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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  40. M. S. Barbosa, A. Bubna-Litic, and T. Maddess, “Locally countable properties and the perceptual salience of textures,” J. Opt. Soc. Am. A30, 1687–1697 (2013).
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  41. J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision13, 21 (2013).
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  42. 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. USA107, 18149–18154 (2010).
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2013

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 One8, e72135 (2013).
[CrossRef] [PubMed]

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision13, 21 (2013).
[CrossRef]

M. S. Barbosa, A. Bubna-Litic, and T. Maddess, “Locally countable properties and the perceptual salience of textures,” J. Opt. Soc. Am. A30, 1687–1697 (2013).
[CrossRef]

2012

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A29, 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 One7, 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

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,” Bone49, 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

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. USA107, 18149–18154 (2010).
[CrossRef]

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software33(1), 1–22 (2010).

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. Vision16, 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,” Blood115, 5102–5110 (2010).
[CrossRef] [PubMed]

2009

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., A344, 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 Protocols4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

2008

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

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., B86, 279–282 (2007).
[CrossRef]

2006

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B52(4), 531–546 (2006).
[CrossRef]

2005

L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir21, 992–1000 (2005).
[CrossRef] [PubMed]

2004

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. B37, 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,” Mitochondrion4, 559–567 (2004).
[CrossRef]

2003

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 Intelligence25(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

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 Processing10, 266–277 (2001).
[CrossRef]

2000

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

1999

T. Karu, “Primary and secondary mechanisms of action of visible to near-IR radiation on cells,” J. Photochem. Photobiol., B49, 1–17 (1999).
[CrossRef]

1997

L. D. Cohen and R. Kimmel, “Global minimum for active contour models: A minimal path approach,” Int. J. Comp. Vision24, 57–78 (1997).
[CrossRef]

1996

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. USA93, 1591–1595 (1996).
[CrossRef] [PubMed]

1991

L. Vincent, “Morphological transformations of binary images with arbitrary structuring elements,” Signal Processing22, 3–23 (1991).
[CrossRef]

1989

D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics42, 577–685 (1989).
[CrossRef]

1976

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 Processing5, 13–40 (1976).
[CrossRef]

1973

R. Sibson, “SLINK: an optimally efficient algorithm for the single-link cluster method,” The Computer Journal16, 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 Protocols4(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,” Bone49, 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. USA107, 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., A344, 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 One8, 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. B52(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. A30, 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. B37, 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. B52(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. B37, 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. Vision16, 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,” Bone49, 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,” Mitochondrion4, 559–567 (2004).
[CrossRef]

Chan, T. F.

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing10, 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 Protocols4(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. Vision24, 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 Protocols4(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. Vision13, 21 (2013).
[CrossRef]

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A29, 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. B52(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. B37, 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 One8, 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,” Mitochondrion4, 559–567 (2004).
[CrossRef]

De Hosson, J.

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K. Michielsen and H. De Raedt, “Integral-geometry morphological image analysis,” Phys. Rep.347(6), 461–538 (2001).
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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).
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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., A344, 107–112 (2009).
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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,” Mitochondrion4, 559–567 (2004).
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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 Protocols4(11), 1565–1573 (2009).
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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 One7, e32167 (2012).
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J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software33(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,” Mitochondrion4, 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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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., A344, 107–112 (2009).
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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, 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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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., A344, 107–112 (2009).
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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).
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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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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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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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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,” Bone49, 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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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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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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K. Michielsen and H. De Raedt, “Integral-geometry morphological image analysis,” Phys. Rep.347(6), 461–538 (2001).
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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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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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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 One8, e72135 (2013).
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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 One7, 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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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 One8, e72135 (2013).
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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 Intelligence25(2), 265–270 (2003).
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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 Intelligence25(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. B37, 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,” Langmuir21, 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 One8, e72135 (2013).
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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., A344, 107–112 (2009).
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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 Protocols4(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.
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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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L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir21, 992–1000 (2005).
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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.

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. USA93, 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 Mathematics42, 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., A344, 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 One7, e32167 (2012).
[CrossRef] [PubMed]

Sibson, R.

R. Sibson, “SLINK: an optimally efficient algorithm for the single-link cluster method,” The Computer Journal16, 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., B86, 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 Protocols4(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 Protocols4(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. Vision16, 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,” Blood115, 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., B86, 279–282 (2007).
[CrossRef]

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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,” Blood115, 5102–5110 (2010).
[CrossRef] [PubMed]

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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,” Bone49, 580–587 (2011).
[CrossRef] [PubMed]

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J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision13, 21 (2013).
[CrossRef]

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J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software33(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. USA107, 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 One7, 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 One8, 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. Vision16, 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,” Bone49, 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,” Bone49, 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,” Mitochondrion4, 559–567 (2004).
[CrossRef]

Vese, L. A.

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing10, 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. Vision13, 21 (2013).
[CrossRef]

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A29, 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. USA107, 18149–18154 (2010).
[CrossRef]

Vincent, L.

L. Vincent, “Morphological transformations of binary images with arbitrary structuring elements,” Signal Processing22, 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. B52(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., A344, 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,” Mitochondrion4, 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 Protocols4(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,” Mitochondrion4, 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. Vision16, 1801–1822 (2010).

Adv. Mater.

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

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,” Blood115, 5102–5110 (2010).
[CrossRef] [PubMed]

Bone

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,” Bone49, 580–587 (2011).
[CrossRef] [PubMed]

Brain Res.

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

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., A344, 107–112 (2009).
[CrossRef]

Communications on Pure and Applied Mathematics

D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics42, 577–685 (1989).
[CrossRef]

Computer Graphics and Image Processing

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 Processing5, 13–40 (1976).
[CrossRef]

Eur. Phys. J. B

C. Beisbart, M. Barbosa, H. Wagner, and L. d. F. Costa, “Extended morphometric analysis of neuronal cells with minkowski valuations,” Eur. Phys. J. B52(4), 531–546 (2006).
[CrossRef]

IEEE Trans. Image Processing

T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing10, 266–277 (2001).
[CrossRef]

IEEE Trans. Pattern Analysis and Machine Intelligence

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 Intelligence25(2), 265–270 (2003).
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Int. J. Comp. Vision

L. D. Cohen and R. Kimmel, “Global minimum for active contour models: A minimal path approach,” Int. J. Comp. Vision24, 57–78 (1997).
[CrossRef]

Invest. Ophthalmol. Visual Sci.

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

J. Opti. Soc. Am. A

J. D. Victor and M. M. Conte, “Local image statistics: maximum-entropy constructions and perceptual salience,” J. Opti. Soc. Am. A29, 1313–1345 (2012).
[CrossRef]

J. Photochem. Photobiol., B

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., B86, 279–282 (2007).
[CrossRef]

T. Karu, “Primary and secondary mechanisms of action of visible to near-IR radiation on cells,” J. Photochem. Photobiol., B49, 1–17 (1999).
[CrossRef]

J. Stat. Mech.: Theory Exp.

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

J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Software33(1), 1–22 (2010).

J. Vision

J. D. Victor, D. J. Thengone, and M. M. Conte, “Perception of second- and third-order orientation signals and their interactions,” J. Vision13, 21 (2013).
[CrossRef]

Langmuir

L. Knüfing, H. Schollmeyer, H. Riegler, and K. Mecke, “Fractal analysis methods for solid alkane monolayer domains at SiO2/Air interfaces,” Langmuir21, 992–1000 (2005).
[CrossRef] [PubMed]

Mitochondrion

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,” Mitochondrion4, 559–567 (2004).
[CrossRef]

Mol. Vision

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. Vision16, 1801–1822 (2010).

Nature Protocols

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 Protocols4(11), 1565–1573 (2009).
[CrossRef] [PubMed]

Photochem. Photobiol.

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.

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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Phys. Rev. E

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PLoS One

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 One8, 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 One7, e32167 (2012).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci. USA

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. USA107, 18149–18154 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. USA

J. A. Sethian, “A fast marching level set method for monotonically advancing fronts,” Proc. Natl. Acad. Sci. USA93, 1591–1595 (1996).
[CrossRef] [PubMed]

Prog. Theor. Phys. Suppl.

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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R. Sibson, “SLINK: an optimally efficient algorithm for the single-link cluster method,” The Computer Journal16, 30–34 (1973).
[CrossRef]

Other

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