MATAIM

Bibliography

R. J. Adler.
The Geometry of Random Field.
John Wiley & Sons, 1981.

G. Aufort, R. Jennane, R. Harba, and C.L. Benhamou.
Hybrid skeleton graph analysis of disordered porous media. application to trabecular bone.
In IEEE International Conf. on Acoustic, Speech and Signal Proc, Toulouse, France, 2006.

Auf08

G. Aufort.
Caractérisation morphologique et mécanique de milieux poreux 3D. Application à la microarchitecture osseuse.
PhD thesis, Univesity of Orleans, 2008.

BBF+94

J. Byng, N. Boyd, E. Fishell, et al.
The quantitative analysis of mammographic density.
Phys. Med. Biol., 39:1629-1638, 1994.

BDN72

I. Bar-David and A. Nemirovsky.
Level crossings of nondifferentiable shot processes.
IEEE Transactions on Information Theory, 18:27-34, 1972.

BE03

A. Bonami and A. Estrade.
Anisotropic analysis of some Gaussian models.
J. Fourier Anal. Appl., 9:215-236, 2003.

BE06

H. Biermé and A. Estrade.
Poisson microballs: self-simmilarity and X-ray transforms.
Adv. Appl. Prob., 38:1-20, 2006.

BEK07

H. Biermé, A. Estrade, and I. Kaj.
Self-similar random fields and rescaled random balls models.
Submitted Preprint, 2007.

BGR06

C. Bordenave, Y. Gousseau, and F. Roueff.
The dead leaves model : an example of a general tessellation.
Advances in Applied Probability, 38(1):31-46, 2006.

BILC+05

B. Brunet-Imbault, G. Lemineur, C. Chappard, et al.
A new anisotropy index on trabecular bone radiographic images using the fast Fourier transform.
BMC Med. Imaging, 5(4), 2005.

BJJ01a

A.E. Burgess, F.L. Jacobson, and P.F. Judy.
Human observer detection experiments with mammograms and power-law noise.
Medical Physics, 28(4):419-437, 2001.

BJJ01b

A.E. Burgess, F.L. Jacobson, and P.F. Judy.
Lesion detection in digital mammograms.
In Proceedings of SPIE, Medical Imaging, volume 4320, pages 555-560, 2001.

BJR97

A. Benassi, S. Jaffard, and D. Roux.
Elliptic Gaussian random processes.
Rev. Mathem. Iberoamericana, 13(1):19-89, 1997.

BLJ+94

C.L. Benhamou, E. Lespessailles, G. Jacquet, R. Harba, R. Jennane, T. Loussot, D. Tourlière, and W. Ohley.
Fractal organization of trabecular bone images on calcaneus radiographs.
Journal of Bone and Mineral Research, 9:1909-1918, 1994.

BMR05

G. Blanchet, L. Moisan, and B. Rougé.
A linear prefilter for image sampling with ringing artifact control.
In International Conference on Image Processing, volume 3, pages 577-580, 2005.

BMS+82

J. Brisson, F. Merletti, NL Sadowsky, et al.
Mammographic features of the breast and breast cancer risk.
Am J. Epidemiol., 115(3):428-437, 1982.

BMS07

H. Biermé, M. M. Meerschaert, and H. P. Scheffler.
Operator scaling stable random fields.
Stoch. Proc. Appl., 117(3):312-332, 2007.

BNBF+96

J. Byng, N. N. Boyd, E. Fishell, et al.
Automated analysis of mammographic densities.
Phys. Med. Biol., 41:909-923, 1996.

BOC+82

N.F. Boyd, B. O'Sullivan, J.E. Campbell, et al.
Mammographic signs as risk factors for breast cancer.
Br. J. Cancer, 45:185-193, 1982.

BPL+01

C.L. Benhamou, S. Poupon, E. Lespessailles, S. Loiseau, R. Jennane, V. Siroux, W. Ohley, and L. Pothuaud.
Fractal analysis of radiographic trabecular bone texture and bone mineral density.
Journal of Bone and Mineral Research, 16(4):697-703, 2001.

BR08

H. Biermé and F. Richard.
Estimation of anisotropic gaussian fields through radon transform.
ESAIM: Probability and Statistics, 12(1):30-50, 2008.

BYL+97

J. Byng, M. Yaffe, G. Lockwood, et al.
Automated analysis of mammographic densities and breast carcinoma risk.
Cancer, 80(1):66-74, 1997.

CBIL+05

C. Chappard, B. Brunet-Imbault, G. Lemineur, B. Giraudeau, Basillais A., and C.L. Benhamou.
Anisotropy changes in post-menopausal osteoporosis : Characterization by a new index applied to trabecular bone radiographic images.
Osteoporosis International, 16:1193-1202, 2005.

CDF89

C.-C. Chen, J. Daponte, and M. Fox.
Fractal feature analysis and classification in medical imaging.
IEEE Trans. on Med. Imaging, 8(2):133-142, 1989.

CGPP06

S. Cohen, X. Guyon, O. Perrin, and M. Pontier.
Singularity functions for fractional processes, and application to fractional brownian sheet.
Ann. Inst. H. Poincaré, Prob. Stat., 42(2):187-205, 2006.

Cha07

P. Chainais.
Infinitely divisible cascades to model the statistics of natural images.
IEEE Trans. on Pattern Analysis and Machine Intelligence, 29(12), 2007.

CL05

P. Chainais and J-J. Li.
Synthèse de champs scalaires multifractals: application à la synthèse de texture.
GRETSI 2005, 2005.

CSH+90

C. Caldwell, S. Stapleton, D. Holdsworth, et al.
Characterisation of mammographic parenchymal patterns by fractal dimension.
Phys. Med. Biol., 35(2):235-247, 1990.

CTR+08

V. Chajès, A.C. Thiébaut, M. Rotival, E. Gauthier, V. Maillard, M.C. Boutron-Ruault, V. Joulin, G.M. Lenoir, and Clavel-Chapelon F.
Association between serum trans-monounsaturated fatty acids and breast cancer risk in the E3N-EPIC study.
Am J Epidemiol., 4, 2008.

DG00

P.G. De Gennes.
The Physics of Liquid Crystals.
Oxford Science publication, 2000.

DH99

S. Davies and P. Hall.
Fractal analysis of surface roughness by using spatial data.
J. R. Stat. Soc. Ser. B, 61:3-37, 1999.

DMM08

A. Desolneux, L. Moisan, and J.-M. Morel.
From Gestalt Theory to Image Analysis - A Probabilistic Approach, volume 34.
Springer-Verlag, 2008.

DWW+08

J. Ding, R. Warren, I. Warsi, et al.
Evaluating the effectiveness of Using Standard Mammogram Form to predict Breast Cancer Risk:case-control study.
Cancer Epidemiology Biomarkers and Prevention, 17:1074-1081, 2008.

EAC08

E. E. Anderes and S. Chatterjee.
Consistent estimates of deformed isotropic gaussian random fields on the plane.
Ann. Statist., 2008.
to appear.

EAS05

E. E. Anderes and M. Stein.
Estimating deformations of isotropic gaussian random fields on the plane.
Ann. Statist., 36(2):719-741, 2005.

EG92

L. C. Evans and R. F. Gariepy.
Measure theory and fine properties of functions.
Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1992.

FFM+08

A. Fournier, A. Fabre, S. Mesrine, MC Boutron-Ruault, F. Berrino, and F. Clavel-Chapelon.
Use of different postmenopausal hormone therapies and risk of histology- and hormone receptor-defined invasive breast cancer.
J Clin Oncol., 26(8):1260-1268, 2008.

FRS07

G. Faÿ, F. Roueff, and P. Soulier.
Estimation of the memory parameter of the infinite source Poisson process.
Bernoulli, 13(2):473-491, 2007.

GGM08

B. Galerne, Y. Gousseau, and J.-M. Morel.
Shift and phase invariant texture models.
submitted preprint, 2008.

GM09

B. Grosjean and L. Moisan.
A-contrario detectability of spots in textured backgrounds.
J. of Mathematical Imaging and Vision, in press, 2008 or early 2009.

GPT07

M. G. Genton, O. Perrin, and M. Taqqu.
Self-similarity and lamperti transformation for random fields.
Stochastic Models, 23:397-411, 2007.

GR07

Y. Gousseau and F. Roueff.
Modeling occlusion and scaling in natural images.
SIAM Multiscale Modeling and Simulations, 6(1):105-134, 2007.

HDV+99

J. Heine, S. Deine, R. Velthuizen, et al.
On the statistical nature of mammograms.
Med. Phys., 26(11):2254-2269, 1999.

HM02a

J. Heine and P. Malhorta.
Mammographic tissue, breast cancer risk, serial image analysis, and digital mammography: serial breast tissue change and related temporal influences.
Acad. Radiol, 9:317-335, 2002.

HM02b

J. Heine and P. Malhorta.
Mammographic tissue, breast cancer risk, serial image analysis, and digital mammography: tissue and related risk factors.
Acad. Radiol, 9:298-316, 2002.

HP96

P. Hall and J. Polzehl.
On the dimension of the boundary of clumps in a multi-type Boolean model.
Ann. Statist., 24(4):1521-1535, 1996.

HP04

P. Hall and J. Park.
Nonparametric inference about service time distribution from indirect measurements.
J. R. Stat. Soc. Ser. B Stat. Methodol., 66(4):861-875, 2004.

HS85

L. Heinrich and V. Schmidt.
Normal convergence of multidimensional shot-noise and rates of this convergence.
Adv. Appl. Prob, 17:193-210, 1985.

HV02

J. Heine and R. Velthuizen.
Spectral analysis of full field digital mammography data.
Med. Phys., 29(5):647-661, 2002.

Kam96

A. Kamont.
On the fractional anisotropic Wiener field.
Probab. Math. Statist., 16:85-98, 1996.

KLNS07

I. Kaj, L. Leskelä, I. Norros, and V. Schmidt.
Scaling limits for random fields with long-range dependence.
Ann. Probab., 35(2):528-550, 2007.

KLSJ+01

P. Kestener, J.-M. Lina, P. Saint-Jean, et al.
Wavelet-based multifractal formalism to assist in diagnosis in digitized mammograms.
Image Anal. Stereol., 20:169-174, 2001.

KMF+07

M. Kvaskoff, S. Mesrine, A. Fournier, M.C. Boutron-Ruault, and Clavel-Chapelon F.
Personal history of endometriosis and risk of cutaneous melanoma in a large prospective cohort of french women.
Arch Intern Med., 167(19):2061-2065, 2007.

Kot98

C.J. Kotre.
The effect of background structure on the detection of low contrast objects in mammography.
The British Journal of Radiology, 71:1162-1167, 1998.

Lam62

J. Lamperti.
Semi-stable stochastic processes.
Journal of Time Series Analysis, 9:62-78, 1962.

Leg00

S. Leger.
Analyse stochastique de signaux multi-fractaux et estimations de paramètres.
PhD thesis, Université d'Orléans, 2000.

LGK+08

E. Lespessailles, C. Gadois, I. Kousignian, S. Kolta, J.P. Neveu, P. Fardellone, C. Roux, J.P. Do-Huu, and C.L. Benhamou.
Clinical interest of bone texture analysis in osteoporosis : a case control multicenter study.
Osteoporosis International, 19:1019-1028, 2008.

LHJ+04

G. Lemineur, R. Harba, R. Jennane, et al.
Fractal anisotropy measurement of bone texture radiographs.
In First International Symposium on Control, Communications and Signal Processing, pages 275-278, 2004.

LJH+96

E. Lespessailles, G. Jacquet, R. Harba, R. Jennane, T. Loussot, J.F. Viala, and C.L. Benhamou.
Anisotropy measurement obtained by fractal analysis of trabecular bone at the calcaneus and radius.
Rev. Rhum., 1996.

Mat68

G. Matheron.
Modèle séquentiel de partition aléatoire.
Technical report, CMM, 1968.

MG01

D. Mumford and B. Gidas.
Stochastic models for generic images.
Quarterly of Applied Mathematics, 59, 2001.

MRST07

E. Moulines, F. Roueff, A. Souloumiac, and T. Trigano.
Nonparametric inference of photon energy distribution from indirect measurements.
Bernoulli, 13(2):365-388, 2007.

MS83

S. A. Molchanov and A. K. Stepanov.
Percolation in random fields.
Theoretical and Mathematical Physics, 55(3):592-599, 1983.

MVN68

B. B. Mandelbrot and J. Van Ness.
Fractional Brownian motion, fractionnal noises and applications.
SIAM Review, 10:422-437, 1968.

OB82

E. Orsingher and F. Battaglia.
Probability distributions and level crossings of shot noise models.
Stochastics, 8(1):45-61, 1982.

PBP+00

L. Pothuaud, C. Benhamou, P. Porion, E. Lespessailles, R. Harba, and P. Levitz.
Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture.
J. of Bone and mineral research, 15(4), 2000.

PG00

0. Perrin and X. Guyon.
Identification of space deformation using linear and superficial quadratic variations.
Statistics and Probability Letters, 47:307-316, 2000.

PLB01

L. Pothuaud, P. Levitz, and C.L. Benhamou.
Simulation of osteoporosis bone changes : effects on the degree of anisotropy, volume 1, chapter "Noninvasive assessment of trabecular bone architecture and the competence of bone". Advances in experimental medicine and biology, pages 111-121.
Kluwer Academic/Plenum Publishers, New-York, 2001.

PLL+02

L. Pothuaud, A. Laib, P. Levitz, C. Benhamou, and S. Majumdar.
Three dimensionnal-line skeleton graph analysis of high resolution magnetic resonance images 35 mm- resolution microcomputed tomography.
J. of Bone and mineral research, 17, 2002.

PLV96

R.F. Peltier and J. Levy Vehel.
Multifractional Brownian motion: definition and preliminary results.
Technical report, INRIA, 1996.

PPL+00

L. Pothuaud, P. Porion, E. Lespessailles, C.L. Benhamou, and P. Levitz.
A new method for three-dimensionnal skeleton graph analysis of porous media : application to trabecular bone microarchitecture.
J. of Microscopy, 14:149-161, 2000.

PRM+02

L. Pothuaud, B. Rietbergen, L. Mosekilde, O. Beuf, P. Levitz, C. Benhamou, and S. Majumdar.
Combination of topological parameters and bone volume fraction better predicts the mechanical properties of trabecular bone.
Journal of Biomechanics, 35:1091, 2002.

RB07

F. Richard and H. Biermé.
A statistical methodology for testing the anisotropy of brownian textures with an application to full-field digital mammography.
Technical report, HAL-00177770, 2007.

RGS85

M. Rosso, J.F Gouyet, and B. Sapoval.
Determination of percolation probability from the use of a concentration gradient.
Phys. Rev., 32(6035), 1985.

Ric77

J. Rice.
On generalized shot noise.
Adv. Appl. Prob., 9:553-565, 1977.

Ser88

J. Serra.
Image analysis and Mathematical morphology, vol.2.
Academic Press, London, New York, 1988.

SKM87

D. Stoyan, W. S. Kendall, and J. Mecke.
Stochastic geometry and its applications.
Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons Ltd., Chichester, 1987.
With a foreword by D. G. Kendall.

SM05

M. Stauber and R. Muller.
Volumetric spatial decomposition of trabecular bone into rods and plates-a new method for local bone morphometry.
Bone, 38:475-484, 2005.

TFOCC06

B. Tehard, C.M. Friedenreich, J.M. Oppert, and F. Clavel-Chapelon.
Effect of physical activity on women at increased risk of breast cancer: results from the E3N cohort study.
Cancer Epidemiol Biomarkers Prev., 15(1):57-64, 2006.

TK99

E. Thonnes and W. S. Kendall.
Perfect simulation in stochastic geometry.
Pattern Recognition, 32:1569-1586, 1999.

TTF+07

M.S. Touillaud, A.C. Thiebaut, A. Fournier, M. Niravong, M.C. Boutron-Ruault, and F. Clavel-Chapelon.
Dietary lignan intake and postmenopausal breast cancer risk by estrogen and progesterone receptor status.
J Natl Cancer Inst, 99:475-486, 2007.

VESH+08

S. Van Engeland, P. Snoeren, H. Huisman, et al.
Volumetric breast density estimation full-field digital mammograms.
IEEE Transactions on Medical Imaging, 25(3):273-282, 2008.

VW91

J.J. Van Wijk.
Spot noise texture synthesis for data visualization.
In Proceedings of the 18th annual conference on Computer graphics and interactive techniques (SIGGRAPH '91), pages 309-318, 1991.

Wol67a

J.N. Wolfe.
Ducts as a sole indicator of breast carcinoma.
Radiology, 89:206-210, 1967.

Wol67b

J.N. Wolfe.
A study of breast parenchyma by mammography in the normal woman and those with benign and malignant disease.
Radiology, 89:201-205, 1967.