/ANNES’99 International Workshop, University of Otago Press, pp. 88–91 (1999)

  43. Yu S., Guan L.: A CAD system for the automatic detection of clustered microcalcifications in digitized mammogram. IEEE Trans. Med. Imag. 19(2), 115–126 (2000)

    Article  Google Scholar 

  44. Zhang D., Lu G.: Review of shape representation and description techniques. Pattern Recognit. 37(1), 1–19 (2004)

    Article  MATH  Google Scholar 

  45. Zunic J., Rosin P., Kopanja L.: Shape orientability. ACCV 2, 11–20 (2006)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, UCR, Riverside, CA, USA

    Eamonn Keogh, Li Wei & Xiaopeng Xi

  2. IBM T.J. Watson Research Center, Yorktown Heights, NY, USA

    Michail Vlachos

  3. Department of Anthropology, UCR, Riverside, CA, USA

    Sang-Hee Lee

  4. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA

    Pavlos Protopapas

Authors
  1. Eamonn Keogh
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  2. Li Wei
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  3. Xiaopeng Xi
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  4. Michail Vlachos
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  5. Sang-Hee Lee
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  6. Pavlos Protopapas
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Correspondence to Eamonn Keogh.

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Reproducible Research Statement: All datasets and images used in this work are freely available at www.cs.ucr.edu/~eamonn/shape/shape.htm.

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Keogh, E., Wei, L., Xi, X. et al. Supporting exact indexing of arbitrarily rotated shapes and periodic time series under Euclidean and warping distance measures. The VLDB Journal 18, 611–630 (2009). https://doi.org/10.1007/s00778-008-0111-4

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  • DOI: https://doi.org/10.1007/s00778-008-0111-4

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