Advertisement

Enhancing Signal Discontinuities with Shearlets: An Application to Corner Detection

  • Miguel Alejandro Duval-Poo
  • Francesca OdoneEmail author
  • Ernesto De Vito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9280)

Abstract

Shearlets are a relatively new and very effective multi-resolution framework for signal analysis able to capture efficiently the anisotropic information in multivariate problem classes. For this reason, Shearlets appear to be a valid choice for multi-resolution image processing and feature detection. In this paper we provide a brief review of the theory, referring in particular to the problem of enhancing signal discontinuities. We then discuss the specific application to corner detection, and provide a novel algorithm based on the concept of a cornerness measure. The appropriateness of the algorithm in detecting good matchable corners is evaluated on benchmark data including different image transformations.

Keywords

Corner Point Corner Detection Multivariate Problem Class Texture Scene Signal Discontinuity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Aanes, H., Dahl, A.L., Pedersen, K.S.: Interesting interest points. IJCV (2011)Google Scholar
  2. 2.
    Candes, E.J., Donoho, D.L.: New tight frames of curvelets and optimal representations of objects with piecewise c2 singularities. Communications on Pure and Applied Mathematics 57(2), 219–266 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Chen, C.H., Lee, J.S., Sun, Y.N.: Wavelet transformation for gray-level corner detection. Pattern Recognition 28(6), 853–861 (1995)CrossRefGoogle Scholar
  4. 4.
    Easley, G., Labate, D., Lim, W.Q.: Sparse directional image representations using the discrete shearlet transform. Applied and Computational Harmonic Analysis 25(1), 25–46 (2008)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Gao, X., Sattar, F., Venkateswarlu, R.: Multiscale corner detection of gray level images based on log-gabor wavelet transform. IEEE Transactions on Circuits and Systems for Video Technology 17(7), 868–875 (2007)CrossRefGoogle Scholar
  6. 6.
    Guo, K., Labate, D.: Characterization and analysis of edges using the continuous shearlet transform. SIAM Journal on Imaging Sciences 2(3), 959–986 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Alvey Vision Conference, Manchester, UK, vol. 15, p. 50 (1988)Google Scholar
  8. 8.
    Häuser, S., Steidl, G.: Fast finite shearlet transform: a tutorial. ArXiv (1202.1773) (2014)Google Scholar
  9. 9.
    Kitchen, L., Rosenfeld, A.: Gray-level corner detection. Pattern Recognition Letters 1(2), 95–102 (1982)CrossRefGoogle Scholar
  10. 10.
    Kittipoom, P., Kutyniok, G., Lim, W.Q.: Construction of compactly supported shearlet frames. Constr. Approx. 35(1), 21–72 (2012)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Kutyniok, G., Labate, D.: Shearlets: Multiscale analysis for multivariate data. Springer (2012)Google Scholar
  12. 12.
    Kutyniok, G., Petersen, P.: Classification of edges using compactly supported shearlets. ArXi (1411.5657) (2014)Google Scholar
  13. 13.
    Labate, D., Lim, W.Q., Kutyniok, G., Weiss, G.: Sparse multidimensional representation using shearlets. In: Optics & Photonics 2005, pp. 59140U–59140U. International Society for Optics and Photonics (2005)Google Scholar
  14. 14.
    Mallat, S., Hwang, W.L.: Singularity detection and processing with wavelets. IEEE Transactions on Information Theory 38(2), 617–643 (1992)CrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    Mallat, S., Zhong, S.: Characterization of signals from multiscale edges. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(7), 710–732 (1992)CrossRefGoogle Scholar
  16. 16.
    Mikolajczyk, K., Tuytelaars, T., Schmid, C., Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., Van Gool, L.: A comparison of affine region detectors. International Journal of Computer Vision 65(1–2), 43–72 (2005)CrossRefGoogle Scholar
  17. 17.
    Pedersini, F., Pozzoli, E., Sarti, A., Tubaro, S.: Multi-resolution corner detection. In: ICIP, pp. 881–884 (2000)Google Scholar
  18. 18.
    Po, D.D., Do, M.N.: Directional multiscale modeling of images using the contourlet transform. Image Processing 15(6), 1610–1620 (2006)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Rosten, E., Porter, R., Drummond, T.: Faster and better: A machine learning approach to corner detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(1), 105–119 (2010)CrossRefGoogle Scholar
  20. 20.
    Selesnick, I.W., Baraniuk, R.G., Kingsbury, N.C.: The dual-tree complex wavelet transform. IEEE Signal Processing Magazine 22(6), 123–151 (2005)CrossRefGoogle Scholar
  21. 21.
    Shi, J., Tomasi, C.: Good features to track. In: Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 1994, pp. 593–600. IEEE (1994)Google Scholar
  22. 22.
    Yi, S., Labate, D., Easley, G.R., Krim, H.: A shearlet approach to edge analysis and detection. IEEE Transactions on Image Processing 18(5), 929–941 (2009)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Miguel Alejandro Duval-Poo
    • 1
  • Francesca Odone
    • 1
    Email author
  • Ernesto De Vito
    • 2
  1. 1.DIBRIS - Università Degli Studi di GenovaGenoaItaly
  2. 2.DIMA - Università Degli Studi di GenovaGenoaItaly

Personalised recommendations