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Research Papers: Fractal Engineering and Biomedicine

Three-Dimensional Reconstruction of Blood Vessels of the Human Retina by Fractal Interpolation

[+] Author and Article Information
Hichem Guedri

Electronics and Microelectronics Laboratory,
Faculty of Science,
Monastir 5019, Tunisia
e-mail: himougu@yahoo.fr

Jihen Malek

Electronics and Microelectronics Laboratory,
Faculty of Science,
Monastir 5019, Tunisia
e-mail: Jihenemalek14@gmail.com

Hafedh Belmabrouk

Electronics and Microelectronics Laboratory,
Faculty of Science,
Monastir 5019, Tunisia
e-mail: hafedh.belmabrouk@fsm.rnu.tn

Manuscript received June 21, 2015; final manuscript received November 30, 2015; published online March 17, 2016. Assoc. Editor: Charalabos Doumanidis.

J. Nanotechnol. Eng. Med 6(3), 031003 (Mar 17, 2016) (5 pages) Paper No: NANO-15-1047; doi: 10.1115/1.4032170 History: Received June 21, 2015; Revised November 30, 2015

In this work, data from two-dimensional (2D) images of the human retina were taken as a case study. First, the characteristic data points had been removed using the Douglas–Peucker (DP) method, and subsequently, more data points were added using random fractal interpolation approach, to reconstruct a three-dimensional (3D) model of the blood vessel. By visualizing the result, we can see that all the small blood vessels in the human retina are more visible and detailed. This algorithm of 3D reconstruction has the advantage of being fast with calculation time less than 40 s and also can reduce the 3D image storage level on a disk with a reduction ratio between 78% and 96.65%.

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References

Zeng, J. , Zhang, Y. , and Zhan, S. , 2006, “ 3D Tree Models Reconstruction From a Single Image,” ISDA’06, pp. 445–450.
Sturm, P. , and Maybank, S. J. , 1999, “ A Method for Interactive 3D Reconstruction of Piecewise Planar Objects From Single Images,” BMVC, pp. 265–274.
Colombo, C. , Del Bimbo, A. , and Pernici, F. , 2005, “ Metric 3D Reconstruction and Texture Acquisition of Surfaces of Revolution From a Single Uncalibrated View,” Pattern Anal. Mach. Intell., 27(1), pp. 99–114. [CrossRef]
Horry, Y. , Aniyo, K. , and Arai, K. , 1997, “ Tour Into the Picture: Using a Spidery Mesh Interface to Make Animation From a Single Image,” ACM SIGGRAPH, pp. 225–232.
Zhang, L. , Dugas-Phocion, G. , Samson, J. S. , and Seitz, S. M. , 2001, “ Single View Modeling of Free-Form Scenes,” Computer Vision and Pattern Recognition (CVPR), pp. 990–997.
Barnsley, M. F. , and Harrington, A. N. , 1989, “ The Calculus of Fractal Interpolation Functions,” J. Approximation Theory, 57(1), pp. 14–34. [CrossRef]
Mandelbrot, B. B. , 1977, Fractals: Form, Chance and Dimension, W.H. Freeman, San Francisco, CA.
Barnsley, M. F. , 1988, Fractals Everywhere, Academic Press, Boston, MA.
Barnsley, M. F. , 1986, “ Fractal Functions and Interpolations,” Constr. Approximation, 2(1), pp. 303–329. [CrossRef]
STARE (Structured Analysis of the Retina) project website, http://www.ces.clemson.edu/∼ahoover/stare
Gegúndez-Arias, M. E. , Aquino, A. , Bravo, J. M. , and Marín, D. , 2012, “ A Function for Quality Evaluation of Retinal Vessel Segmentations,” IEEE Trans. Med. Imaging, 31(2), pp. 231–239. [CrossRef] [PubMed]
Hoover, A. , Kouznetsova, V. , and Goldbaum, M. , 2000, “ Locating Blood Vessels in Retinal Images by Piecewise Threshold Probing of a Matched Filter Response,” IEEE Trans. Med. Imaging, 19(3), pp. 931–935. [CrossRef]
Zhang, E. , Zhang, Y. , and Zhang, T. , 2002, “ Automatic Retinal Image Registration Based on Blood Vessel Feature Point,” First International Conference on Machine Learning and Cybernetics, Vol. 4, pp. 2010–2015.
El Abbadi, N. K. , and El Saadi, E. H. , 2013, “ Automatic Detection of Vascular Bifurcations and Crossovers in Retinal Fundus Image,” IJCSI Int. J. Comput. Sci. Issues, 10(6), pp. 162–166.
Shahzad, R. , Li, H. K. , Metz, C. , Tang, H. , Schaap, M. , van Vliet, L. , Niessen, W. , and van Walsum, T. , 2013, “ Automatic Segmentation, Detection and Quantification of Coronary Artery Stenoses on CTA,” Int. J. Cardiovasc. Imaging, 29(8), pp. 1847–1859. [CrossRef] [PubMed]
White, E. R. , 1985, “ Assessment of Line-Generalization Algorithms Using Characteristic Point,” Am. Cartographer, 12(1), pp. 17–27. [CrossRef]
Marino, J. S. , 1979, “ Identification of Characteristic Points Along Naturally Occurring Lines,” Cartographic A: Int. J. Geogr. Inf. Geovisualization, 16(1), pp. 70–80. [CrossRef]
Spiegel, M. , Redel, T. , Struffert, T. , Hornegger, J. , and Doerfler, A. , 2011, “ A 2D Driven 3D Vessel Segmentation Algorithm for 3D Digital Subtraction Angiography Data,” Phys. Med. Biol., 56(19), pp. 6401–6419. [CrossRef] [PubMed]
Bourke, P. D. , and Felinto, D. Q. , 2010, “ Blender and Immersive Gaming in a Hemispherical Dome,” Computer Games & Allied Technology 10 (CGAT10), Vol. 1, pp. 280–284.
Sun, H. , 2012, “ A Practical MATLAB Program for Multifractal Interpolation Surface,” 8th International Conference on Natural Computation (ICNC), pp. 909–913.
Sun, H. , 2012, “ The Theory of Fractal Interpolated Surface and Its MATLAB Program,” IEEE Symposium on Electrical & Electronics Engineering (EEESYM), pp. 231–234.
Chen, Y. Q. , and Bi, G. , 1997, “ 3-D IFS Fractals as Real-Time Graphics Model,” Comput. Graphics, 21(3), pp. 367–370. [CrossRef]
Sun, H. , 2012, “ The Theory of Fractal Interpolated Surface and Its MATLAB Program,” IEEE Symposium on Electrical and Electronics Engineering (EEESYM), pp. 231–234.
Chen, Y. Q. , and Bi, G. , 1997, “ 3-D IFS Fractals as Real-time Graphics Model,” Computers & Graphics, 21(3), pp. 367–370. [CrossRef]
Guérin, E. , Tosan, E. , and Baskurt, A. , 2001, “ Fractal Approximation of Surfaces Based on Projected IFS Attractors,” The Eurographics Association, 9(1), pp. 95–103.
Chen, C. , Lee, T. , Huang, Y. M. , and Lai, F. , 2009, “ Extraction of Characteristic Points and Its Fractal Reconstruction for Terrain Profile Data,” Chaos, Solitons Fractals, 39(4), pp. 1732–1743. [CrossRef]

Figures

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Fig. 1

(a) Original image, (b) the skeleton of image, and (c) pixel classification

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Fig. 2

The different stages of DP algorithm

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Fig. 3

Three-dimensional circle

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Fig. 4

Example of a raw image in jpeg

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Fig. 5

Douglas-Peucker (DP) algorithm for ε = 1 (the rectangle symbol represents the: characteristic point and white pixel: blood vessel)

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Fig. 6

Three-dimensional fractal interpolation example

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Fig. 7

The different stages of reconstruction 3D with fractal interpolation

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