Abstract

Phase contrast X-ray tomography (PCT) enables the study of systems consisting of elements with similar atomic numbers. Processing datasets acquired using PCT is nontrivial because of the low-pass characteristics of the commonly used single-image phase retrieval algorithm. In this study, we introduce an image processing methodology that simultaneously utilizes both phase and attenuation components of an image obtained at a single detector distance. This novel method, combined with regularized Perona-Malik filter and bias-corrected fuzzy C-means algorithm, allows for automated segmentation of data acquired through four-dimensional PCT. Using this integrated approach, the three-dimensional coarsening morphology of an Aluminum-29.9wt% Silicon alloy can be analyzed.

© 2014 Optical Society of America

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References

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2014 (1)

E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
[Crossref]

2013 (2)

G. Lovric, S. Barré, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast x-ray microtomography of the lung alveoli,” J. Appl. Cryst. 46, 856–860 (2013).
[Crossref]

M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
[Crossref] [PubMed]

2012 (2)

D. J. Rowenhorst and P. W. Voorhees, “Measurement of interfacial evolution in three dimensions,” Ann. Rev. Mater. Res. 42, 105–124 (2012).
[Crossref]

F. Marone and M. Stampanoni, “Regridding reconstruction algorithm for real-time tomographic imaging,” J. Synchrotron Rad. 19, 1029–1037 (2012).
[Crossref]

2011 (3)

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: Software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron Rad. 18, 617–629 (2011).
[Crossref]

A. Burvall, U. Lundström, P. A. Takman, D. H. Larsson, and H. M. Hertz, “Phase retrieval in x-ray phase-contrast imaging suitable for tomography,” Opt. Express 19, 10359–10376 (2011).
[Crossref] [PubMed]

M. Mainberger, A. Bruhn, J. Weickert, and S. Forchhammer, “Optimising spatial and tonal data for homogeneous diffusion inpainting,” Pattern Recognit. 44, 1859–1873 (2011).
[Crossref]

2010 (1)

2009 (1)

P. Simmons, P. Chuang, M. L. Comer, J. E. Spowart, M. D. Uchic, and M. de Graef, “Application and further development of advanced image processing algorithms for automated analysis of serial section image data,” Modelling Simul. Mater. Sci. Eng. 17, 025002 (2009).
[Crossref]

2008 (2)

X. Wu, H. Lu, and A. Yan, “Phase-contrast x-ray tomography: Contrast mechanism and roles of phase retrieval,” Eur. J. Radiol. 68S, S8–S12 (2008).
[Crossref]

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved multidimensional velocimetric analysis of x-ray blood flow speckle patterns,” Appl. Phys. Lett. 93, 153901 (2008).
[Crossref]

2007 (1)

P. Mondregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Stat. Solidi A 204, 2746–2752 (2007).
[Crossref]

2006 (1)

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

2004 (2)

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
[Crossref]

F. Voci, S. Eiho, N. Sugimoto, and H. Sekiguchi, “Estimating the gradient threshold in the perona-malik equation,” IEEE Signal Proc. Mag. 21, 39–46 (2004).
[Crossref]

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

2000 (1)

T. Otaki, “Artifact halo reduction in phase contrast microscopy using apodization,” Opt. Rev. 7, 119–122 (2000).
[Crossref]

1999 (1)

M. L. Comer and E. J. Delp, “Segmentation of textured images using a multiresolution gaussian autoregressive model,” IEEE Trans. Image Process. 8, 408–420 (1999).
[Crossref]

1996 (1)

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[Crossref]

1992 (1)

F. Catté, P. L. Lions, J. M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[Crossref]

1990 (2)

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[Crossref]

Y. K. Lee and W. T. Rhodes, “Nonlinear image processing by a rotating kernel transformation,” Opt. Lett. 15, 1383–1385 (1990).
[Crossref] [PubMed]

1985 (2)

J. A. Hartigan and P. M. Hartigan, “The dip test of unimodality,” Ann. Stat. 13, 70–83 (1985).
[Crossref]

L. Hubert and P. Arabie, “Comparing partitions,” J. Classif. 2, 193–218 (1985).
[Crossref]

1984 (1)

J. C. Bezdek, R. Ehrlich, and W. Full, “Fcm: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10, 191–203 (1984).
[Crossref]

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. SMC-9, 62–66 (1979).

1973 (1)

J. C. Dunn, “A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters,” J. Cybern. 3, 32–57 (1973).
[Crossref]

1971 (1)

W. M. Rand, “Objective criteria for the evaluation of clustering methods,” J. Am. Stat. Assoc. 66, 846–850 (1971).
[Crossref]

Abela, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

Ahmed, M. N.

M. N. Ahmed, S. M. Yamany, A. A. Farag, and T. Moriarty, “Bias field estimation and adaptive segmentation of mri data using a modified fuzzy c-means algorithm,” in Proc. IEEE Int. Conf. Computer Vision and Pattern Recogn. (1999), Vol. 1.

Arabie, P.

L. Hubert and P. Arabie, “Comparing partitions,” J. Classif. 2, 193–218 (1985).
[Crossref]

Ballester, C.

M. Bertalmío, G. Sapiro, V. Caselles, and C. Ballester, “Image inpainting,” in Proc. SIGGRAPH 2000 (2000).

Barré, S.

G. Lovric, S. Barré, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast x-ray microtomography of the lung alveoli,” J. Appl. Cryst. 46, 856–860 (2013).
[Crossref]

Barrett, R.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[Crossref]

Baruchel, J.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[Crossref]

Beltran, M. A.

Bertalmío, M.

M. Bertalmío, G. Sapiro, V. Caselles, and C. Ballester, “Image inpainting,” in Proc. SIGGRAPH 2000 (2000).

Bertrand, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

Betemps, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

Bezdek, J. C.

J. C. Bezdek, R. Ehrlich, and W. Full, “Fcm: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10, 191–203 (1984).
[Crossref]

Bhler, P.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

Bruhn, A.

M. Mainberger, A. Bruhn, J. Weickert, and S. Forchhammer, “Optimising spatial and tonal data for homogeneous diffusion inpainting,” Pattern Recognit. 44, 1859–1873 (2011).
[Crossref]

Burvall, A.

Caselles, V.

M. Bertalmío, G. Sapiro, V. Caselles, and C. Ballester, “Image inpainting,” in Proc. SIGGRAPH 2000 (2000).

Catté, F.

F. Catté, P. L. Lions, J. M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[Crossref]

Cavallaro, A.

M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
[Crossref] [PubMed]

Chen, Q.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

Chuang, P.

P. Simmons, P. Chuang, M. L. Comer, J. E. Spowart, M. D. Uchic, and M. de Graef, “Application and further development of advanced image processing algorithms for automated analysis of serial section image data,” Modelling Simul. Mater. Sci. Eng. 17, 025002 (2009).
[Crossref]

Cloetens, P.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[Crossref]

Coll, T.

F. Catté, P. L. Lions, J. M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[Crossref]

Comer, M. L.

P. Simmons, P. Chuang, M. L. Comer, J. E. Spowart, M. D. Uchic, and M. de Graef, “Application and further development of advanced image processing algorithms for automated analysis of serial section image data,” Modelling Simul. Mater. Sci. Eng. 17, 025002 (2009).
[Crossref]

M. L. Comer and E. J. Delp, “Segmentation of textured images using a multiresolution gaussian autoregressive model,” IEEE Trans. Image Process. 8, 408–420 (1999).
[Crossref]

Dankerl, P.

M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
[Crossref] [PubMed]

de Graef, M.

P. Simmons, P. Chuang, M. L. Comer, J. E. Spowart, M. D. Uchic, and M. de Graef, “Application and further development of advanced image processing algorithms for automated analysis of serial section image data,” Modelling Simul. Mater. Sci. Eng. 17, 025002 (2009).
[Crossref]

Debeir, O.

O. Debeir, N. Warzee, P. V. Ham, and C. Decaestecker, “Phase contrast image segmentation by weak watershed transform assembly,” in 5th IEEE Int. Symp. Biomed. Imaging (2008), pp. 724–727.

Decaestecker, C.

O. Debeir, N. Warzee, P. V. Ham, and C. Decaestecker, “Phase contrast image segmentation by weak watershed transform assembly,” in 5th IEEE Int. Symp. Biomed. Imaging (2008), pp. 724–727.

Delp, E. J.

M. L. Comer and E. J. Delp, “Segmentation of textured images using a multiresolution gaussian autoregressive model,” IEEE Trans. Image Process. 8, 408–420 (1999).
[Crossref]

Drechsler, K.

M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
[Crossref] [PubMed]

Dubsky, S.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved multidimensional velocimetric analysis of x-ray blood flow speckle patterns,” Appl. Phys. Lett. 93, 153901 (2008).
[Crossref]

Dunn, J. C.

J. C. Dunn, “A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters,” J. Cybern. 3, 32–57 (1973).
[Crossref]

Ehrlich, R.

J. C. Bezdek, R. Ehrlich, and W. Full, “Fcm: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10, 191–203 (1984).
[Crossref]

Eiho, S.

F. Voci, S. Eiho, N. Sugimoto, and H. Sekiguchi, “Estimating the gradient threshold in the perona-malik equation,” IEEE Signal Proc. Mag. 21, 39–46 (2004).
[Crossref]

Erdt, M.

M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
[Crossref] [PubMed]

Farag, A. A.

M. N. Ahmed, S. M. Yamany, A. A. Farag, and T. Moriarty, “Bias field estimation and adaptive segmentation of mri data using a modified fuzzy c-means algorithm,” in Proc. IEEE Int. Conf. Computer Vision and Pattern Recogn. (1999), Vol. 1.

Fife, J. L.

E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
[Crossref]

Forchhammer, S.

M. Mainberger, A. Bruhn, J. Weickert, and S. Forchhammer, “Optimising spatial and tonal data for homogeneous diffusion inpainting,” Pattern Recognit. 44, 1859–1873 (2011).
[Crossref]

Fouras, A.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved multidimensional velocimetric analysis of x-ray blood flow speckle patterns,” Appl. Phys. Lett. 93, 153901 (2008).
[Crossref]

Frommherz, U.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
[Crossref]

Full, W.

J. C. Bezdek, R. Ehrlich, and W. Full, “Fcm: The fuzzy c-means clustering algorithm,” Comput. Geosci. 10, 191–203 (1984).
[Crossref]

Gibbs, J. W.

E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
[Crossref]

A. J. Shahani, E. B. Gulsoy, J. W. Gibbs, and P. W. Voorhees, “Four-dimensional morphological characterization of Al-Si alloy during coarsening” (2014), Manuscript in preparation.

Groso, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
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E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
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A. J. Shahani, E. B. Gulsoy, J. W. Gibbs, and P. W. Voorhees, “Four-dimensional morphological characterization of Al-Si alloy during coarsening” (2014), Manuscript in preparation.

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D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
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T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: Software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron Rad. 18, 617–629 (2011).
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M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
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M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
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M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
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M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
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D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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Köhler, R.

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M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
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Lee, Y. K.

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S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved multidimensional velocimetric analysis of x-ray blood flow speckle patterns,” Appl. Phys. Lett. 93, 153901 (2008).
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D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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X. Wu, H. Lu, and A. Yan, “Phase-contrast x-ray tomography: Contrast mechanism and roles of phase retrieval,” Eur. J. Radiol. 68S, S8–S12 (2008).
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P. Mondregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Stat. Solidi A 204, 2746–2752 (2007).
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D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
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M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
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D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
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G. Lovric, S. Barré, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast x-ray microtomography of the lung alveoli,” J. Appl. Cryst. 46, 856–860 (2013).
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P. Mondregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Stat. Solidi A 204, 2746–2752 (2007).
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D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: Software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron Rad. 18, 617–629 (2011).
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G. Lovric, S. Barré, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast x-ray microtomography of the lung alveoli,” J. Appl. Cryst. 46, 856–860 (2013).
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P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
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E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
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G. Lovric, S. Barré, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast x-ray microtomography of the lung alveoli,” J. Appl. Cryst. 46, 856–860 (2013).
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F. Marone and M. Stampanoni, “Regridding reconstruction algorithm for real-time tomographic imaging,” J. Synchrotron Rad. 19, 1029–1037 (2012).
[Crossref]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the sls experience,” Proc. SPIE 6318, 63180M (2006).
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P. Simmons, P. Chuang, M. L. Comer, J. E. Spowart, M. D. Uchic, and M. de Graef, “Application and further development of advanced image processing algorithms for automated analysis of serial section image data,” Modelling Simul. Mater. Sci. Eng. 17, 025002 (2009).
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M. Hammon, A. Cavallaro, M. Erdt, P. Dankerl, M. Kirshner, K. Drechsler, S. Wesarg, M. Uder, and R. Janka, “Model-based pancreas segmentation in portal venous phase contrast-enhanced ct images,” J. Digit. Imaging 26, 1082–1090 (2013).
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Voci, F.

F. Voci, S. Eiho, N. Sugimoto, and H. Sekiguchi, “Estimating the gradient threshold in the perona-malik equation,” IEEE Signal Proc. Mag. 21, 39–46 (2004).
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E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
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A. J. Shahani, E. B. Gulsoy, J. W. Gibbs, and P. W. Voorhees, “Four-dimensional morphological characterization of Al-Si alloy during coarsening” (2014), Manuscript in preparation.

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O. Debeir, N. Warzee, P. V. Ham, and C. Decaestecker, “Phase contrast image segmentation by weak watershed transform assembly,” in 5th IEEE Int. Symp. Biomed. Imaging (2008), pp. 724–727.

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T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: Software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron Rad. 18, 617–629 (2011).
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M. Mainberger, A. Bruhn, J. Weickert, and S. Forchhammer, “Optimising spatial and tonal data for homogeneous diffusion inpainting,” Pattern Recognit. 44, 1859–1873 (2011).
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W. M. Rand, “Objective criteria for the evaluation of clustering methods,” J. Am. Stat. Assoc. 66, 846–850 (1971).
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G. Lovric, S. Barré, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast x-ray microtomography of the lung alveoli,” J. Appl. Cryst. 46, 856–860 (2013).
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J. Microsc. (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
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J. Phys. D Appl. Phys. (1)

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T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: Software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron Rad. 18, 617–629 (2011).
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E. B. Gulsoy, A. J. Shahani, J. W. Gibbs, J. L. Fife, and P. W. Voorhees, “Four-dimensional morphological evolution of coarsening of Aluminum Silicon alloy using phase-contrast x-ray tomography,” Mater. Trans., JIM 55, 161–164 (2014).
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Modelling Simul. Mater. Sci. Eng. (1)

P. Simmons, P. Chuang, M. L. Comer, J. E. Spowart, M. D. Uchic, and M. de Graef, “Application and further development of advanced image processing algorithms for automated analysis of serial section image data,” Modelling Simul. Mater. Sci. Eng. 17, 025002 (2009).
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D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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Opt. Express (2)

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Figures (9)

Fig. 1
Fig. 1 PCT experiment, where R2 is the detector distance, θ is the projection angle and λ is the wavelength of propagating wave. The frame (x, y, z) is the reference frame, while (r1, r2) lie in the plane of the imaging detector [4].
Fig. 2
Fig. 2 PAG images of Al-29.9 wt% Si sample coarsening for an elapsed time of 50 minutes. (a) As-cast microstructure is shown. Samples were coarsened in an isothermal furnace for (b–f) 10 minute increments at 590 °C.
Fig. 3
Fig. 3 Flowchart of PCT image-processing steps, beginning with the X-ray projections (at top) and ending with binarized output (at bottom).
Fig. 4
Fig. 4 Multimodal images with (a) c1 = 0, (b) c1 = 0.25, (c) c1 = 0.5, (d) c1 = 0.75, and (e) c1 = 1. (f) These images were assessed with respect to CN̂R and SH ^, where k1 > k2 > k3 are three different high-pass cut-off frequencies used in measuring SH ^. Optimal trade-off between CN̂R and SH ^ occurs at an intermediate value of c1.
Fig. 5
Fig. 5 Measurement of the resolution criterion for a line profile in (a) FBP image and (b) PAG image where |C(k)|2 is the spectral power of the detected signal, μs is the noise baseline, and kres is the maximum spatial frequency. Spatial frequencies are given in units of inverse pixels, px−1. The FBP image has a resolution that is approx. 40% greater than the PAG image.
Fig. 6
Fig. 6 (a) Plot of κ versus number of iterations of RPM algorithm. Static κ is fixed at a value of 0.05 which dynamic κ is given by Eq. (12), where κ0 = 0.1 and ω = 0.05. The filtered images produced using static κ and dynamic κ after 250 iterations are shown in (b) and (c), respectively. Dynamic κ preserves the edges of the Si laths better than the static case.
Fig. 7
Fig. 7 Segmentation steps on (a) 1D pre-processed, hybrid image: (b–d) isotropic, nonlinear diffusion smoothing with 50, 200, and 1,000 iterations, respectively, and final result (e) with bias-field corrections. The dotted line indicates that the eutectic-Si interface positions are preserved during the segmentation process, while the intra-phase noise is removed.
Fig. 8
Fig. 8 Segmentation steps on (a) 2D hybrid image: (b) pre-processing step with inpainted void, (c) isotropic, non-linear diffusion smoothing, (d) bias-field estimation and (e) subtraction from RPM filtered image, and (f) Otsu-thresholded output. Interface positions are preserved. All images are scaled to the range [0,255].
Fig. 9
Fig. 9 3D Si laths coarsening in time. The dark gray background is the eutectic. (a) As-cast microstructure is shown. Samples were coarsened in an isothermal furnace for (b–f) 10 minute increments at 590 °C. ROI shown is 296×296×159μm.

Equations (16)

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μ PAG ( x , y , z ) δ ( x , y , z )
μ FBP ( x , y , z ) 2 δ ( x , y , z ) + μ atten ( x , y , z ) + μ mixed ( x , y , z )
μ atten ( x , y , z ) = 4 π λ β ( x , y , z )
μ + ( x , y , z ) = c 1 μ PAG ( x , y , z ) + ( 1 c 1 ) μ FBP ( x , y , z )
CNR = 2 ( | S f S b | σ f + σ b )
SH = ξ ¯ H | μ + ( ξ ¯ ) | 2 d ξ ¯ / ξ ¯ B | μ + ( ξ ¯ ) | 2 d ξ ¯
x res = 2 π k res
t ( μ σ ( x , y , t ) ) = Div ( D ( | u σ ( x , y , t ) | 2 ) u σ ( x , y , t ) )
D ( | u σ ( x , y , t ) | 2 ) = Exp ( | u σ ( x , y , t ) | 2 κ 2 )
u σ ( x , y , t ) = K σ u ( x , y , t )
u ( x , y , 0 ) = μ + ( x , y )
κ ( t ) κ 0 Exp ( ω t )
J m = i = 1 c k = 1 N u i k p x k ν i 2 + α N R i = 1 c k = 1 N u i k p ( x r 𝒩 k x r ν i 2 )
y k = x k + β k
ARI = i j ( n i j 2 ) ( i ( a i 2 ) j ( b j 2 ) ) / ( n 2 ) 1 2 ( i ( a i 2 ) + j ( b j 2 ) ) ( i ( a i 2 ) j ( b j 2 ) ) / ( n 2 )
a i = j n i j , b j = i n i j , and n = i j n i j

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