Abstract
This study focuses on modelling and analysis of obstetric ultrasound by using fractal interpolation. Firstly, a new way of representing ultrasounds achieving remarkable compression ratios while maintaining the quality of the original images is presented. Then, based on this representation, the possibility of grouping ultrasounds as well as the automatic detection of points of interest in them with the aim of diagnosis is examined. The experimental results indicate that fractal interpolation is a feasible and effective approach to this problem.
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References
M. Ali, T.G. Clarkson, Using linear fractal interpolation functions to compress video images. Fractals 2(3), 417–421 (1994)
M. Ali, X. Meng, T.G. Clarkson, J.G. Taylor, “Using fractal interpolation function encoded ultrasonic signals to train a neural network”, IEE, 5/1–5/3 (1995)
M.F. Barnsley, Fractal functions and interpolation. Constr. Approx. 2, 303–329 (1986)
M.F. Barnsley, Fractals everywhere, 3rd ed., Dover Publications, Inc. (2012)
M.F. Barnsley, S. Demko, Iterated function systems and the global construction of fractals. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 399(1817), 243–275 (1985)
O.I. Craciunescu, S.K. Das, J.M. Poulson, T.V. Samulski, Three-dimensional tumor perfusion reconstruction using fractal interpolation functions. IEEE Trans. Biomed. Eng. 48(4), 462–473 (2001)
V. Drakopoulos, Fractal-based image encoding and compression techniques, Commun. – Scientific Letters of the University of Žilina 15(3), 48–55 (2013)
K.J. Falconer, Fractal geometry: mathematical foundations and applications, 3rd edn. (Wiley, Chichester, 2014)
D.P. Ferro, M.A. Falconi, R.L. Adam, M.M. Ortega, C.P. Lima, C.A. de Souza, I. Lorand-Metze, K. Metze, Fractal characteristics of May-Grünwald-Giemsa stained chromatin are independent prognostic factors for survival in multiple myeloma. PLoS ONE 6(6), e20706 (2011)
J.E. Hutchinson, Fractals and self similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981)
F.E. Lennon, G.C. Cianci, N.A. Cipriani, T.A. Hensing, H.J. Zhang, C.T. Chen, S.D. Murgu, E.E. Vokes, M.W. Vannier, R. Salgia, Lung cancer-a fractal viewpoint. Nat. Rev. Clin. Oncol. 12(11), 664–675 (2015)
P. Manousopoulos, V. Drakopoulos, T. Theoharis, Curve fitting by fractal interpolation. Trans. Comput. Sci. 1, 85–103 (2008)
P. Manousopoulos, V. Drakopoulos, T. Theoharis, Parameter identification of 1D fractal interpolation functions using bounding volumes. J. Comput. Appl. Math. 233(4), 1063–1082 (2009)
P. Manousopoulos, V. Drakopoulos, T. Theoharis, Parameter identification of 1D recurrent fractal interpolation functions with applications to imaging and signal processing. J. Mathem. Imaging Vision 40(2), 162–170 (2011)
P. Manousopoulos, V. Drakopoulos, T. Theoharis, P. Stavrou, Effective representation of 2D and 3D data using fractal interpolation, in Proceedings of International Conference on Cyberworlds, pp. 457–464. IEEE Computer Society (2007)
P.R. Massopust, Fractal functions, fractal surfaces and wavelets (Academic Press, San Diego, CA, 1994)
D.S. Mazel, M.H. Hayes, Hidden-variable fractal interpolation of discrete sequences, in Proc. Int. Conf. Acoust., Speech, Signal Processing, pp. 3393–3396 (1991)
D.S. Mazel, M.H. Hayes, Using iterated function systems to model discrete sequences. IEEE Trans. Signal Process. 40(7), 1724–1734 (1992)
D.S. Mazel, Representation of discrete sequences with three-dimensional iterated function systems. IEEE Trans. Signal Process. 42(11), 3269–3271 (1994)
K. Metze, R. Adam, J.B. Florindo, The fractal dimension of chromatin—a potential molecular marker for carcinogenesis, tumor progression and prognosis. Expert Rev. Mol. Diagn. 19(4), 299–312 (2019)
C.M. Păcurar, B.R. Necula, An analysis of COVID-19 spread based on fractal interpolation and fractal dimension. Chaos, Solitons Fractals 139, 110073 (2020)
A.I. Penn, M.H. Loew, Estimating fractal dimension of medical images, Proceedings of SPIE—The International Society for Optical Engineering, 2710 (1996)
A.I. Penn, M.H. Loew, Fractal dimension of low-resolution medical images, Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, vol. 3, pp. 1163–1165 (1996)
A.I. Penn, M.H. Loew, Estimating fractal dimension with fractal interpolation function models. IEEE Trans. Med. Imaging 16(6), 930–937 (1997)
A.I. Penn, L. Bolinger, M.D. Schnall, M.H. Loew, Discrimination of MR images of breast masses with fractal-interpolation function models. Acad. Radiol. 6(3), 156–163 (1999)
D.P. Popescu, C. Flueraru, Y. Mao, S. Chang, M.G. Sowa, Signal attenuation and box-counting fractal analysis of optical coherence tomography images of arterial tissue. Biomed. Opt. Express 1(1), 268–277 (2010)
J.R. Price, M.H. Hayes, Resampling and reconstruction with fractal interpolation functions. IEEE Signal Process. Letters 5(9), 228–230 (1998)
S. Tălu, Fractal analysis of normal retinal vascular network. Oftalmologia 55(4), 11–16 (2011)
J.L. Véhel, K. Daoudi, E. Lutton, Fractal modeling of speech signals. Fractals 2(3), 379–382 (1994)
Acknowledgements
The authors would like to thank Athanasia Karamani, M.D. for her helpful advice on various technical and medical issues examined in this article.
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Drakopoulos, V., Manousopoulos, P. (2023). Obstetric Ultrasound Modelling and Analysis with Fractal Interpolation Methods. In: Daimi, K., Alsadoon, A., Seabra Dos Reis, S. (eds) Current and Future Trends in Health and Medical Informatics. Studies in Computational Intelligence, vol 1112. Springer, Cham. https://doi.org/10.1007/978-3-031-42112-9_10
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