Synthesis of Mammographic Images Based on the Fractional Brownian Motion

Ines Slim Sahli; Hanen Bettaieb; Asma Ben Abdallah; Imen Bhouri; Mohamed Hedi Bedoui

doi:doi:10.11648/j.ijmi.20180601.11

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Synthesis of Mammographic Images Based on the Fractional Brownian Motion

Ines Slim Sahli, Hanen Bettaieb, Asma Ben Abdallah, Imen Bhouri, Mohamed Hedi Bedoui

Published in International Journal of Medical Imaging (Volume 6, Issue 1)

Received: 25 January 2018 Accepted: 5 February 2018 Published: 27 February 2018

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Abstract

This paper presents a new approach for synthesizing breast tissue images based on a random fractal process, the fractional Brownian motion (fBm). This work deals with modeling Regions of Interest (ROIs) of mammographic images. Diverse synthetic ROIs were generated: healthy ones and others with microcalcifications according to fatty and dense tissue. Microcalcifications were injected in several dispositions in order to model benign and malignant cases. The aim of this study resides in two points: (1) the generation of synthetic images of mammograms for researchers and radiologists in order to test their tools and orient the choice of their parameters to enhance the diagnostic accuracy; and (2) to compare two microcalcification segmentation approaches: ‘Sq-Sq’ approach based on multifractal analysis and the ‘MM’ approach based on Mathematical Morphology. In fact, the results proved that the ‘Sq-Sq’ method can detect microcalcifications with different arrangements for any type of tissue and were evaluated using a qualitative test by an expert and a quantitative one based on the Area Overlap Measure (AOM) and the Dice coefficient. The ‘Sq-Sq’ approach yield a mean of 0.8±0.06 for AOM and 0.8446 for Dice coefficient for all segmented images.

Published in	International Journal of Medical Imaging (Volume 6, Issue 1)
DOI	10.11648/j.ijmi.20180601.11
Page(s)	1-8
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Synthetic Images, fBm, Mammography, Microcalcifications, Segmentation

References

[1]	Centers for Disease Control and Prevention, Cancer Among Women, 2015. Available from: http://www.cdc.gov/cancer/dcpc/data/women.html (accessed on 15-12-2017).
[2]	Elmore, Joann G. "Breast cancer screening: balancing evidence with culture, politics, money, and media." Breast Cancer Screening. 2016. 1-27.
[3]	Pretorius, E. Scott, and Jeffrey A. Solomon. Radiology Secrets Plus E-Book. Elsevier Health Sciences, 2010.
[4]	L. Tabar, S. Duffy, L. Burhenne, New Swedish breast cancer detection results for women aged 40–49, Cancer 72 (suppl.) (1993)1437. http://dx.doi.org/10.1002/1097-0142(19930815).
[5]	J. Bronzino (Ed.), Biomedical Engineering Handbook, CRC Press, Boca Raton, FL, 1995.
[6]	American College of Radiology. ACR BI-RADS – Mammographie (2e édition française basée sur la 4e édition américaine). In: ACR Breast Imaging Reporting and Data System, Breast Imaging Atlas, 2003.
[7]	Soares, Filipe, et al. "3D lacunarity in multifractal analysis of breast tumor lesions in dynamic contrast-enhanced magnetic resonance imaging." IEEE Transactions on Image Processing22.11 (2013): 4422-4435.
[8]	McGarry, G., & Deriche, M. (1997, December). Modelling mammographic images using fractional Brownian motion. In TENCON'97. IEEE Region 10 Annual Conference. Speech and Image Technologies for Computing and Telecommunications., Proceedings of IEEE (Vol. 1, pp. 299-302). IEEE.
[9]	Li, H., Giger, M. L., Olopade, O. I., & Chinander, M. R. (2008). Power spectral analysis of mammographic parenchymal patterns for breast cancer risk assessment. Journal of digital imaging, 21(2), 145-152. http://dx.doi.org/10.1007/s10278-007-9093-9
[10]	Mandelbrot, B. B., & Van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM review, 10(4), 422-437. http://dx.doi.org/10.1137/1010093
[11]	Tate, N. J. (1998). Estimating the fractal dimension of synthetic topographic surfaces. Computers & Geosciences, 24(4), 325-334. http://dx.doi.org/10.1016/S0098-3004(97)00119-2
[12]	Juneja, A., Lathrop, D. P., Sreenivasan, K. R., & Stolovitzky, G. (1994). Synthetic turbulence. Physical Review E, 49(6), 5179. http://dx.doi.org/10.1103/PhysRevE.49.5179
[13]	Wendt, H., Roux, S. G., Jaffard, S., & Abry, P. (2009). Wavelet leaders and bootstrap for multifractal analysis of images. Signal Processing, 89(6), 1100-1114.
[14]	Plourde, S. M., Marin, Z., Smith, Z. R., Toner, B. C., Batchelder, K. A., & Khalil, A. (2016). Computational growth model of breast microcalcification clusters in simulated mammographic environments. Computers in biology and medicine, 76, 7-13.
[15]	Mehdi, M. Z., Ayed, N. G. B., Masmoudi, A. D., Sellami, D., & Abid, R. (2017). An efficient microcalcifications detection based on dual spatial/spectral processing. Multimedia Tools and Applications, 76(11), 13047-13065.
[16]	N. S. Arikids, S. Skiadopoulos, A. Karajaliou, “B-spline active rays segmentation of microcalcifications in mammography”, Medical Physics, vol. 35, no. 11, pp. 5161-5171, Nov. 2008. http://dx.doi.org/10.1118/1.2991286J.
[17]	Mohanalin, P. K. Kalra, N. Kumar, “Microcalcification segmentation using normalized tsallis entropy: an automatic q” calculation by exploiting type II fuzzy sets”, IETE Journal ofResearch, vol. 25, no. 2, pp. 90-96, Feb. 2009. http://dx.doi.org/10.4103/0377-2063.53240
[18]	Papadopoulos, A., Fotiadis, D. I., & Costaridou, L. (2008). Improvement of microcalcification cluster detection in mammography utilizing image enhancement techniques. Computers in biology and medicine, 38(10), 1045-1055.
[19]	Duarte, M. A., Alvarenga, A. V., Azevedo, C. M., Calas, M. J. G., Infantosi, A. F., & Pereira, W. C. (2015). Evaluating geodesic active contours in microcalcifications segmentation on mammograms. Computer Methods and Programs in Biomedicine, 122(3), 304-315. http://dx.doi.org/10.1016/j.cmpb.2015.08.016
[20]	Dhahbi, S., Barhoumi, W., & Zagrouba, E. (2015). Breast cancer diagnosis in digitized mammograms using curvelet moments. Computers in biology and medicine, 64, 79-90.
[21]	Malar, E., Kandaswamy, A., Chakravarthy, D., & Dharan, A. G. (2012). A novel approach for detection and classification of mammographic microcalcifications using wavelet analysis and extreme learning machine. Computers in biology and medicine, 42(9), 898-905.
[22]	Alasadi, A. H. H., & Al-Saedi, A. K. H. (2017). A Method for Microcalcifications Detection in Breast Mammograms. Journal of medical systems, 41(4), 68.
[23]	Hamilton, E. K., Jeon, S., Ramirez Cobo, P., Lee, K. S., & Vidakovic, B. (2011, November). Diagnostic classification of digital mammograms by wavelet-based spectral tools: A comparative study In Bioinformatics and Biomedicine (BIBM), 2011 IEEE International Conference on (pp. 384-389). IEEE.
[24]	Beheshti, S. M. A., Ahmadi Noubari, H., Fatemizadeh, E., & Khalili, M. (2014). An efficient fractal method for detection and diagnosis of breast masses in mammograms. Journal of digital imaging, 27(5), 661-669. http://dx.doi.org/10.1007/s10278-013-9654-z
[25]	Beheshti, S. M. A., Noubari, H. A., Fatemizadeh, E., & Khalili, M. (2015). Classification of abnormalities in mammograms by new asymmetric fractal features. Biocybernetics and Biomedical Engineering.
[26]	George, L. E., & Mohammed, E. Z. (2011, October). Cancer tissues recognition system using box counting method and artificial neural network. In Soft Computing and Pattern Recognition (SoCPaR), 2011 International Conference of (pp.5-9).IEEE. http://dx.doi.org/10.1109/socpar.2011.6089105
[27]	Stojić, T., Reljin, I., & Reljin, B. (2006). Adaptation of multifractal analysis to segmentation of microcalcifications in digital mammograms. Physica A: Statistical Mechanics and its Applications, 367, 494-508.
[28]	Sahli, I. S., Bettaieb, H. A., Ben Abdallah, A., Bhouri, I., & Bedoui, M. H. (2015, November). Detection and segmentation of microcalcifications in digital mammograms using multifractal analysis. In Image Processing Theory, Tools and Applications (IPTA), 2015 International Conference on (pp. 180-184). IEEE. http://dx.doi.org/10.1109/ipta.2015.7367122
[29]	Duarte, M. A., Alvarenga, A. V., Azevedo, C. M., Infantosi, A. F. C., & Pereira, W. C. A. (2011, March). Automatic microcalcifications segmentation procedure based on Otsu's method and morphological filters. In Health Care Exchanges (PAHCE), 2011 Pan American (pp. 102-106). IEEE. http://dx.doi.org/10.1109/pahce.2011.5871858
[30]	Singh, B., & Kaur, M. (2017). An Approach for Enhancement of Microcalcifications in Mammograms. Journal of Medical and Biological Engineering, 1-13.
[31]	Ciecholewski, M. (2017). Microcalcification Segmentation from Mammograms: A Morphological Approach. Journal of digital imaging, 30(2), 172-184.
[32]	Duarte, M. D. A., Alvarenga, A. V., Azevedo, C. M., Calas, M. J. G., Infantosi, A. F. C., & Pereira, W. C. D. A. (2013). Segmenting mammographic microcalcifications using a semi-automatic procedure based on Otsu's method and morphological filters. Revista Brasileira de Engenharia Biomédica, 29(4), 377-388.
[33]	Tricot, C. (1999). Courbes et dimension fractale, Springer Science & Business Media.
[34]	Otsu, N. (1979). "AA threshold selection method from grey scale histogram." IEEE Transactions on Systems Man and Cybernetics.
[35]	Jaccard, P.: Étude comparative de la distribution orale dans une portion des alpes et des jura. Bulletin de la Société Vaudoise des Sciences Naturelles 37, 547-579 (1901).
[36]	Dice, L. R. (1945). Measures of the amount of ecologic association between species. Ecology, 26(3), 297-302.
[37]	Heine, John J., et al. "On the statistical nature of mammograms." Medical physics 26.11 (1999): 2254-2265.
[38]	Plourde, Shayne M., et al. "Computational growth model of breast microcalcification clusters in simulated mammographic environments." Computers in biology and medicine 76 (2016): 7-13.
[39]	Reed, I. S., Lee, P. C., & Truong, T. K. (1995). Spectral representation of fractional Brownian motion in n dimensions and its properties. Information Theory, IEEE Transactions on, 41(5), 1439-1451. http://dx.doi.org/10.1109/18.412687
[40]	Stein, M. L. (2002). Fast and exact simulation of fractional Brownian surfaces. Journal of Computational and Graphical Statistics, 11(3), 587-599. http://dx.doi.org/10.1198/106186002466
[41]	Kestener, P., et al. (2001). "Wavelet-based multifractal formalism to assist in diagnosis in digitized mammograms." Image Anal. Stereol 20(3): 169-174.
[42]	Suckling J, The MiniMIAS database, Mammographic Image Analysis Society MIAS. http://peipa.essex.ac.uk/info/mias.html
[43]	Bousson, V., Bergot, C., Sutter, B., Levitz, P., & Cortet, B. (2012). Scientific Committee of the Groupe de Recherche et d'Information sur les Ostéoporoses. Trabecular bone score (TBS): available knowledge, clinical relevance, and future prospects. Osteoporos Int, 23(5), 1489-1501.
[44]	M.M. De Santo M, F. Tortorella, M. Vento, Automated classification of clustered microcalcifications by a multiple expert system, Pattern Recogn. 36 (2003) 1467–1477.
[45]	J.C. Fu, S. Lee, S.T.C. Wong, J.Y. Yeh, A.H. Wang, H.K. Wu, Image segmentation feature selection and pattern classification for mammographic microcalcifications, Comput. Med. Imag. Graph. 29 (2005) 419–429.
[46]	Ayman A. Abu Baker, R. S. Qahwaji, Musbah J. Aqel, Mohmmad H. Saleh, Mammogram image size reduction using 16-8 bit conversion technique, Int. J. Biomed. Sci. 1 (2) (2006) 1306-1216.
[47]	Classification de Le Gal des microcalcifications mammaires. Available online: http://www.aly-abbara.com/echographie/biometrie/scores/microcalcification_classification_le_gal.html (accessed on 16-11-2017).

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APA Style

Ines Slim Sahli, Hanen Bettaieb, Asma Ben Abdallah, Imen Bhouri, Mohamed Hedi Bedoui. (2018). Synthesis of Mammographic Images Based on the Fractional Brownian Motion. International Journal of Medical Imaging, 6(1), 1-8. https://doi.org/10.11648/j.ijmi.20180601.11

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ACS Style

Ines Slim Sahli; Hanen Bettaieb; Asma Ben Abdallah; Imen Bhouri; Mohamed Hedi Bedoui. Synthesis of Mammographic Images Based on the Fractional Brownian Motion. Int. J. Med. Imaging 2018, 6(1), 1-8. doi: 10.11648/j.ijmi.20180601.11

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AMA Style

Ines Slim Sahli, Hanen Bettaieb, Asma Ben Abdallah, Imen Bhouri, Mohamed Hedi Bedoui. Synthesis of Mammographic Images Based on the Fractional Brownian Motion. Int J Med Imaging. 2018;6(1):1-8. doi: 10.11648/j.ijmi.20180601.11

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@article{10.11648/j.ijmi.20180601.11,
  author = {Ines Slim Sahli and Hanen Bettaieb and Asma Ben Abdallah and Imen Bhouri and Mohamed Hedi Bedoui},
  title = {Synthesis of Mammographic Images Based on the Fractional Brownian Motion},
  journal = {International Journal of Medical Imaging},
  volume = {6},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.ijmi.20180601.11},
  url = {https://doi.org/10.11648/j.ijmi.20180601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmi.20180601.11},
  abstract = {This paper presents a new approach for synthesizing breast tissue images based on a random fractal process, the fractional Brownian motion (fBm). This work deals with modeling Regions of Interest (ROIs) of mammographic images. Diverse synthetic ROIs were generated: healthy ones and others with microcalcifications according to fatty and dense tissue. Microcalcifications were injected in several dispositions in order to model benign and malignant cases. The aim of this study resides in two points: (1) the generation of synthetic images of mammograms for researchers and radiologists in order to test their tools and orient the choice of their parameters to enhance the diagnostic accuracy; and (2) to compare two microcalcification segmentation approaches: ‘Sq-Sq’ approach based on multifractal analysis and the ‘MM’ approach based on Mathematical Morphology. In fact, the results proved that the ‘Sq-Sq’ method can detect microcalcifications with different arrangements for any type of tissue and were evaluated using a qualitative test by an expert and a quantitative one based on the Area Overlap Measure (AOM) and the Dice coefficient. The ‘Sq-Sq’ approach yield a mean of 0.8±0.06 for AOM and 0.8446 for Dice coefficient for all segmented images.},
 year = {2018}
}

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TY  - JOUR
T1  - Synthesis of Mammographic Images Based on the Fractional Brownian Motion
AU  - Ines Slim Sahli
AU  - Hanen Bettaieb
AU  - Asma Ben Abdallah
AU  - Imen Bhouri
AU  - Mohamed Hedi Bedoui
Y1  - 2018/02/27
PY  - 2018
N1  - https://doi.org/10.11648/j.ijmi.20180601.11
DO  - 10.11648/j.ijmi.20180601.11
T2  - International Journal of Medical Imaging
JF  - International Journal of Medical Imaging
JO  - International Journal of Medical Imaging
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2330-832X
UR  - https://doi.org/10.11648/j.ijmi.20180601.11
AB  - This paper presents a new approach for synthesizing breast tissue images based on a random fractal process, the fractional Brownian motion (fBm). This work deals with modeling Regions of Interest (ROIs) of mammographic images. Diverse synthetic ROIs were generated: healthy ones and others with microcalcifications according to fatty and dense tissue. Microcalcifications were injected in several dispositions in order to model benign and malignant cases. The aim of this study resides in two points: (1) the generation of synthetic images of mammograms for researchers and radiologists in order to test their tools and orient the choice of their parameters to enhance the diagnostic accuracy; and (2) to compare two microcalcification segmentation approaches: ‘Sq-Sq’ approach based on multifractal analysis and the ‘MM’ approach based on Mathematical Morphology. In fact, the results proved that the ‘Sq-Sq’ method can detect microcalcifications with different arrangements for any type of tissue and were evaluated using a qualitative test by an expert and a quantitative one based on the Area Overlap Measure (AOM) and the Dice coefficient. The ‘Sq-Sq’ approach yield a mean of 0.8±0.06 for AOM and 0.8446 for Dice coefficient for all segmented images.
VL  - 6
IS  - 1
ER  -

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Author Information

Ines Slim Sahli

Faculty of Medecine of Monastir, University of Monastir, Monastir, Tunisia
Hanen Bettaieb

Faculty of Medecine of Monastir, University of Monastir, Monastir, Tunisia
Asma Ben Abdallah

Faculty of Medecine of Monastir, University of Monastir, Monastir, Tunisia
Imen Bhouri

Research Unit Wavelet and Multifractal, Faculty of Science of Monastir, University of Monastir, Monastir, Tunisia
Mohamed Hedi Bedoui

Faculty of Medecine of Monastir, University of Monastir, Monastir, Tunisia

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APA Style

Ines Slim Sahli, Hanen Bettaieb, Asma Ben Abdallah, Imen Bhouri, Mohamed Hedi Bedoui. (2018). Synthesis of Mammographic Images Based on the Fractional Brownian Motion. International Journal of Medical Imaging, 6(1), 1-8. https://doi.org/10.11648/j.ijmi.20180601.11

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ACS Style

Ines Slim Sahli; Hanen Bettaieb; Asma Ben Abdallah; Imen Bhouri; Mohamed Hedi Bedoui. Synthesis of Mammographic Images Based on the Fractional Brownian Motion. Int. J. Med. Imaging 2018, 6(1), 1-8. doi: 10.11648/j.ijmi.20180601.11

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AMA Style

Ines Slim Sahli, Hanen Bettaieb, Asma Ben Abdallah, Imen Bhouri, Mohamed Hedi Bedoui. Synthesis of Mammographic Images Based on the Fractional Brownian Motion. Int J Med Imaging. 2018;6(1):1-8. doi: 10.11648/j.ijmi.20180601.11

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@article{10.11648/j.ijmi.20180601.11,
  author = {Ines Slim Sahli and Hanen Bettaieb and Asma Ben Abdallah and Imen Bhouri and Mohamed Hedi Bedoui},
  title = {Synthesis of Mammographic Images Based on the Fractional Brownian Motion},
  journal = {International Journal of Medical Imaging},
  volume = {6},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.ijmi.20180601.11},
  url = {https://doi.org/10.11648/j.ijmi.20180601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmi.20180601.11},
  abstract = {This paper presents a new approach for synthesizing breast tissue images based on a random fractal process, the fractional Brownian motion (fBm). This work deals with modeling Regions of Interest (ROIs) of mammographic images. Diverse synthetic ROIs were generated: healthy ones and others with microcalcifications according to fatty and dense tissue. Microcalcifications were injected in several dispositions in order to model benign and malignant cases. The aim of this study resides in two points: (1) the generation of synthetic images of mammograms for researchers and radiologists in order to test their tools and orient the choice of their parameters to enhance the diagnostic accuracy; and (2) to compare two microcalcification segmentation approaches: ‘Sq-Sq’ approach based on multifractal analysis and the ‘MM’ approach based on Mathematical Morphology. In fact, the results proved that the ‘Sq-Sq’ method can detect microcalcifications with different arrangements for any type of tissue and were evaluated using a qualitative test by an expert and a quantitative one based on the Area Overlap Measure (AOM) and the Dice coefficient. The ‘Sq-Sq’ approach yield a mean of 0.8±0.06 for AOM and 0.8446 for Dice coefficient for all segmented images.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Synthesis of Mammographic Images Based on the Fractional Brownian Motion
AU  - Ines Slim Sahli
AU  - Hanen Bettaieb
AU  - Asma Ben Abdallah
AU  - Imen Bhouri
AU  - Mohamed Hedi Bedoui
Y1  - 2018/02/27
PY  - 2018
N1  - https://doi.org/10.11648/j.ijmi.20180601.11
DO  - 10.11648/j.ijmi.20180601.11
T2  - International Journal of Medical Imaging
JF  - International Journal of Medical Imaging
JO  - International Journal of Medical Imaging
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2330-832X
UR  - https://doi.org/10.11648/j.ijmi.20180601.11
AB  - This paper presents a new approach for synthesizing breast tissue images based on a random fractal process, the fractional Brownian motion (fBm). This work deals with modeling Regions of Interest (ROIs) of mammographic images. Diverse synthetic ROIs were generated: healthy ones and others with microcalcifications according to fatty and dense tissue. Microcalcifications were injected in several dispositions in order to model benign and malignant cases. The aim of this study resides in two points: (1) the generation of synthetic images of mammograms for researchers and radiologists in order to test their tools and orient the choice of their parameters to enhance the diagnostic accuracy; and (2) to compare two microcalcification segmentation approaches: ‘Sq-Sq’ approach based on multifractal analysis and the ‘MM’ approach based on Mathematical Morphology. In fact, the results proved that the ‘Sq-Sq’ method can detect microcalcifications with different arrangements for any type of tissue and were evaluated using a qualitative test by an expert and a quantitative one based on the Area Overlap Measure (AOM) and the Dice coefficient. The ‘Sq-Sq’ approach yield a mean of 0.8±0.06 for AOM and 0.8446 for Dice coefficient for all segmented images.
VL  - 6
IS  - 1
ER  -

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