Mimetic finite difference methods for restoration of fundus images for automatic detection of glaucoma suspects

ABSTRACT

Glaucoma is one of the leading causes of irreversible blindness in people over 40 years old. Previously, it was developed acomputational tool for automatic glaucoma detection, which implements anovel method that has shown improvement in the accuracy of the detection compared to other classical methods. However, this method is sensitive to the quality of the acquired image. For this reason, automatic image restoration of the source images is needed to improve the quality of glaucoma suspect detection. We propose to use the Perona–Malik anisotropic diffusion filter as part of the pre-processing step because apart from attenuating noise and brilliance in the images, it preserves essential information such as the borders of the optic disc and the cup boundaries, which are of particular interest in this work. We solve numerically the problem in partial differential equations, which represent the Perona–Malik diffusion filter, using explicit finite mimetic differences methods, which have the advantage of preserving the continuum properties of the mathematical operators often encountered in image processing and analysis equations, ensuring better orders of convergence. By guaranteeing these mathematical properties, the original structure of the source image is maintained, improving the diagnosis of the patient.

KEYWORDS:

• Glaucoma
• anisotropic filtering
• image restoration
• partial differential equations

Acknowledgments

G. Calderón and J.C. Carrillo E. would like to acknowledge the financial support provided by the VIE-UIS under grant No 2415.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Vicerrectoría de Investigación y Extensión [24155].

Notes on contributors

Jorge Villamizar

Jorge Villamizar is a PhD student at Universidad de Los Andes, Venezuela. The topic of his thesis is in numerical analysis and specifically the applications of mimetic methods. He obtained a MSc. in Computer Engineering from the University of Puerto Rico, Mayagüez Campus in 2006, his main area of work was Digital Signal Processing. He is a professor at Universidad Industrial de Santander, School of Mathematics and a member of the Biomedical Imaging, Vision, and Learning Laboratory.

Giovanni Calderón

Giovanni Calderón is a Doctor in Mathematics from the Polytechnic University of Catalunya in 2005. Trained in the area of Numerical Analysis and Computational Mechanics. He was a full-time professor for 25 years at the Universidad de Los Andes, Mérida, Venezuela. Since 2015 he has been working as instructor at Universidad Industrial de Santander, Colombia.

Julio Carrillo

Julio Carrillo received his BSc. in July 1987 from Universidad del Quindío, Colombia. He received his MSc. in Mathematics in April 1992 from Universidad del Valle, Colombia, and his PhD from University of Louisiana at Lafayette in December 2007. He is a full-time professor at Universidad Industrial de Santander at Bucaramanga, Santander, Colombia, since September 2011.

Lola Bautista Rozo

Lola Bautista Rozo is a Computer Systems Engineer from Universidad Industrial de Santander, Colombia (2003), MSc. in Computer Engineering from University of Puerto Rico, Mayagüez Campus (2007), and PhD in Digital Signal Processing and Imaging from Université Côte d'Azur, France (2017).  She joined the Computer Systems Engineering and Informatics School at Universidad Industrial de Santander in 2011.  Currently, she is the director of the Biomedical Imaging, Vision and Learning Laboratory and adjoint director of the BSc. program in Computer Systems Engineering.  Her research interests are inverse problems for medical imaging as well as virtual and augmented reality for medical training.

Juan Carrillo

Juan Carrillo is a Computer Systems Engineer from Universidad Industrial de Santander, Colombia (2020). The topic of his thesis was eye diseases detection using fundus images of the eye. His main areas of work are image processing and deep learning. He is a member of the Biomedical Imaging, Vision and Learning Laboratory.

Juan Rueda

Juan Rueda is an ophthalmologist, director of the Centro de prevención y consultoría en glaucoma in Bucaramanga, Colombia.  He was a fellow in glaucoma at the Bascom Palmer Eye Institute of the University of Miami Health System (1994).  He has been Chief of the Ophthalmology Department and of the Glaucoma Department at Clínica FOSCAL.  He has been also the Chief of the Colombian Society of Glaucoma, he is member of the Panamerican Society of Ophthalmology and of the Latinamerican Society of Glaucoma.  His main interest is the creation of programs for prevention of blindness, focused on underrepresented communities, as well as in state-of-the-art technology for diagnostic and treatment of glaucoma.

José Castillo

José Castillo is a Professor in the Department of Mathematics and Statistics at San Diego State University (SDSU). He joined the SDSU faculty in 1987 after he received his Ph.D. in Applied Mathematics from the University of New Mexico. His research in mimetic discretization methods have been applied to problems in oil exploration, coastal ocean modeling and carbon sequestration. Dr. Castillo is the Founder and Director of the Computational Science Research Center and the Computational Science Program at SDSU. The Center, founded in 1999, facilitates cooperation between the university and industry as well as national laboratories. Dr. Castillo also created the MS in Computational Science in 1999 and the Ph.D. in Computational Science in 2002 respectively. Dr. Castillo has been named twice to the top 25 most influential people at SDSU (2003 and 2008). He has graduated eight (8) doctoral and 12 masters students. He is currently directing three (3) doctoral and two (2) masters’ students. Dr. Castillo has presented and organized sessions at numerous SIAM conferences. He is the founder, faculty and advisor of a SIAM student chapter at SDSU and represents SIAM in the Mathematical Council of the Americas (MCofA). He has also chaired the Pan American Advanced Studies Institute in Computational Science and Engineering four times and has given many invited talks at various international conferences as well. Dr. Castillo is currently an associate editor for three (3) journals, and has been a guest editor for several Elsevier Journals (i.e. Applied Numerical Mathematics, Computer and Mathematical Modeling, Computational and Applied Mathematics).