Abstract

We report an autocorrelation-based approach that accurately measures fractal organization within arbitrarily shaped (nonrectangular) regions of interest of gray-scale images. It extends fractal analysis beyond what is possible using fast Fourier transforms and improves on a previous autocorrelation algorithm. We illustrate its use in detecting subtle changes in mitochondrial organization within murine fibroblasts expressing the human papillomavirus E7 oncogene.

© 2013 Optical Society of America

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References

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  1. W. F. Sensakovic, A. Starkey, and S. G. Armato, Med. Phys. 34, 3465 (2007).
    [CrossRef]
  2. F. Sabetghadam, S. Sharafatmandjoor, and F. Norouzi, J. Comput. Phys. 228, 55 (2009).
    [CrossRef]
  3. D. Nečas and P. Klapetek, Ultramicroscopy 124, 13 (2013).
    [CrossRef]
  4. J. A. Fessler and B. P. Sutton, IEEE Trans. Signal Process. 51, 560 (2003).
    [CrossRef]
  5. H. Gothwal, S. Kedawat, and R. Kumar, J. Biomed. Sci. Eng. 4, 289 (2011).
    [CrossRef]
  6. R. Rajeswari and P. Anandhakumar, ACEEE Int. J. Commun. 2, 1 (2011).
  7. J. Xylas, K. P. Quinn, M. Hunter, and I. Georgakoudi, Opt. Express 20, 23442 (2012).
    [CrossRef]
  8. A. J. Einstein, H.-S. Wu, and J. Gil, Phys. Rev. Lett. 80, 397 (1998).
    [CrossRef]
  9. K. Metze, Epigenomics 2, 601 (2010).
    [CrossRef]
  10. R. F. Voss, Phys. Scr. T13, 27 (1986).
    [CrossRef]
  11. H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
    [CrossRef]
  12. C. L. Nguyen and K. Münger, J. Virol. 83, 1700 (2009).
    [CrossRef]

2013 (1)

D. Nečas and P. Klapetek, Ultramicroscopy 124, 13 (2013).
[CrossRef]

2012 (1)

2011 (2)

H. Gothwal, S. Kedawat, and R. Kumar, J. Biomed. Sci. Eng. 4, 289 (2011).
[CrossRef]

R. Rajeswari and P. Anandhakumar, ACEEE Int. J. Commun. 2, 1 (2011).

2010 (1)

K. Metze, Epigenomics 2, 601 (2010).
[CrossRef]

2009 (2)

F. Sabetghadam, S. Sharafatmandjoor, and F. Norouzi, J. Comput. Phys. 228, 55 (2009).
[CrossRef]

C. L. Nguyen and K. Münger, J. Virol. 83, 1700 (2009).
[CrossRef]

2007 (1)

W. F. Sensakovic, A. Starkey, and S. G. Armato, Med. Phys. 34, 3465 (2007).
[CrossRef]

2004 (1)

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

2003 (1)

J. A. Fessler and B. P. Sutton, IEEE Trans. Signal Process. 51, 560 (2003).
[CrossRef]

1998 (1)

A. J. Einstein, H.-S. Wu, and J. Gil, Phys. Rev. Lett. 80, 397 (1998).
[CrossRef]

1986 (1)

R. F. Voss, Phys. Scr. T13, 27 (1986).
[CrossRef]

Anandhakumar, P.

R. Rajeswari and P. Anandhakumar, ACEEE Int. J. Commun. 2, 1 (2011).

Armato, S. G.

W. F. Sensakovic, A. Starkey, and S. G. Armato, Med. Phys. 34, 3465 (2007).
[CrossRef]

Deligdisch, L.

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

Einstein, A. J.

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

A. J. Einstein, H.-S. Wu, and J. Gil, Phys. Rev. Lett. 80, 397 (1998).
[CrossRef]

Fessler, J. A.

J. A. Fessler and B. P. Sutton, IEEE Trans. Signal Process. 51, 560 (2003).
[CrossRef]

Georgakoudi, I.

Gil, J.

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

A. J. Einstein, H.-S. Wu, and J. Gil, Phys. Rev. Lett. 80, 397 (1998).
[CrossRef]

Gothwal, H.

H. Gothwal, S. Kedawat, and R. Kumar, J. Biomed. Sci. Eng. 4, 289 (2011).
[CrossRef]

Hunter, M.

Kalir, T.

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

Kedawat, S.

H. Gothwal, S. Kedawat, and R. Kumar, J. Biomed. Sci. Eng. 4, 289 (2011).
[CrossRef]

Klapetek, P.

D. Nečas and P. Klapetek, Ultramicroscopy 124, 13 (2013).
[CrossRef]

Kumar, R.

H. Gothwal, S. Kedawat, and R. Kumar, J. Biomed. Sci. Eng. 4, 289 (2011).
[CrossRef]

Metze, K.

K. Metze, Epigenomics 2, 601 (2010).
[CrossRef]

Münger, K.

C. L. Nguyen and K. Münger, J. Virol. 83, 1700 (2009).
[CrossRef]

Necas, D.

D. Nečas and P. Klapetek, Ultramicroscopy 124, 13 (2013).
[CrossRef]

Nguyen, C. L.

C. L. Nguyen and K. Münger, J. Virol. 83, 1700 (2009).
[CrossRef]

Norouzi, F.

F. Sabetghadam, S. Sharafatmandjoor, and F. Norouzi, J. Comput. Phys. 228, 55 (2009).
[CrossRef]

Quinn, K. P.

Rajeswari, R.

R. Rajeswari and P. Anandhakumar, ACEEE Int. J. Commun. 2, 1 (2011).

Sabetghadam, F.

F. Sabetghadam, S. Sharafatmandjoor, and F. Norouzi, J. Comput. Phys. 228, 55 (2009).
[CrossRef]

Sensakovic, W. F.

W. F. Sensakovic, A. Starkey, and S. G. Armato, Med. Phys. 34, 3465 (2007).
[CrossRef]

Sharafatmandjoor, S.

F. Sabetghadam, S. Sharafatmandjoor, and F. Norouzi, J. Comput. Phys. 228, 55 (2009).
[CrossRef]

Starkey, A.

W. F. Sensakovic, A. Starkey, and S. G. Armato, Med. Phys. 34, 3465 (2007).
[CrossRef]

Sutton, B. P.

J. A. Fessler and B. P. Sutton, IEEE Trans. Signal Process. 51, 560 (2003).
[CrossRef]

Voss, R. F.

R. F. Voss, Phys. Scr. T13, 27 (1986).
[CrossRef]

Wu, H. S.

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

Wu, H.-S.

A. J. Einstein, H.-S. Wu, and J. Gil, Phys. Rev. Lett. 80, 397 (1998).
[CrossRef]

Xylas, J.

ACEEE Int. J. Commun. (1)

R. Rajeswari and P. Anandhakumar, ACEEE Int. J. Commun. 2, 1 (2011).

Epigenomics (1)

K. Metze, Epigenomics 2, 601 (2010).
[CrossRef]

Fractals (1)

H. S. Wu, A. J. Einstein, L. Deligdisch, T. Kalir, and J. Gil, Fractals 12, 157 (2004).
[CrossRef]

IEEE Trans. Signal Process. (1)

J. A. Fessler and B. P. Sutton, IEEE Trans. Signal Process. 51, 560 (2003).
[CrossRef]

J. Biomed. Sci. Eng. (1)

H. Gothwal, S. Kedawat, and R. Kumar, J. Biomed. Sci. Eng. 4, 289 (2011).
[CrossRef]

J. Comput. Phys. (1)

F. Sabetghadam, S. Sharafatmandjoor, and F. Norouzi, J. Comput. Phys. 228, 55 (2009).
[CrossRef]

J. Virol. (1)

C. L. Nguyen and K. Münger, J. Virol. 83, 1700 (2009).
[CrossRef]

Med. Phys. (1)

W. F. Sensakovic, A. Starkey, and S. G. Armato, Med. Phys. 34, 3465 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (1)

A. J. Einstein, H.-S. Wu, and J. Gil, Phys. Rev. Lett. 80, 397 (1998).
[CrossRef]

Phys. Scr. (1)

R. F. Voss, Phys. Scr. T13, 27 (1986).
[CrossRef]

Ultramicroscopy (1)

D. Nečas and P. Klapetek, Ultramicroscopy 124, 13 (2013).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Comparison of FFT and ACF methods. Each data point is an average of measured H values from eight independently generated and masked synthetic FBS images.

Fig. 2.
Fig. 2.

ACF-based fractal analysis of nonrectangular objects. Insets: NAD(P)H fluorescence image and ACF of murine fibroblasts (a) without and (b) with HPV-16 E7 expression. Yellow=cellular ROI; cyan=external sources; tinted semicircular ACF overlay=points fitted. Solid black lines=exponential fit to the data.

Fig. 3.
Fig. 3.

ACF-based fractal analysis of null and E7-expressing cells. Box-and-whisker plots show improved discrimination using the calibrated Hurst parameter.

Equations (1)

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r(δ)=1NMδ[(Iδμ(Iδ)σ(Iδ))(Iμ(I)σ(I))],

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