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

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Abstract

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.

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Notes

  1. A good chicken egg has values for parameters \(a=m=1\) and \(5\le b\le 6\); this is the reason why one also refers to the “egg” naming the family.

  2. Note that if two or more local maxima are obtained in different cells, they essentially correspond to two or more different curves from the family.

  3. An angular resolution of 1.2-arcsec corresponds to a spatial resolution of about \(800\) km on the sun.

  4. The geostationary operational environment satellites (GOES) classification system classifies flares based on their X-ray flux in the wavelength range 1–8 Å. According to this classification, M-class flares are medium large flares.

    Fig. 8
    figure 8

    Detection of solar prominence profiles as seen in EUV 304 Å SDO/AIA images . a Quartic curve with a tacnode detected on the September 8, 2010 solar eruption, Eq. (10) with \(a=1.75\) and \(b=4.75\). The value of parameter \(m\) was fixed a priori (\(m=1\)). b Quartic curves with a tacnode detected on the March 30, 2010 solar eruption, Eq. (9) with \(a=8.82\cdot 10^{4}\) and \(m=3.85\cdot 10^{5}\) for the inner profile, \(a=7.92\cdot 10^{4}\) and \(m=3.7\cdot 10^{5}\) for the outer profile. In both cases the value of parameter \(b\) was fixed a priori (\(b=0.5\))

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Acknowledgments

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.

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Authors and Affiliations

  1. CNR-SPIN, Via Dodecaneso 33, 16146 , Genova, Italy

    Anna Maria Massone & Cristina Campi

  2. Dip. di Matematica, Università di Genova, Via Dodecaneso 35, 16146 , Genova, Italy

    Annalisa Perasso & Mauro C. Beltrametti

Authors
  1. Anna Maria Massone
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  2. Annalisa Perasso
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  3. Cristina Campi
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  4. Mauro C. Beltrametti
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Correspondence to Anna Maria Massone.

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Massone, A.M., Perasso, A., Campi, C. et al. Profile Detection in Medical and Astronomical Images by Means of the Hough Transform of Special Classes of Curves. J Math Imaging Vis 51, 296–310 (2015). https://doi.org/10.1007/s10851-014-0521-4

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  • DOI: https://doi.org/10.1007/s10851-014-0521-4

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