Abstract

The morphological characterization of quasi-planar structures represented by gray-scale images is challenging when object identification is sub-optimal due to registration artifacts. We propose two alternative procedures that enhances object identification in the integral-geometry morphological image analysis (MIA) framework. The first variant streamlines the framework by introducing an active contours segmentation process whose time step is recycled as a multi-scale parameter. In the second variant, we used the refined object identification produced in the first variant to perform the standard MIA with exact dilation radius as multi-scale parameter. Using this enhanced MIA we quantify the extent of vaso-obliteration in oxygen-induced retinopathic vascular growth, the preventative effect (by photobiomodulation) of exposure during tissue development to near-infrared light (NIR, 670 nm), and the lack of adverse effects due to exposure to NIR light.

© 2014 Optical Society of America

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2013 (3)

R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
[CrossRef] [PubMed]

M. S. Barbosa, A. Bubna-Litic, and T. Maddess, “Locally countable properties and the perceptual salience of textures,” J. Opt. Soc. Am. A 30, 1687–1697 (2013).
[CrossRef]

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision 13, 21 (2013).
[CrossRef]

2012 (3)

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A 29, 1313–1345 (2012).
[CrossRef]

S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
[CrossRef] [PubMed]

R. Albarracin and K. Valter, “670 nm red light preconditioning supports muller cell function: Evidence from the white light-induced damage model in the rat retina,” Photochem. Photobiol. 88, 1418–1427 (2012).
[CrossRef] [PubMed]

2011 (3)

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
[CrossRef] [PubMed]

R. Albarracin, J. Eells, and K. Valter, “Photobiomodulation protects the retina from light-induced photoreceptor degeneration,” Invest. Ophthalmol. Visual Sci. 52, 3582–3592 (2011).
[CrossRef]

2010 (5)

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software 33(1), 1–22 (2010).

G. Tkačik, J. S. Prentice, J. D. Victor, and V. Balasubramanian, “Local statistics in natural scenes predict the saliency of synthetic textures,” Proc. Nat. Acad. Sci. USA 107, 18149–18154 (2010).
[CrossRef]

R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
[CrossRef] [PubMed]

G. A. Strasser, J. S. Kaminker, and M. Tessier-Lavigne, “Microarray analysis of retinal endothelial tip cells identifies CXCR4 as a mediator of tip cell morphology and branching,” Blood 115, 5102–5110 (2010).
[CrossRef] [PubMed]

2009 (2)

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

2008 (3)

H. Mantz, K. Jacobs, and K. Mecke, “Utilizing minkowski functionals for image analysis: a marching square algorithm,” J. Stat. Mech.: Theory Exp. 2008, P12015 (2008).
[CrossRef]

R. A. Neher, K. Mecke, and H. Wagner, “Topological estimation of percolation thresholds,” J. Stat. Mech.: Theory Exp. 2008, P01011 (2008).
[CrossRef]

R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

2007 (1)

P. C. L. Silveira, E. L. Streck, and R. A. Pinho, “Evaluation of mitochondrial respiratory chain activity in wound healing by low-level laser therapy,” J. Photochem. Photobiol., B 86, 279–282 (2007).
[CrossRef]

2006 (1)

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B 52(4), 531–546 (2006).
[CrossRef]

2005 (1)

L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir 21, 992–1000 (2005).
[CrossRef] [PubMed]

2004 (2)

M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

2003 (2)

J. Maurer, R. Qi, and V. Raghavan, “A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence 25(2), 265–270 (2003).
[CrossRef]

M. Barbosa, L. da F. Costa, and E. de S. Bernardes, “Neuromorphometric characterization with shape functionals,” Phys. Rev. E.  67, 061910 (2003).
[CrossRef]

2001 (2)

K. Michielsen and H. De Raedt, “Integral-geometry morphological image analysis,” Phys. Rep. 347(6), 461–538 (2001).
[CrossRef]

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing 10, 266–277 (2001).
[CrossRef]

2000 (1)

K. Michielsen, H. De Raedt, and J. Fraaije, “Morphological characterization of spatial patterns,” Prog. Theor. Phys. Suppl. 138, 543–548 (2000).
[CrossRef]

1999 (1)

T. Karu, “Primary and secondary mechanisms of action of visible to near-IR radiation on cells,” J. Photochem. Photobiol., B 49, 1–17 (1999).
[CrossRef]

1997 (1)

L. D. Cohen and R. Kimmel, “Global minimum for active contour models: A minimal path approach,” Int. J. Comp. Vision 24, 57–78 (1997).
[CrossRef]

1996 (1)

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. USA 93, 1591–1595 (1996).
[CrossRef] [PubMed]

1991 (1)

L. Vincent, “Morphological transformations of binary images with arbitrary structuring elements,” Signal Processing 22, 3–23 (1991).
[CrossRef]

1989 (1)

D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics 42, 577–685 (1989).
[CrossRef]

1976 (1)

J. F. Jarvis, C. N. Judice, and W. H. Ninke, “A survey of techniques for the display of continuous tone pictures on bilevel displays,” Computer Graphics and Image Processing 5, 13–40 (1976).
[CrossRef]

1973 (1)

R. Sibson, “SLINK: an optimally efficient algorithm for the single-link cluster method,” The Computer Journal 16, 30–34 (1973).
[CrossRef]

Aderman, C. M.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Albarracin, R.

R. Albarracin and K. Valter, “670 nm red light preconditioning supports muller cell function: Evidence from the white light-induced damage model in the rat retina,” Photochem. Photobiol. 88, 1418–1427 (2012).
[CrossRef] [PubMed]

R. Albarracin, J. Eells, and K. Valter, “Photobiomodulation protects the retina from light-induced photoreceptor degeneration,” Invest. Ophthalmol. Visual Sci. 52, 3582–3592 (2011).
[CrossRef]

Armstrong, P.

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
[CrossRef] [PubMed]

Atti, E.

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

Balasubramanian, V.

G. Tkačik, J. S. Prentice, J. D. Victor, and V. Balasubramanian, “Local statistics in natural scenes predict the saliency of synthetic textures,” Proc. Nat. Acad. Sci. USA 107, 18149–18154 (2010).
[CrossRef]

Banhart, J.

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

Barbosa, M.

R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
[CrossRef] [PubMed]

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B 52(4), 531–546 (2006).
[CrossRef]

M. Barbosa, L. da F. Costa, and E. de S. Bernardes, “Neuromorphometric characterization with shape functionals,” Phys. Rev. E.  67, 061910 (2003).
[CrossRef]

Barbosa, M. S.

M. S. Barbosa, A. Bubna-Litic, and T. Maddess, “Locally countable properties and the perceptual salience of textures,” J. Opt. Soc. Am. A 30, 1687–1697 (2013).
[CrossRef]

M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

Beisbart, C.

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B 52(4), 531–546 (2006).
[CrossRef]

Bernardes, E. de S.

M. Barbosa, L. da F. Costa, and E. de S. Bernardes, “Neuromorphometric characterization with shape functionals,” Phys. Rev. E.  67, 061910 (2003).
[CrossRef]

Bernardes, E. S.

M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

Bisti, S.

R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

Boskey, A.

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

Breidenbach, B.

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

Bubna-Litic, A.

Buchman, E. V.

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

Chan, T. F.

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing 10, 266–277 (2001).
[CrossRef]

Chen, J.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Cohen, L. D.

L. D. Cohen and R. Kimmel, “Global minimum for active contour models: A minimal path approach,” Int. J. Comp. Vision 24, 57–78 (1997).
[CrossRef]

Connor, K. M.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Conte, M. M.

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision 13, 21 (2013).
[CrossRef]

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A 29, 1313–1345 (2012).
[CrossRef]

Costa, L. d. F.

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B 52(4), 531–546 (2006).
[CrossRef]

M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

Costa, L. da F.

M. Barbosa, L. da F. Costa, and E. de S. Bernardes, “Neuromorphometric characterization with shape functionals,” Phys. Rev. E.  67, 061910 (2003).
[CrossRef]

Dahlstrom, J.

R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
[CrossRef] [PubMed]

Das, R.

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

De Hosson, J.

K. Michelsen, H. De Raedt, and J. De Hosson, “Aspects of mathematical morphology,” in Advances in Imaging and Electron Physics (B. K. Peter, W. Hawkes, and T. Mulvey, eds.) (Elsevier, 2003) vol. Volume 125, pp. 119–194,.

De Raedt, H.

K. Michielsen and H. De Raedt, “Integral-geometry morphological image analysis,” Phys. Rep. 347(6), 461–538 (2001).
[CrossRef]

K. Michielsen, H. De Raedt, and J. Fraaije, “Morphological characterization of spatial patterns,” Prog. Theor. Phys. Suppl. 138, 543–548 (2000).
[CrossRef]

K. Michelsen, H. De Raedt, and J. De Hosson, “Aspects of mathematical morphology,” in Advances in Imaging and Electron Physics (B. K. Peter, W. Hawkes, and T. Mulvey, eds.) (Elsevier, 2003) vol. Volume 125, pp. 119–194,.

Dennison, R. J.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
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R. Albarracin, J. Eells, and K. Valter, “Photobiomodulation protects the retina from light-induced photoreceptor degeneration,” Invest. Ophthalmol. Visual Sci. 52, 3582–3592 (2011).
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R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

Eells, J. T.

R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

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K. Michielsen, H. De Raedt, and J. Fraaije, “Morphological characterization of spatial patterns,” Prog. Theor. Phys. Suppl. 138, 543–548 (2000).
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J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software 33(1), 1–22 (2010).

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M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

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J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

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K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Hara, H.

S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
[CrossRef] [PubMed]

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J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software 33(1), 1–22 (2010).

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J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

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J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
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A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

Hutzler, S.

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

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A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
[CrossRef] [PubMed]

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S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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H. Mantz, K. Jacobs, and K. Mecke, “Utilizing minkowski functionals for image analysis: a marching square algorithm,” J. Stat. Mech.: Theory Exp. 2008, P12015 (2008).
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J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
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J. F. Jarvis, C. N. Judice, and W. H. Ninke, “A survey of techniques for the display of continuous tone pictures on bilevel displays,” Computer Graphics and Image Processing 5, 13–40 (1976).
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J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

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L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir 21, 992–1000 (2005).
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K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

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R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

Losnegård, A.

A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
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K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

Lundervold, A.

A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
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Mantz, H.

H. Mantz, K. Jacobs, and K. Mecke, “Utilizing minkowski functionals for image analysis: a marching square algorithm,” J. Stat. Mech.: Theory Exp. 2008, P12015 (2008).
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J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
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J. Maurer, R. Qi, and V. Raghavan, “A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence 25(2), 265–270 (2003).
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K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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H. Mantz, K. Jacobs, and K. Mecke, “Utilizing minkowski functionals for image analysis: a marching square algorithm,” J. Stat. Mech.: Theory Exp. 2008, P12015 (2008).
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R. A. Neher, K. Mecke, and H. Wagner, “Topological estimation of percolation thresholds,” J. Stat. Mech.: Theory Exp. 2008, P01011 (2008).
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L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir 21, 992–1000 (2005).
[CrossRef] [PubMed]

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

Michelsen, K.

K. Michelsen, H. De Raedt, and J. De Hosson, “Aspects of mathematical morphology,” in Advances in Imaging and Electron Physics (B. K. Peter, W. Hawkes, and T. Mulvey, eds.) (Elsevier, 2003) vol. Volume 125, pp. 119–194,.

Michielsen, K.

K. Michielsen and H. De Raedt, “Integral-geometry morphological image analysis,” Phys. Rep. 347(6), 461–538 (2001).
[CrossRef]

K. Michielsen, H. De Raedt, and J. Fraaije, “Morphological characterization of spatial patterns,” Prog. Theor. Phys. Suppl. 138, 543–548 (2000).
[CrossRef]

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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

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A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
[CrossRef] [PubMed]

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S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
[CrossRef] [PubMed]

Natoli, R.

R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
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R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

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R. A. Neher, K. Mecke, and H. Wagner, “Topological estimation of percolation thresholds,” J. Stat. Mech.: Theory Exp. 2008, P01011 (2008).
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J. F. Jarvis, C. N. Judice, and W. H. Ninke, “A survey of techniques for the display of continuous tone pictures on bilevel displays,” Computer Graphics and Image Processing 5, 13–40 (1976).
[CrossRef]

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S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
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M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

Peterson, M.

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
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Qi, R.

J. Maurer, R. Qi, and V. Raghavan, “A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence 25(2), 265–270 (2003).
[CrossRef]

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J. Maurer, R. Qi, and V. Raghavan, “A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence 25(2), 265–270 (2003).
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M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
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L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir 21, 992–1000 (2005).
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R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
[CrossRef] [PubMed]

Saadatfar, M.

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

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K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
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G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
[CrossRef] [PubMed]

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

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Schollmeyer, H.

L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir 21, 992–1000 (2005).
[CrossRef] [PubMed]

Schröder-Turk, G. E.

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
[CrossRef] [PubMed]

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

Schwieger, W.

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
[CrossRef] [PubMed]

Serra, J. P.

J. P. Serra, Image Analysis and Mathematical Morphology (Kluwer Academic, Mar. 1984).

J. P. Serra, Image Analysis and Mathematical Morphology: Theoretical Advances (Kluwer Academic, 1988).

Sethian, J. A.

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. USA 93, 1591–1595 (1996).
[CrossRef] [PubMed]

Shah, J.

D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics 42, 577–685 (1989).
[CrossRef]

Sheppard, A.

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

Shimazawa, M.

S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
[CrossRef] [PubMed]

Sibson, R.

R. Sibson, “SLINK: an optimally efficient algorithm for the single-link cluster method,” The Computer Journal 16, 30–34 (1973).
[CrossRef]

Silveira, P. C. L.

P. C. L. Silveira, E. L. Streck, and R. A. Pinho, “Evaluation of mitochondrial respiratory chain activity in wound healing by low-level laser therapy,” J. Photochem. Photobiol., B 86, 279–282 (2007).
[CrossRef]

Smith, L. E. H.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Soille, P.

P. Soille, Morphological Image Analysis: Principles and Applications (Springer, 1999).
[CrossRef]

Stahl, A.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Stone, J.

R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

Strasser, G. A.

G. A. Strasser, J. S. Kaminker, and M. Tessier-Lavigne, “Microarray analysis of retinal endothelial tip cells identifies CXCR4 as a mediator of tip cell morphology and branching,” Blood 115, 5102–5110 (2010).
[CrossRef] [PubMed]

Streck, E. L.

P. C. L. Silveira, E. L. Streck, and R. A. Pinho, “Evaluation of mitochondrial respiratory chain activity in wound healing by low-level laser therapy,” J. Photochem. Photobiol., B 86, 279–282 (2007).
[CrossRef]

Tessier-Lavigne, M.

G. A. Strasser, J. S. Kaminker, and M. Tessier-Lavigne, “Microarray analysis of retinal endothelial tip cells identifies CXCR4 as a mediator of tip cell morphology and branching,” Blood 115, 5102–5110 (2010).
[CrossRef] [PubMed]

Tetradis, S.

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

Thengone, D. J.

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision 13, 21 (2013).
[CrossRef]

Tibshirani, R.

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software 33(1), 1–22 (2010).

Tkacik, G.

G. Tkačik, J. S. Prentice, J. D. Victor, and V. Balasubramanian, “Local statistics in natural scenes predict the saliency of synthetic textures,” Proc. Nat. Acad. Sci. USA 107, 18149–18154 (2010).
[CrossRef]

Tsuruma, K.

S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
[CrossRef] [PubMed]

Valter, K.

R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
[CrossRef] [PubMed]

R. Albarracin and K. Valter, “670 nm red light preconditioning supports muller cell function: Evidence from the white light-induced damage model in the rat retina,” Photochem. Photobiol. 88, 1418–1427 (2012).
[CrossRef] [PubMed]

R. Albarracin, J. Eells, and K. Valter, “Photobiomodulation protects the retina from light-induced photoreceptor degeneration,” Invest. Ophthalmol. Visual Sci. 52, 3582–3592 (2011).
[CrossRef]

R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

van der Meulen, M.

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

Verdelis, K.

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

VerHoeve, J.

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

Vese, L. A.

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing 10, 266–277 (2001).
[CrossRef]

Victor, J. D.

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision 13, 21 (2013).
[CrossRef]

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A 29, 1313–1345 (2012).
[CrossRef]

G. Tkačik, J. S. Prentice, J. D. Victor, and V. Balasubramanian, “Local statistics in natural scenes predict the saliency of synthetic textures,” Proc. Nat. Acad. Sci. USA 107, 18149–18154 (2010).
[CrossRef]

Vincent, L.

L. Vincent, “Morphological transformations of binary images with arbitrary structuring elements,” Signal Processing 22, 3–23 (1991).
[CrossRef]

L. Vincent, “Exact euclidean distance function by chain propagations,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991. Proceedings CVPR ’91, pp. 520–525, June 1991.

Wagner, H.

R. A. Neher, K. Mecke, and H. Wagner, “Topological estimation of percolation thresholds,” J. Stat. Mech.: Theory Exp. 2008, P01011 (2008).
[CrossRef]

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B 52(4), 531–546 (2006).
[CrossRef]

Weaire, D.

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

Weil, W.

R. Schneider and W. Weil, Stochastic and Integral Geometry (Springer, Oct. 2008).
[CrossRef]

Whelan, H. T.

R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

Willett, K. L.

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Wong-Riley, M. T.

R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

Wong-Riley, M. T. T.

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

Ying, R.

R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

Zhu, Y.

R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

Adv. Mater. (1)

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski tensor shape analysis of cellular, granular and porous structures,” Adv. Mater. 23(22), 2535–2553, 2011.
[CrossRef] [PubMed]

Blood (1)

G. A. Strasser, J. S. Kaminker, and M. Tessier-Lavigne, “Microarray analysis of retinal endothelial tip cells identifies CXCR4 as a mediator of tip cell morphology and branching,” Blood 115, 5102–5110 (2010).
[CrossRef] [PubMed]

Bone (1)

K. Verdelis, L. Lukashova, E. Atti, P. Mayer-Kuckuk, M. Peterson, S. Tetradis, A. Boskey, and M. van der Meulen, “MicroCT morphometry analysis of mouse cancellous bone: Intra- and inter-system reproducibility,” Bone 49, 580–587 (2011).
[CrossRef] [PubMed]

Brain Res. (1)

R. Ying, H. L. Liang, H. T. Whelan, J. T. Eells, and M. T. Wong-Riley, “Pretreatment with near-infrared light via light-emitting diode provides added benefit against rotenone- and MPP+-induced neurotoxicity,” Brain Res. 1243, 167–173 (2008).
[CrossRef] [PubMed]

Colloids Surf., A (1)

M. Saadatfar, F. Garcia-Moreno, S. Hutzler, A. Sheppard, M. Knackstedt, J. Banhart, and D. Weaire, “Imaging of metallic foams using x-ray micro-CT,” Colloids Surf., A 344, 107–112 (2009).
[CrossRef]

Communications on Pure and Applied Mathematics (1)

D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics 42, 577–685 (1989).
[CrossRef]

Computer Graphics and Image Processing (1)

J. F. Jarvis, C. N. Judice, and W. H. Ninke, “A survey of techniques for the display of continuous tone pictures on bilevel displays,” Computer Graphics and Image Processing 5, 13–40 (1976).
[CrossRef]

Eur. Phys. J. B (1)

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B 52(4), 531–546 (2006).
[CrossRef]

IEEE Trans. Image Processing (1)

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing 10, 266–277 (2001).
[CrossRef]

IEEE Trans. Pattern Analysis and Machine Intelligence (1)

J. Maurer, R. Qi, and V. Raghavan, “A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence 25(2), 265–270 (2003).
[CrossRef]

Int. J. Comp. Vision (1)

L. D. Cohen and R. Kimmel, “Global minimum for active contour models: A minimal path approach,” Int. J. Comp. Vision 24, 57–78 (1997).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

R. Albarracin, J. Eells, and K. Valter, “Photobiomodulation protects the retina from light-induced photoreceptor degeneration,” Invest. Ophthalmol. Visual Sci. 52, 3582–3592 (2011).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opti. Soc. Am. A (1)

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A 29, 1313–1345 (2012).
[CrossRef]

J. Photochem. Photobiol., B (2)

P. C. L. Silveira, E. L. Streck, and R. A. Pinho, “Evaluation of mitochondrial respiratory chain activity in wound healing by low-level laser therapy,” J. Photochem. Photobiol., B 86, 279–282 (2007).
[CrossRef]

T. Karu, “Primary and secondary mechanisms of action of visible to near-IR radiation on cells,” J. Photochem. Photobiol., B 49, 1–17 (1999).
[CrossRef]

J. Stat. Mech.: Theory Exp. (2)

H. Mantz, K. Jacobs, and K. Mecke, “Utilizing minkowski functionals for image analysis: a marching square algorithm,” J. Stat. Mech.: Theory Exp. 2008, P12015 (2008).
[CrossRef]

R. A. Neher, K. Mecke, and H. Wagner, “Topological estimation of percolation thresholds,” J. Stat. Mech.: Theory Exp. 2008, P01011 (2008).
[CrossRef]

J. Stat. Software (1)

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software 33(1), 1–22 (2010).

J. Vision (1)

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision 13, 21 (2013).
[CrossRef]

Langmuir (1)

L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir 21, 992–1000 (2005).
[CrossRef] [PubMed]

Mitochondrion (1)

J. T. Eells, M. T. T. Wong-Riley, J. VerHoeve, M. Henry, E. V. Buchman, M. P. Kane, L. J. Gould, R. Das, M. Jett, B. D. Hodgson, D. Margolis, and H. T. Whelan, “Mitochondrial signal transduction in accelerated wound and retinal healing by near-infrared light therapy,” Mitochondrion 4, 559–567 (2004).
[CrossRef]

Mol. Vision (1)

R. Natoli, Y. Zhu, K. Valter, S. Bisti, J. Eells, and J. Stone, “Gene and noncoding RNA regulation underlying photoreceptor protection: microarray study of dietary antioxidant saffron and photobiomodulation in rat retina,” Mol. Vision 16, 1801–1822 (2010).

Nature Protocols (1)

K. M. Connor, N. M. Krah, R. J. Dennison, C. M. Aderman, J. Chen, K. I. Guerin, P. Sapieha, A. Stahl, K. L. Willett, and L. E. H. Smith, “Quantification of oxygen-induced retinopathy in the mouse: a model of vessel loss, vessel regrowth and pathological angiogenesis,” Nature Protocols 4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Photochem. Photobiol. (1)

R. Albarracin and K. Valter, “670 nm red light preconditioning supports muller cell function: Evidence from the white light-induced damage model in the rat retina,” Photochem. Photobiol. 88, 1418–1427 (2012).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

A. Losnegård, L. B. Hysing, L. P. Muren, E. Hodneland, and A. Lundervold, “Semi-automated segmentation of the sigmoid and descending colon for radiotherapy planning using the fast marching method,” Phys. Med. Biol. 55, 5569 (2010).
[CrossRef] [PubMed]

Phys. Rep. (1)

K. Michielsen and H. De Raedt, “Integral-geometry morphological image analysis,” Phys. Rep. 347(6), 461–538 (2001).
[CrossRef]

Phys. Rev. E (1)

M. Barbosa, L. da F. Costa, and E. de S. Bernardes, “Neuromorphometric characterization with shape functionals,” Phys. Rev. E.  67, 061910 (2003).
[CrossRef]

PLoS One (2)

R. Natoli, K. Valter, M. Barbosa, J. Dahlstrom, M. Rutar, A. Kent, and J. Provis, “670nm photobiomodulation as a novel protection against retinopathy of prematurity: Evidence from oxygen induced retinopathy models,” PLoS One 8, e72135 (2013).
[CrossRef] [PubMed]

S. Nakamura, S. Imai, H. Ogishima, K. Tsuruma, M. Shimazawa, and H. Hara, “Morphological and functional changes in the retina after chronic oxygen-induced retinopathy,” PLoS One 7, e32167 (2012).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci. USA (1)

G. Tkačik, J. S. Prentice, J. D. Victor, and V. Balasubramanian, “Local statistics in natural scenes predict the saliency of synthetic textures,” Proc. Nat. Acad. Sci. USA 107, 18149–18154 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. USA 93, 1591–1595 (1996).
[CrossRef] [PubMed]

Prog. Theor. Phys. Suppl. (1)

K. Michielsen, H. De Raedt, and J. Fraaije, “Morphological characterization of spatial patterns,” Prog. Theor. Phys. Suppl. 138, 543–548 (2000).
[CrossRef]

Signal Processing (1)

L. Vincent, “Morphological transformations of binary images with arbitrary structuring elements,” Signal Processing 22, 3–23 (1991).
[CrossRef]

TEur. Phys. J. B (1)

M. S. Barbosa, L. d. F. Costa, E. S. Bernardes, G. Ramakers, and J. v. Pelt, “Characterizing neuromorphologic alterations with additive shape functionals,” TEur. Phys. J. B 37, 109–115 (2004).

The Computer Journal (1)

R. Sibson, “SLINK: an optimally efficient algorithm for the single-link cluster method,” The Computer Journal 16, 30–34 (1973).
[CrossRef]

Other (8)

F. Matheron, Random Sets and Integral Geometry (John Wiley & Sons Inc, Feb. 1975).

J. P. Serra, Image Analysis and Mathematical Morphology (Kluwer Academic, Mar. 1984).

J. P. Serra, Image Analysis and Mathematical Morphology: Theoretical Advances (Kluwer Academic, 1988).

P. Soille, Morphological Image Analysis: Principles and Applications (Springer, 1999).
[CrossRef]

G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” arXiv:1009.2340, Sept. 2010.

R. Schneider and W. Weil, Stochastic and Integral Geometry (Springer, Oct. 2008).
[CrossRef]

L. Vincent, “Exact euclidean distance function by chain propagations,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991. Proceedings CVPR ’91, pp. 520–525, June 1991.

K. Michelsen, H. De Raedt, and J. De Hosson, “Aspects of mathematical morphology,” in Advances in Imaging and Electron Physics (B. K. Peter, W. Hawkes, and T. Mulvey, eds.) (Elsevier, 2003) vol. Volume 125, pp. 119–194,.

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Figures (7)

Fig. 1
Fig. 1

The flow chart of the sMIA procedure. A gray scale image of a retina exposed with near-infrared light (top middle), its mezzotint version (top left) and the final binary image (top right) produced from Chan-Vese active contour method at a time-step close to convergence.

Fig. 2
Fig. 2

Examples of multi-scale morphological signatures from the standard MIA.

Fig. 3
Fig. 3

Examples of multi-scale morphological signatures from the variant gMIA.

Fig. 4
Fig. 4

Examples of multi-scale morphological signatures from the variant sMIA.

Fig. 5
Fig. 5

Examples of multi-scale morphological signatures from variant cMIA.

Fig. 6
Fig. 6

Full size images of samples from the four different treatment groups of the retina.

Fig. 7
Fig. 7

Hierarchical clustering dendrogram of treatments samples from cross-validated confusion matrix for each MIA variant technique: standard MIA (MIA), streamlined MIA (sMIA), MIA initiated with a Chan-Vese segmentation (cMIA) and with a grayscale mia (gMIA). The treatment groups are: A (670 nm only), group B (OIR+670 nm), group C (OIR only), and group D (Control).

Tables (1)

Tables Icon

Table 1 Cross-validated confusion matrices between treatment groups for each variant of MIA.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

E ( c , Γ ) = μ P ( Γ ) + ν A ( Γ ) + λ 1 in ( Γ ) | u 0 ( x , y ) c 1 | 2 d x d y + λ 2 out ( Γ ) | u 0 ( x , y ) c 2 | 2 d x d y ,
inf c , Γ { E ( c , Γ ) } .

Metrics