References

[1]

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

[2]

H. Biermé and F.J.P. Richard. Estimation of anisotropic Gaussian fields through Radon transform. ESAIM: Probab. Stat., 12(1):30–50, 2008.

[3]

F.J.P. Richard. Anisotropy of Hölder Gaussian random fields: characterization, estimation, and application to image textures. Stat. Comput., pages 1–14, oct 2017.

[4]

F.J.P. Richard. Some anisotropy indices for the characterization of Brownian textures and their application to breast images. Spat. Stat., 18:147–162, 2016.

[5]

F.J.P. Richard. Analysis of anisotropic Brownian textures and application to lesion detection in mammograms. Procedia Environ. Sci., 27:16–20, 2015.

[6]

F.J.P. Richard. Tests of isotropy for rough textures of trended images. Stat. Sinica, 26(3):1279–1304, 2016.

[7]

F.J.P. Richard and H. Biermé. Statistical tests of anisotropy for fractional Brownian textures. Application to full-field digital mammography. J. Math. Imaging Vis., 36(3):227–240, 2010.

[8]

H. Vu and F. Richard. Statistical tests of heterogeneity for anisotropic multifractional Brownian fields. Stoch. Proc. Appl., 130(8):4667–4692, 2020.

[9]

H. Biermé and F. Richard. Analysis of texture anisotropy based on some Gaussian fields with spectral density. In M. Bergounioux, editor, Mathematical Image Processing, pages 59–73. Springer Proceedings, 2011.

[10]

H. Biermé, F. Richard, M. Rachidi, and C.L. Benhamou. Anisotropic texture modeling and applications to medical image analysis. In H. Ammari, editor, Mathematical Methods for Imaging and Inverse Problems, volume 26 of ESAIM Proceedings, pages 100–122. 2009.

[11]

H. Biermé, M. Moisan, and F. Richard. A turning-band method for the simulation of anisotropic fractional Brownian field. J. Comput. Graph. Statist., 24(3):885–904, 2015.

[12]

F.J.P. Richard. PyAFBF: a python library for sampling image textures from the anisotropic fractional brownian field. Journal of Open Source Software, 7(75):3821, 2022.

[13]

J.P. Chilès and P. Delfiner. Geostatistics: modeling spatial uncertainty. J. Wiley, 2nd edition, 2012.

[14]

A. Wood and G. Chan. Simulation of stationary Gaussian processes in [0, 1]d. J. Comput. Graph. Statist., 3(4):409–432, 1994.

[15]

X. Guyon and O. Perrin. Identification of space deformation using linear and superficial quadratic variations. Stat Probabil Lett, 47(3):307–316, 2000.

[16]

K. Polisano, M. Clausel, V. Perrier, and L. Condat. Texture modeling by Gaussian fields with prescribed local orientation. In Int Conf on Image Processing (ICIP), 2014 IEEE, 6091–6095. 2014.

[17]

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

[18]

R.F. Peltier and J. Levy Vehel. Multifractional Brownian motion: definition and preliminary results. Technical Report 2645, INRIA, 1996.

[19]

G. Golub and V. Pereyra. Separable nonlinear least squares: the variable projection method and its applications. Inverse Probl., 19(2):R1, 2003.