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Multiscale Corner Detection in Planar Shapes

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Abstract

This paper presents a multiscale corner detection method in planar shapes, which applies an undecimated Mexican hat wavelet decomposition of the angulation signal to identify significant points on a shape contour. The advantage of using this wavelet is that it is well suited for detecting singularities as corners and contours due to its excellent selectivity in position. Thus, this wavelet plays an important role in our approach because it identifies changes in non-stationary angulation signals, and it can be extended to multidimensional approaches in an efficient way when approximating this wavelet by difference of Gaussians. The proposed algorithm detects peaks on a correlation signal which is generated from different wavelet scales and retains relevant points on the decomposed angulation signal while discards poor information. Our approach assumes that only peaks which persist through several scales correspond to corners. Furthermore, we introduce a novel procedure to tune parameters for the corner detection algorithms that corresponds to the best relation between Precision and Recall measures. This technique guides the parameter adjustment of the algorithms according to the image database and it improves their performance with regard to true corner detection. Concerning the performance assessment of the algorithms, we compare the proposed one to other corner detectors by using Precision and Recall measures which are based on ground-truth information. Tests were carried out using more than a hundred images from a non-homogenous database that contains noisy and non-noisy binary shapes.

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References

  1. Almeida, C.W.D., Souza, R.M.C.R., Cavalcanti, N.L.J.: A shape-based image retrieval system using the curvature scale space (CSS) technique and the self-organizing map (SOM) model. In: Proceedings of the 6th International Conference on Hybrid Intelligent Systems, Auckland, New Zealand, pp. 25–29 (2006)

    Google Scholar 

  2. Antoine, J.P., Carrette, P., Murenzi, R., Piette, B.: Image analysis with two-dimensional continuous wavelet transform. Signal Process. 31(3), 241–272 (1993)

    Article  MATH  Google Scholar 

  3. Awrangjeb, M., Lu, G.: An improved curvature scale-space corner detector and a robust corner matching approach for transformed image identification. IEEE Trans. Image Process. 17(12), 2425–2441 (2008)

    Article  MathSciNet  Google Scholar 

  4. Balmashnova, E., Florack, L.M.J.: Novel similarity measures for differential invariant descriptors for generic object retrieval. J. Math. Imaging Vis. 31(2), 121–132 (2008)

    Article  MathSciNet  Google Scholar 

  5. Bezerra, F.N., Paula, I.C., Medeiros, F.N.S., Ushizima, D.M., Cintra, L.H.S.: Morphological segmentation for sagittal plane image analysis. In: Proceedings of the 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, Argentina, pp. 4773–4776 (2010)

    Google Scholar 

  6. Canny, J.F.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)

    Article  Google Scholar 

  7. Costa, L.F., Cesar, R.M.J.: Shape Analysis and Classification: Theory and Practice, 2nd edn. CRC Press, Boca Raton (2009)

    Book  MATH  Google Scholar 

  8. Gao, X., Sattar, F., Quddus, A., Venkateswarlu, R.: Multiscale contour corner detection based on local natural scale and wavelet transform. Image Vis. Comput. 25(6), 890–898 (2007)

    Article  Google Scholar 

  9. Harris, C.J., Stephens, M.: A combined corner and edge detector. In: Proceedings of the Fourth Alvey Vision Conference, Manchester, England, pp. 147–151 (1988)

    Google Scholar 

  10. Hua, J., Liao, Q.: Wavelet-based multiscale corner detection. In: Proceedings of 5th International Conference on Signal Processing, Beijing, China, vol. 1, pp. 341–344. IEEE Press, New York (2000)

    Chapter  Google Scholar 

  11. Kindratenko, V.V.: On using functions to describe the shape. J. Math. Imaging Vis. 18(3), 225–245 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kutter, M., Bhattacharjee, K.S., Ebrahimi, T.: Towards second generation watermarking schemes. In: Proceedings IEEE Conference on Image Processing, pp. 320–323 (1999)

    Google Scholar 

  13. Latecki, L.J., Lakamper, R., Eckhardt, U.: Shape descriptors for non-rigid shapes with a single closed contour. In: Proceedings IEEE Conference on Computer Vision and Pattern Recognition, pp. 424–429 (2000)

    Google Scholar 

  14. Lee, J.S., Sun, Y.N., Chen, C.H.: Multiscale corner detection by using wavelet transform. IEEE Trans. Image Process. 4(1), 100–104 (1995)

    Article  Google Scholar 

  15. Liu, H.C., Srinath, M.D.: Partial shape classification using contour matching in distance transformation. IEEE Trans. Pattern Anal. Mach. Intell. 12(11), 1072–1079 (1990)

    Article  Google Scholar 

  16. Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Academic Press, San Diego (1998)

    MATH  Google Scholar 

  17. Mokhtarian, F., Mackworth, A.: Scale-based description and recognize. of planar curves and two-dimensional shapes. IEEE Trans. Pattern Anal. Mach. Intell. 8(1), 34–43 (1986)

    Article  Google Scholar 

  18. Mokhtarian, F., Mackworth, A.: A theory of multiscale, curvature-based shape representation for planar curves. IEEE Trans. Pattern Anal. Mach. Intell. 14(8), 789–805 (1992)

    Article  Google Scholar 

  19. Mokhtarian, F., Mohanna, F.: Performance evaluation of corner detectors using consistency and accuracy measures. Comput. Vis. Image Underst. 102(1), 81–94 (2006)

    Article  Google Scholar 

  20. Mokhtarian, F., Suomela, R.: Robust image corner detection through curvature scale space. IEEE Trans. Pattern Anal. Mach. Intell. 20(12), 1376–1381 (1998)

    Article  Google Scholar 

  21. Paula, I.C., Medeiros, F.N.S., Mendonca, G.A., Passarinho, C.J.P., Oliveira, I.N.S.: Correlating multiple redundant scales for corner detection. In: Proceedings of VI International Telecommunications Symposium, Fortaleza, Brazil, pp. 650–655 (2006)

    Google Scholar 

  22. Paula, I., Medeiros, F.N.S., Bezerra, F.N., Ushizima, D.M.: Corner detection within a multiscale framework. In: Proceedings of Sibgrapi 2011 (XXIV Conference on Graphics, Patterns and Images), Maceió, Brasil (2011)

    Google Scholar 

  23. Pedrosa, G.V., Barcelos, C.A.Z.: Anisotropic diffusion for effective shape corner point detection. Pattern Recognit. Lett. 31, 1658–1664 (2010)

    Article  Google Scholar 

  24. Pedrosa, G.V., Barcelos, C.A.Z., Batista, M.A.: An image retrieval system using shape salience points. In: Proceedings of 2011 IEEE International Symposium on Circuits and System (ISCAS 2011), Rio de Janeiro, Brazil, pp. 2797–2800 (2011)

    Chapter  Google Scholar 

  25. Rattarangsi, A., Chin, R.T.: Scale-based detection of corners of planar curves. IEEE Trans. Pattern Anal. Mach. Intell. 14(4), 430–449 (1992)

    Article  Google Scholar 

  26. Roh, M.C., Christmas, B., Kittler, J., Lee, S.W.: Gesture spotting in low-quality video with features based on curvature scale space. In: Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition, Southampton, UK, pp. 375–380 (2006)

    Google Scholar 

  27. Rosenfeld, A., Johnston, E.: Angle detection on digital curves. IEEE Trans. Comput. 22(9), 875–878 (1973)

    Article  Google Scholar 

  28. Rosenfeld, A., Weszka, J.S.: An improved method of angle detection on digital curves. IEEE Trans. Comput. 24(9), 940–941 (1975)

    Article  Google Scholar 

  29. Rosten, E., Porter, R., Drummond, T.: Faster and better: a machine learning approach to corner detection. IEEE Trans. Pattern Anal. Mach. Intell. 32(1), 105–119 (2010)

    Article  Google Scholar 

  30. Torres, R.S., Falcão, A.X.: Contour salience descriptors for effective image retrieval and analysis. Image Vis. Comput. 25(1), 3–13 (2007)

    Article  Google Scholar 

  31. Wang, S.J., Kuo, L.C., Jong, H.H., Wu, Z.H.: Representing images using points on image surfaces. IEEE Trans. Image Process. 14(8), 1043–1056 (2005)

    Article  MathSciNet  Google Scholar 

  32. Wang, Y.P., Lee, S.L.: Scale-space derived from B-splines. IEEE Trans. Pattern Anal. Mach. Intell. 20(10), 1040–1055 (1998)

    Article  Google Scholar 

  33. Zhang, C., Mengyang, Z., Yuan, L.: An improved algorithm for corner detection. In: International Conference on Electronic and Mechanical Engineering and Information Technology 2011 (EMEIT), vol. 9, pp. 4639–4641 (2011)

    Chapter  Google Scholar 

  34. Zhang, X., Wang, H., Hong, M., Xu, L., Yang, D., Lovell, B.C.: Robust image corner detection based on scale evolution difference of planar curves. Pattern Recognit. Lett. 30(4), 449–455 (2009)

    Article  Google Scholar 

  35. Zhang, X., Wang, H., Smith, A.W.B., Xu, L., Lovell, B.C., Yang, D.: Corner detection based on gradient correlation matrices of planar curves. Pattern Recognit. 43(4), 1207–1223 (2010)

    Article  MATH  Google Scholar 

  36. Zhong, B., Liao, W.: Direct curvature scale space: theory and corner detection. IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 508–512 (2007)

    Article  Google Scholar 

  37. Zhong, B., Ma, K.K., Liao, W.: Scale-space behavior of planar-curve corners. IEEE Trans. Pattern Anal. Mach. Intell. 31(8), 1517–1524 (2009)

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to CNPq and FUNCAP for the support and financial help. Also, it was partially supported by the Office of Energy Research, U.S. Department of Energy, under Contract Number DE-AC02-05CH11231. We thank Prof. Barcellos for the helpful discussions and her student Glauco Pedrosa for providing and explaining his source code. And we are also thankful to Carlos W.D. de Almeida for the available CSS source code.

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Authors and Affiliations

  1. Depto. de Eng. de Teleinformática, Universidade Federal do Ceará, Fortaleza, CE, Brazil

    Ialis C. Paula Jr. & Fatima N. S. Medeiros

  2. Inst. Fed. de Educação, Ciência e Tecnologia, Campus Maracanaú, Maracanaú, CE, Brazil

    Francisco N. Bezerra

  3. Math and Visualization Groups, Lawrence Berkeley National Lab., Berkeley, CA, USA

    Daniela M. Ushizima

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  1. Ialis C. Paula Jr.
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  2. Fatima N. S. Medeiros
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  3. Francisco N. Bezerra
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  4. Daniela M. Ushizima
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Correspondence to Ialis C. Paula Jr..

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Paula, I.C., Medeiros, F.N.S., Bezerra, F.N. et al. Multiscale Corner Detection in Planar Shapes. J Math Imaging Vis 45, 251–263 (2013). https://doi.org/10.1007/s10851-012-0365-8

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