Abstract
This paper considers the problem of image segmentation for medical images, in particular, cutaneous lesions. Given a digital image of a skin lesion, our goal is to compute the border curve separating the lesion from the image background. This problem can be formulated as an optimization problem, where the border curve is computed through data fitting from a set of points lying on the lesion boundary. Some recent papers have applied artificial intelligence techniques to tackle this issue. However, they usually focus on the polynomial case, ignoring the more powerful (but also more difficult) case of rational curves. In this paper, we address this problem with rational Bézier curves by applying functional networks, a powerful extension of the classical neural networks. Experimental results on some benchmark medical images show that this method performs well and can be successfully applied to this problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abbas, A.A., Guo, X., Tan, W.H., Jalab, H.A.: Combined spline and B-spline for an improved automatic skin lesion segmentation in dermoscopic images using optimal color channel. J. Med. Syst. 38, 80–80 (2014)
Castillo, E.: Functional networks. Neural Process. Lett. 7, 151–159 (1998)
Castillo, E., Iglesias, A., Ruiz-Cobo, R.: Functional Equations in Applied Sciences. Elsevier, Amsterdam (2005)
Celebi, M.E., Iyatomi, H., Schaefer, G., Stoecker, W.V.: Lesion border detection in dermoscopy images. Comp. Med. Imaging Graph. 33(2), 148–153 (2009)
Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, Oxford (1993)
Farin, G.: Curves and Surfaces for CAGD, 5th edn. Morgan Kaufmann, San Francisco (2002)
Friedman, R.J., Rigel, D.S., Kopf, A.W.: Early detection of malignant melanoma: the role of physician examination and self-examination of the skin. Cancer J. Clin. 35(3), 130–151 (1985)
Funahashi, K.I.: On the approximate realization of continuous mappings by neural networks. Neural Netw. 2(3), 183–192 (1989)
Gálvez, A., Iglesias, A., Cobo, A., Puig-Pey, J., Espinola, J.: Bézier curve and surface fitting of 3D point clouds through genetic algorithms, functional networks and least-squares approximation. Lectures Notes in Computer Science, vol. 4706, pp. 680–693 (2007)
Gálvez, A., Fister, I., Fister Jr., I., Osaba, E., Ser, J.D., Iglesias, A.: Automatic fitting of feature points for border detection of skin lesions in medical images with bat algorithm. Stud. Comput. Intell. 798, 357–368 (2018)
Gálvez, A., Fister, I., Osaba, E., Ser, J.D., Iglesias, A.: Hybrid modified firefly algorithm for border detection of skin lesions in medical imaging. In: Proceeding of IEEE Congress on Evolutionary Computation, IEEE CEC 2019, pp. 111–118. IEEE Computer Society Press, Los Alamitos (2019)
Garnavi, R., Aldeen, M., Celebi, M.E., Varigos, G., Finch, S.: Border detection in dermoscopy images using hybrid thresholding on optimized color channels. Comput. Med. Imaging Graph. 35(2), 105–115 (2011)
Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2(5), 359–366 (1989)
Iglesias, A., Gálvez, A.: Hybrid functional-neural approach for surface reconstruction. Math. Prob. Eng. 2014, 13 (2014). Article ID 351648
Levenberg, K.: A method for the solution of certain non-linear problems in least squares. Q. Appl. Math. 2(2), 164–168 (1944)
Ma, Z., Tavares, J.M.: A novel approach to segment skin lesions in dermoscopic images based on a deformable model. IEEE J. Biomed. Health Inform. 20, 615–623 (2016)
Machado, D.A., Giraldi, G., Novotny, A.A.: Multi-object segmentation approach based on topological derivative and level set method. Integr. Comput. Aided Eng. 18, 301–311 (2011)
Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11(2), 431–441 (1963)
The MathWorks polyfit web page. https://www.mathworks.com/help/matlab/ref/polyfit.html. Accessed 20 Feb 2020
Nachbar, F., Stolz, W., Merkle, T., Cognetta, A.B., Vogt, T., Landthaler, M., Bilek, P., Braun-Falco, O., Plewig, G.: The ABCD rule of dermatoscopy: high prospective value in the diagnosis of doubtful melanocytic skin lesions. J. Am. Acad. Dermatol. 30(4), 551–559 (1994)
Pathan, S., Prabhu, K.G., Siddalingaswamy, P.C.: Techniques and algorithms for computer aided diagnosis of pigmented skin lesions - a review. Biomed. Signal Process. Control 39, 237–262 (2018)
Schmid, P.: Segmentation of digitized dermatoscopic images by two-dimensional color clustering. IEEE Trans. Med. Imaging 18(2), 164–171 (1999)
Sezgin, M., Sankur, B.: Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13, 146–165 (2004)
Zhou, H., Schaefer, G., Sadka, A., Celebi, M.E.: Anisotropic mean shift based fuzzy c-means segmentation of dermoscopy images. IEEE J. Sel. Top. Sign. Proces. 3(1), 26–34 (2009)
Acknowledgments
Akemi Gálvez and Andrés Iglesias thank the financial support from the project PDE-GIR of the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 778035, and from the Spanish Ministry of Science, Innovation and Universities (Computer Science National Program) under grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds FEDER (AEI/FEDER, UE). Iztok Fister Jr. thanks the financial support from the Slovenian Research Agency (Research Core Funding No. P2-0057). Iztok Fister acknowledges the financial support from the Slovenian Research Agency (Research Core Funding No. P2-0042).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Gálvez, A., Fister, I., Fister, I., Iglesias, A. (2021). Functional Networks for Image Segmentation of Cutaneous Lesions with Rational Curves. In: Herrero, Á., Cambra, C., Urda, D., Sedano, J., Quintián, H., Corchado, E. (eds) 15th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2020). SOCO 2020. Advances in Intelligent Systems and Computing, vol 1268. Springer, Cham. https://doi.org/10.1007/978-3-030-57802-2_75
Download citation
DOI: https://doi.org/10.1007/978-3-030-57802-2_75
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57801-5
Online ISBN: 978-3-030-57802-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)