Determination of the parabola of the retinal vasculature using a segmentation computational algorithm

David Jaime Giacinti, Fernando Cervantes-Sanchez, Ivan Cruz Aceves, Martha Alicia Hernández González, Luis Miguel López Montero


Quantitative analysis of the architecture of the superior and inferior temporal retinal veins and their monitoring over time could facilitate the diagnosis and timely treatment of diabetic retinopathy. This paper presents a novel method consisting of two stages for automatic segmentation and parabolic modeling of the superior and inferior temporal arcade vessels in retinal fundus images. In the first stage, the Multiscale Line Detector (MLD) is used to detect vessel-like structures in the retinal images. Since the MLD, is a vessel enhancement method, a thresholding strategy has to be used to classify vessel and non-vessel pixels, where an experimental threshold value is compared with five state-of-the-art thresholding methods. In this stage, the proposed segmentation method is compared with six state-of-the-art specialized methods in terms of segmentation accuracy. In the second stage, a parabolic modeling using an optimization strategy based on the Univariate Marginal Distribution Algorithm (UMDA) is performed over the segmented vessels and the results are compared with two state-of-the-art parametric methods and with the ground-truth images outlined by specialists. The results of vessel segmentation using the multiscale line detector demonstrated a high segmentation accuracy with a 0.9618 value using the DRIVE database of retinal fundus images. In addition, the parabolic modeling results provided an average accuracy of 0.825 with the ground-truth of the superior and inferior temporal arcade vessels outlined by ophthalmologists. According to the accuracy and the computational time (5.62 seconds) results, the proposed method can be considered as highly appropriate to perform computer-aided diagnosis in Ophthalmology.


estimation of distribution algorithms; computer-aided diagnosis; retinal fundus images; parabolic modeling; automatic segmentation; diabetic retinopathy; Multiscale Line Detector; ophthalmology


Ballard, D. H. (1981). Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition, XIII (2): 111–122.

Barraza Lloréns, M., Guajardo Barrón, V. J., Hernández Viveros, C., Picó Guzmán, F. J., Crable, E., García González, R., Mora Alba, F., Althié Meza, J. y Urtiz Madrigal, A. (2015). Carga económica de la diabetes mellitus en México, 2013. México D.F.: Fundación Mexicana para la Salud, A.C. Recuperado de

Center for Information Technology (2015). Medical Image Processing, Analysis and Visualization. National Institutes of Health. Recuperado de

Cervantes-Castaneda, R. A., Menchaca-Díaz, R., Alfaro-Trujillo, B., Guerrero-Gutierrez, M. y Chayet-Berdowsky, A. S. (2014). Deficient prevention and late treatment of diabetic retinopathy in Mexico. Gaceta Médica de México, CL (6): 518–526.

Cervantes-Sanchez, F., Cruz-Aceves, I., Hernández-Aguirre, A., Aviña-Cervantes, J. G., Solorio-Meza, S., Ornelas-Rodríguez, M. y Torres-Cisneros, M., (2016), Segmentation of coronary angiograms using Gabor filters and Boltzmann univariate marginal distribution algorithm. Computational Intelligence and Neuroscience, vol. 2016, pp. 1–9.

Chanwimaluang, T., Fan, G. y Fransen, S. R. (2006). Hybrid retinal image registration. IEEE Transactions on Information Technology in Biomedicine, X (1): 129–142.

Chaudhuri, S., Chatterjee, S., Katz, N., Nelson, M. y Goldbaum, M. (1989). Detection of blood vessels in retinal images using two-dimensional matched filters. IEEE Transactions on Medical Imaging, VIII (3): 263–269.

Cruz-Aceves, I., Guerrero-Turrubiates, J., Sierra-Hernández, J.M., (2017), Parametric object detection using estimation of distribution algorithms. Hybrid intelligent techniques for pattern analysis and understanding. CRC Press, Taylor and Francis Group: 69-92.

Duda, R. O. y Hart, P. E. (1972). Use of the Hough Transformation to Detect Lines and Curves in Pictures. Communications of the ACM, XV (1): 11–15.

Frangi, A., Niessen, W., Vincken, K. y Viergever, M. (1998). Multiscale vessel enhancement filtering. En los procedimientos del Medical Image Computing and Computer-Assisted Intervention - MICCAI’98, 130–137. Springer Berlin Heidelberg.

Guerrero-Turrubiates, J., Cruz-Aceves, I., Ledesma, S., Sierra-Hernández, J. M., Velasco, J., Avina-Cervantes, J. G., Ávila-García, M., Rostro-González, H. y Rojas-Laguna, R. (2017). Fast Parabola Detection Using Estimation of Distribution Algorithms. Computational and Mathematical Methods in Medicine, MMXVII: 1–13.

Jiang, X. y Mojon, D. (2003). Adaptive local thresholding by verification-based multithreshold probing with application to vessel detection in retinal images. IEEE Transactions on Pattern Analysis and Machine Intelligence, XXV (1): 131–137.

Kapur, J. N., Sahoo, P. K. y Wong, A. K. C. (1985). A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision, Graphics, and Image Processing, XXIX: 273–285.

Kittler, J., Illingworth, J. y Föglein, J. (1985). Threshold selection based on a simple image statistic. Computer Vision, Graphics, and Image Processing, XXX: 125–147.

Li, Q., You, J. y Zhang, D. (2012). Vessel segmentation and width estimation in retinal images using multiscale production of matched filter responses. Expert Systems with Applications, XXXIX (9): 7600–7610.

Nguyen, U., Bhuiyan, A., Park, L. y Ramamohanarao, K. (2013). An effective retinal blood vessel segmentation method using multi-scale line detection. Pattern Recognition, XLVI (3): 703–715.

M. Niemeijer, J.J. Staal, B. van Ginneken, M. Loog, M.D. Abramoff, "Comparative study of retinal vessel segmentation methods on a new publicly available database", in: SPIE Medical Imaging, Editor(s): J. Michael Fitzpatrick, M. Sonka, SPIE, 2004, vol. 5370, pp. 648-656.

Oloumi, F., Rangayyan, R. M. y Ells, A. L. (2012). Computer-aided diagnosis of proliferative diabetic retinopathy. En los procedimientos del Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1438–1441.

Oloumi, F., Rangayyan, R. M. y Ells, A. L. (2012). Parabolic Modeling of the Major Temporal Arcade in Retinal Fundus Images. IEEE Transactions on Instrumentation and Measurement, LXI (7): 1825–1838.

Otsu, N. (1979). A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, and Cybernetics, IX (1): 62–66.

Ricci, E. y Perfetti, R. (2007). Retinal blood vessel segmentation using line operators and support vector classification. IEEE Transactions on Medical Imaging, XXVI (10): 1357–1365.

Ridler, T. W. y Calvard, S. (1978). Picture thresholding using an iterative selection method. IEEE Transactions on Systems, Man, and Cybernetics, VIII: 630–632.

Rodriguez-Villalobos, E., Cervantes-Aguayo, F., Vargas-Salado, E., Avalos-Munoz, M. E., Juarez-Becerril, D. M. y Ramirez-Barba, E. J. (2005). Retinopatía Diabética. Incidencia y progresión a 12 años. Cirugía y cirujanos, LXXIII (2): 79–84.

Rosenfeld, A. y De la Torre, P. (1983). Histogram concavity analysis as an aid in threshold selection. IEEE Transactions on Systems, Man, and Cybernetics, XIII: 231–235.

Salem, N. M., Salem, S. A. y Nandi, A. K. (2007). Segmentation of retinal blood vessels based on analysis of the hessian matrix and clustering algorithm. En los procedimientos del 15th European Signal Processing Conference 2007, 428–432.

Soares, J. V. B., Leandro, J. J. G., Cesar, R. M., Jelinek, H. F. y Cree, M. J. (2006). Retinal vessel segmentation using the 2-d Gabor wavelet and supervised classification. IEEE Transactions on Medical Imaging, XXV (9): 1214–1222.

Staal, J., Abramoff, M., Niemeijer, M., Viergever, M. y van Ginneken, B. (2004). Ridge-based vessel segmentation in color images of the retina. IEEE Transactions on Medical Imaging, XXIII (4): 501–509.

Tenorio, G. y Ramírez-Sánchez, V. (2010). Retinopatía diabética; conceptos actuales. Revista Médica Del Hospital General de México, LXXIII (3), 193–201.

Wang, S., Li, B. y Zhou, S. (2012). A segmentation method of coronary angiograms based on multi-scale filtering and region-growing. En los procedimientos del 2012 International Conference on Biomedical Engineering and Biotechnology, 678–681.

Yip, R. K. K., Tam, P. K. S. y Leung, D. N. K. (1992). Modification of Hough transform for circles and ellipses detection using a 2-dimensional array. Pattern Recognition, XXV (9): 1007–1022.

Zhao, Y., Liu, Y., Wu, X., Harding, S. P. y Zheng, Y. (2015). Retinal Vessel Segmentation: An Efficient Graph Cut Approach with Retinex and Local Phase. PLOS ONE, X (4): 1–22.



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