Solar Physics

, Volume 262, Issue 2, pp 373–385 | Cite as

Extraction of Solar Coronal Magnetic Loops with the Directional 2D Morlet Wavelet Transform

  • S. Biskri
  • J.-P. AntoineEmail author
  • B. Inhester
  • F. Mekideche
Open Access
Solar Image Processing and Analysis


We present an automated extraction method based on the continuous wavelet transform (CWT) for analyzing solar magnetic loops. The aim of the work is to extract, from the images taken from solar EUV telescopes, the traces of bright loops presumably shaped by the magnetic field of the solar corona. The technique is that of wavelet analysis, using the two-dimensional Morlet wavelet, because of its efficiency in detecting oriented features, which allows us to follow closely the curvature of the loops. Next, we segment the wavelet modulus image and we threshold it, both globally and locally (i.e., adaptively), in order to eliminate the remaining noise. Altogether, our method performs well, it is robust and fast, and could be used as a standard tool for analyzing large data sets expected from missions like SDO.


Corona Magnetic loops Continuous wavelet transform Extraction Segmentation 


  1. Antoine, J.P., Carrette, P., Murenzi, R., Piette, B.: 1993, Image analysis with two-dimensional continuous wavelet transform. Signal Process. 31, 241 – 272. zbMATHCrossRefGoogle Scholar
  2. Antoine, J.P., Demanet, L., Jacques, L., Hochedez, J.F., Terrier, R., Verwichte, E.: 2002a, Application of the 2-D wavelet to astrophysical images. Phys. Mag. 24, 93 – 116. Google Scholar
  3. Antoine, J.P., Demanet, L., Jacques, L., Vandergheynst, P.: 2002b, Wavelets on the sphere: Implementation and approximations. Appl. Comput. Harmon. Anal. 13, 177 – 200. zbMATHCrossRefMathSciNetGoogle Scholar
  4. Antoine, J.P., Murenzi, R., Vandergheynst, P., Ali, S.T.: 2004, Two-dimensional Wavelets and Their Relatives, Cambridge University Press, Cambridge. Chapter 1. zbMATHCrossRefGoogle Scholar
  5. Aschwanden, M.J., Nightingale, R.W., Alexander, D.: 2000, Evidence for nonuniform heating of coronal loops inferred from multithread modeling of trace data. Astrophys. J. 541, 1059 – 1077. CrossRefADSGoogle Scholar
  6. Aschwanden, M.J., Lee, J.K., Gary, G.A., Smith, M., Inhester, B.: 2008a, Comparison of five numerical codes for automated tracing of coronal loops. Solar Phys. 248, 359 – 377. doi: 10.1007/s11207-007-9064-9. CrossRefADSGoogle Scholar
  7. Aschwanden, M.J., Nitta, N.V., Wülser, J.P., Lemen, J.R.: 2008b, First 3D reconstructions of coronal loops with the STEREO A+B spacecraft. II. Electron density and temperature measurements. Astrophys. J. 680, 1477 – 1495. doi: 10.1086/588014. CrossRefADSGoogle Scholar
  8. Carcedo, L., Brown, D.S., Hood, A.W., Neukirch, T., Wiegelmann, T.: 2003, A quantitative method to optimize magnetic field line fitting of observed coronal loops. Solar Phys. 218, 29 – 40. CrossRefADSGoogle Scholar
  9. Delouille, V., de Patoul, J., Hochedez, J.F., Jacques, L., Antoine, J.P.: 2005, Wavelet spectrum analysis of EIT/SoHO images. Solar Phys. 228, 301 – 321. CrossRefADSGoogle Scholar
  10. Farge, M., Kevlahan, N.K.R., Perrier, V., Schneider, K.: 1998, Turbulence analysis, modelling and computing using wavelets. In: van den Berg, J. (ed.) Wavelets in Physics, Cambridge Univ. Press, Cambridge, 117 – 200. Google Scholar
  11. Feng, L., Inhester, B., Solanki, S.K., Wiegelmann, T., Podlipnik, B., Howard, R.A., Wülser, J.P.: 2007, First stereoscopic coronal loop reconstructions from STEREO-SECCHI images. Astrophys. J. 671, 205 – 208. doi: 10.1086/525525. CrossRefADSGoogle Scholar
  12. Gary, G.A.: 2001, Plasma beta above a solar active region: Rethinking the paradigm. Solar Phys. 203, 71 – 86. CrossRefADSGoogle Scholar
  13. Handy, B.N., Acton, L.W., Kankelborg, C.C., Wolfson, C.J., Akin, D.J., Bruner, M.E., Caravalho, R., Catura, R.C., Chevalier, R., Duncan, D.W., Edwards, C.G., Feinstein, C.N., Freeland, S.L., Friedlaender, F.M., Hoffmann, C.H., Hurlburt, N.E., Jurcevich, B.K., Katz, N.L., Kelly, G.A., Lemen, J.R., Levay, M., Lindgren, R.W., Mathur, D.P., Meyer, S.B., Morrison, S.J., Morrison, M.D., Nightingale, R.W., Pope, T.P., Rehse, R.A., Schrijver, C.J., Shine, R.A., Shing, L., Strong, K.T., Tarbell, T.D., Title, A.M., Torgerson, D.D., Golub, L., Bookbinder, J.A., Caldwell, D., Cheimets, P.N., Davis, W.N., DeLuca, E.E., McMullen, R.A., Warren, H.P., Amato, D., Fisher, R., Maldonado, H., Parkinson, C.: 1999, The transition region and coronal explorer. Solar Phys. 187, 229 – 260. doi: 10.1023/A:1005166902804. CrossRefADSGoogle Scholar
  14. Inhester, B., Feng, L., Wiegelmann, T.: 2008, Segmentation of loops from coronal EUV images. Solar Phys. 248, 379 – 393. CrossRefADSGoogle Scholar
  15. Jacques, L.: 2004, Ondelettes, repères et couronne solaire. PhD thesis, Université Catholique de Louvain, Louvain-la-Neuve. Google Scholar
  16. Jiang, X.: 2003, Adaptive local threshold by verification-based multithreshold probing with application to vessel detection in retinal images. IEEE Trans. Pattern Anal. Mach. Intell. 25, 131 – 137. CrossRefGoogle Scholar
  17. Lee, J.K., Newman, T.S., Gary, G.A.: 2006a, Dynamic aperture-based solar loop segmentation. In: SSIAI ’06: Proceedings of the 2006 IEEE Southwest Symposium on Image Analysis and Interpretation, IEEE Computer Society, Washington, 91 – 94. ISBN 1-4244-0069-4. doi: 10.1109/SSIAI.2006.1633725. Google Scholar
  18. Lee, J.K., Newman, T.S., Gary, G.A.: 2006b, Oriented connectivity-based method for segmenting solar loops. Pattern Recogn. 39, 246 – 259. CrossRefGoogle Scholar
  19. Lindeberg, T.: 1998, Edge detection and ridge detection with automatic scale. Int. J. Comput. Vis. 30(2), 117 – 154. CrossRefGoogle Scholar
  20. Mallat, S.G.: 1999, A Wavelet Tour of Signal Processing, Academic Press, San Diego. zbMATHGoogle Scholar
  21. McEwen, J.D., Vielva, P., Wiaux, Y., Barreiro, R.B., Cayon, L., Hobson, M.P., Lasenby, A.N., Martinez-Gonzalez, E.: 2006, Cosmological applications of a wavelet analysis on the sphere. J. Fourier Anal. Appl. 13, 495 – 510. CrossRefMathSciNetGoogle Scholar
  22. Sakai, J.I., Furusawa, K.: 2002, Nonuniform heating of coronal loop footpoints and formation of loop threads associated with up- and downflows in the solar chromosphere. Astrophys. J. 564, 1048 – 1053. doi: 10.1086/324133. CrossRefADSGoogle Scholar
  23. Slezak, E., Bijaoui, A., Mars, G.: 1990, Identification of structures from galaxy counts. Use of the wavelet transform. Astron. Astrophys. 227, 301 – 316. ADSGoogle Scholar
  24. Soares, J.V.B., Leandro, J.J.G., Cesar, J.R.-M., Jelinek, H.F., Cree, M.J.: 2006, Retinal vessel segmentation using the 2-D Morlet wavelet and supervised classification. IEEE Trans. Med. Imag. 25, 1214 – 1222. CrossRefGoogle Scholar
  25. Torrésani, B.: 1995, Analyse continue par ondelettes. InterEditions, CNRS Editions, Paris. zbMATHGoogle Scholar
  26. Wiegelmann, T.: 2008, Nonlinear force-free modeling of the solar coronal magnetic field. J. Geophys. Res. 113(A12), 3. doi: 10.1029/2007JA012432. Google Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  • S. Biskri
    • 1
    • 2
  • J.-P. Antoine
    • 2
    Email author
  • B. Inhester
    • 3
  • F. Mekideche
    • 1
  1. 1.Laboratoire de Physique Théorique, Faculté de PhysiqueUniv. des Sciences et de la Technologie Houari Boumediène (USTHB)AlgerAlgeria
  2. 2.Institut de Physique ThéoriqueUniversité catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Max-Planck Institute for Solar System ResearchKatlenburg-LindauGermany

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