Eduardo Bayro

This talk presents an integrated exploration of advanced geometric and computational approaches applied to the modeling and analysis of the human eye. Our discussion is divided into three main parts: (1) 3D modeling of the oculomotor system, (2) a novel theory of color perception using conformal geometric algebra, and (3) deep learning-based medical image processing techniques for detecting eye-related illnesses.

1. 3D Eye Model and the Motor Algebra Framework
We begin by presenting a detailed 3D model of the oculomotor system using the Motor Algebra Framework. This mathematical formulation allows for a more accurate representation of rigid body motions and rotations within the eye. Unlike traditional vector-based models, motor algebra offers compact and coordinate-free formulations, making it particularly well-suited for simulating the complex movements of the eyeball and extraocular muscles. This has promising implications for biomedical engineering, particularly in the development of assistive technologies, surgical simulations, and diagnostic tools.

2. A Novel Theory of Color in Conformal Geometric Algebra
In the second part of the lecture, we introduce a groundbreaking theory of color developed using the tools of Conformal Geometric Algebra (CGA). This theory not only generalizes prior models from the last five decades but also provides a unified and consistent framework for representing and processing color information in higher-dimensional spaces. By employing the light cone as a geometric computational framework and utilizing the Minkowski metric in conjunction with Lorentz transformations, we construct a physically coherent space suited for accurate color modeling and processing. The conventional RGB model, represented in 3D Euclidean space, fails to represent color appropriately; instead, a pseudo-Euclidean metric—such as that defined by the light cone—is necessary for a correct depiction of color space. The practical validity of this theory is demonstrated through its ability to model changes in object appearance under different natural lighting conditions, such as those occurring throughout the day. In this context, we introduce the Quaternion Split Fourier Transform (QSFT) for color image filtering within a pseudo-Euclidean metric. This approach proves to be more robust and effective than the conventional Quaternion Fourier Transform, particularly in capturing the chromatic and structural components of images under non-uniform illumination. We further demonstrate how the Quaternion Split Neural Network (QSNN) can be used to equalize and enhance color images by learning the transformations dictated by our geometric framework.

3. Deep Learning in Medical Image Processing of Eye Diseases
In the final section, we shift focus to the application of Deep Learning, specifically Convolutional Neural Networks (CNNs), in the medical analysis of eye diseases. Diseases such as age-related macular degeneration, diabetic retinopathy, glaucoma, and cataracts can be detected and monitored using automated image processing techniques.
By training CNNs on large datasets of retinal and ocular images, we are able to automatically extract and classify critical pathological features. This includes segmentation of lesions, blood vessels, and optic disc regions, which are crucial for accurate diagnosis. The integration of geometric color modeling into the preprocessing pipeline can further enhance feature extraction by correcting lighting variations and improving contrast.
The use of these technologies allows for earlier and more precise diagnosis, supporting ophthalmologists in decision-making and enabling personalized treatment strategies for patients. Moreover, these tools hold potential for deployment in remote or under-resourced healthcare settings, expanding access to high-quality eye care.

Biography:

Prof. Dr. Bayro-Corrochano is a distinguished leader and internationally recognized scientist and educator in Geometric Cybernetics. His expertise lies in applying Clifford geometric algebras across various fields, including pattern recognition, image processing, computer vision, artificial intelligence, neurocomputing, machine learning, control, robotics and quantum computing.

He has pioneered several advancements, including the geometric MLP, Clifford Support Vector Machines, quaternion quantum neural networks, and the innovative quaternion spike neural networks for pattern recognition and neuro control. Additionally, he developed the Quaternion Wavelet Transform and Quaternion Fourier Transform using space-time metrics, along with Quaternion Fractional FFT and Quaternion Quantum FFT for color image processing. His contributions also extend to the interpolation of geometric entities (such as lines, planes, circles, spheres, and hyperplanes) using motor algebra (SE(3)) and a Bézier approach in the Study manifold.

In the realm of geometric algebra, his groundbreaking work includes contributions to kinematics, dynamics, Euler-Lagrange and Newton-Euler recursive algorithms, port Hamiltonians, and the Koopman Operator for phase space computations. His research has significantly impacted nonlinear control, particularly in robot vision and general robotics. Furthermore, he is a strong advocate for geometric quantum computing within the Clifford geometric algebra framework.

 His scientific contributions are particularly well represented in three of his eight books:

• Geometric Algebra Applications Vol. I: for Graphics, Vision, and Neurocomputing (Springer Verlag, 2018)
• Geometric Algebra Applications Vol. II: Robot Modelling and Control (Springer Verlag, 2019)
• Geometric Algebra Applications Vol. III: Integral Transforms for Science and Engineering (Springer Verlag, 2024)

These books serve as valuable resources for graduate courses and provide inspiration for researchers and engineers working in cybernetics and related fields.

Prof. Bayro-Corrochano has served as an Associate Editor for the IEEE Transactions on Neural Networks and Learning Systems and the Journal of Mathematical Imaging and Vision. He is also a member of the editorial boards for the Journal of Pattern Recognition and Journal of Robotica. His achievements have been recognized with the First Prize in Science and Technology from the State of Jalisco, Mexico, in both 2003 and 2009. He is a Fellow of the International Association of Pattern Recognition Society and a senior member of IEEE and IEEE/RAS Ad-Com Member  (GEO Area 1 Representative). 

He has played a key role in organizing major international conferences, serving as General Chair of ICPR 2016 (Dec. 4-8, Cancun, Mexico) and IEEE/RAS Humanoids 2016 (Nov. 15-17, Cancun, Mexico). He is also set to be the General Chair of IEEE/RAS Humanoids 2026 and IEEE/RAS ICRA 2028 both in Guadalajara, Mexico.

Email:

Address:POZNAŃ UNIVERSITY OF TECHNOLOGY, Institute of Automation and Robotics, Poznan, Wielkopolskie, Poland, 60-965