Journal of Mathematical Imaging and Vision

, Volume 51, Issue 2, pp 296–310 | Cite as

Profile Detection in Medical and Astronomical Images by Means of the Hough Transform of Special Classes of Curves

  • Anna Maria MassoneEmail author
  • Annalisa Perasso
  • Cristina Campi
  • Mauro C. Beltrametti


We develop a formal procedure for the automated recognition of rational and elliptic curves in medical and astronomical images. The procedure is based on the extension of the Hough transform concept to the definition of Hough transform of special classes of algebraic curves. We first introduce a catalogue of curves that satisfy the conditions to be automatically extracted from an image and the recognition algorithm, then we illustrate the power of this method to identify skeleton profiles in clinical X-ray tomography maps and front ends of solar eruptions in astronomical images provided by the NASA solar dynamics observatory satellite.


Hough transform Pattern recognition  Image processing Algebraic plane curve Curve detection 



This work would have been impossible without the major contribution from our colleague Michele Piana. We also wish to thank our students Chiara Della Corte and Giorgio Ricca for their contributions at different stages of this project. Special thanks to the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. This work was supported by the European Community Framework Programme 7, High Energy Solar Physics Data in Europe (HESPE), Grant Agreement No. 263086, and by the PO CRO FSE 2007-2013 Asse IV.


  1. 1.
    Aramini, R., Brignone, M., Coyle, J., Piana, M.: Postprocessing of the linear sampling method by means of deformable models. SIAM J. Sci. Comput. 30(5), 2613–2634 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ballard, D.H.: Generalizing the Hough transform to detect arbitrary shapes. Pattern Recogn. 11(2), 111–122 (1981)CrossRefGoogle Scholar
  3. 3.
    Banik, S., Rangayyan, R.M., Boag, G.S.: Automatic segmentation of the ribs, the vertebral column, and the spinal canal in pediatric computed tomographic images. J. Dig. Imag. 23(3), 301–322 (2010)CrossRefGoogle Scholar
  4. 4.
    Beltrametti M.C., Carletti E., Gallarati D., Monti Bragadin G.: Lectures on curves, surfaces and projective varieties–a classical view of algebraic geometry. Textbooks in Mathematics, vol. 9. European Mathematical Society, Zurich. Translated by F. Sullivan (2009)Google Scholar
  5. 5.
    Beltrametti, M.C., Massone, A.M., Piana, M.: Hough transform of special classes of curves. SIAM J. Imag. Sci. 6, 391–412 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Beltrametti, M.C., Robbiano, L.: An algebraic approach to Hough transforms. J. Algebra 371, 669–681 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. PAMI–8(6), 679–698 (1986)CrossRefGoogle Scholar
  8. 8.
    Carranza, N., Cristóbal, G., Bayerl, P., Neumann, H.: Motion estimation of magnetic resonance cardiac images using the Wigner-Ville and Hough transforms. Opt. Spectrosc. 103(6), 877–885 (2007)CrossRefGoogle Scholar
  9. 9.
    Cistaro, A., et al.: Brain hypermetabolism in amyotrophic lateral sclerosis: a FDG PET study in ALS of spinal and bulbar onset. Eur. J. Nucl. Med. Mol. Imag. 39, 251–259 (2012)CrossRefGoogle Scholar
  10. 10.
    Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Commun. ACM 15(1), 11–15 (1972)CrossRefzbMATHGoogle Scholar
  11. 11.
    Godement, R.: Cours d’algèbre. Enseignements de Sciences. Hermann, Paris (1966)Google Scholar
  12. 12.
    Hollitt, C., Johnston-Hollitt, M.: Feature detection in radio astronomy using the circle Hough transform. Publ. Astron. Soc. Aust. 29(3), 309–317 (2012)CrossRefGoogle Scholar
  13. 13.
    Hough P.V.C.: Method and means for recognizing complex patterns. U.S. Patent 3069654 (1962)Google Scholar
  14. 14.
  15. 15.
    Lemen, J.R., et al.: The atmospheric imaging assembly (AIA) on the solar dynamics observatory (SDO). Solar Phys. 275, 17–40 (2012) Google Scholar
  16. 16.
    Liu, W., Chen, Q., Petrosian, V.: Plasmoid ejections and loop contractions in an eruptive M7.7 solar flare: evidence of particle acceleration and heating in magnetic reconnection outflows. ApJ 767, 168 (2013)Google Scholar
  17. 17.
    Martens, P.C.H., et al.: Computer vision for the solar dynamics observatory (SDO). Solar Phys. 275, 79–113 (2012)CrossRefGoogle Scholar
  18. 18.
    Pesnell, W.D., Thompson, B.J., Chamberlain, P.C.: The solar dynamics observatory (SDO). Solar Phys. 275, 3–15 (2012)CrossRefGoogle Scholar
  19. 19.
    Philip, K.P., et al.: The fuzzy Hough transform-feature extraction in medical images. IEEE Trans. Med. Imag. 13(2), 235–240 (1994)CrossRefGoogle Scholar
  20. 20.
    Robbiano L.: Parametrizations, hyperplane sections, Hough transforms. arXiv:1305.0478 (2013)
  21. 21.
    Rosset, A., Spadola, L., Ratib, O.: OsiriX: an open-source software for navigating in multidimensional DICOM images. J. Dig. Imag. 17(3), 205–216 (2004)CrossRefGoogle Scholar
  22. 22.
    Ruppertshofen, H., Lorenz, C., Rose, G., Schramm, H.: Discriminative generalized Hough transform for object localization in medical images. Int. J. CARS 8, 593–606 (2013)CrossRefGoogle Scholar
  23. 23.
    Sambuceti, G., et al.: Estimating the whole bone-marrow asset in humans by a computational approach to integrated PET/CT imaging. Eur. J. Nucl. Med. Mol. Imag. 39, 1326–1338 (2012)CrossRefGoogle Scholar
  24. 24.
    Sheng, C., Xin, Y., Liping, Y., Kun, S.: Segmentation in echocardiographic sequences using shape-based snake model combined with generalized Hough transformation. Int. J. Cardiovasc. Imag. 22, 33–46 (2006)CrossRefGoogle Scholar
  25. 25.
    Shikin, E.V.: Handbook and Atlas of Curves. CRC Press Inc, Boca Raton (1995)zbMATHGoogle Scholar
  26. 26.
    Smith, R., Najarian, K., Ward, K.: A hierarchical method based on active shape models and directed Hough transform for segmentation of noisy biomedical images; application in segmentation of pelvic X-ray images. BMC Med. Inform. Decis. Mak. 9(1), S2 (2009)CrossRefGoogle Scholar
  27. 27.
    Wu, S.M., Shau, Y.W., Chong, F.C., Hsieh, F.J.: Non-invasive assessment of arterial distension waveforms using gradient-based Hough transform and power Doppler ultrasound imaging. Med. Biol. Eng. Comput. 39, 627–632 (2001)CrossRefGoogle Scholar
  28. 28.
    Zana, F., Klein, J.C.: A multimodal registration algorithm of eye fundus images using vessels detection and Hough transform. IEEE Trans. Med. Imag. 18(5), 419–428 (1999)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Anna Maria Massone
    • 1
    Email author
  • Annalisa Perasso
    • 2
  • Cristina Campi
    • 1
  • Mauro C. Beltrametti
    • 2
  1. 1.CNR-SPINGenovaItaly
  2. 2.Dip. di MatematicaUniversità di GenovaGenovaItaly

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