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Paper details
Number 3 - September 2020
Volume 30 - 2020
Implementation and evaluation of medical imaging techniques based on conformal geometric algebra
Silvia Franchini, Antonio Gentile, Giorgio Vassallo, Salvatore Vitabile
Abstract
Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric
problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric
algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of
geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing
in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of CGA-based medical
imaging techniques that makes them effective and practically usable. The paper exploits a new simplified formulation of
CGA operators that allows significantly reduced execution times while maintaining the needed result precision. We have
exploited this novel CGA formulation to re-design a suite of medical imaging automatic methods, including image segmentation, 3D reconstruction and registration. Experimental tests show that the re-formulated CGA-based methods lead
to both higher precision results and reduced computation times, which makes them suitable for big data image processing
applications. The segmentation algorithm provides the Dice index, sensitivity and specificity values of 98.14%, 98.05%
and 97.73%, respectively, while the order of magnitude of the errors measured for the registration methods is 10−5.
Keywords
medical image segmentation, medical image registration, computational geometry, Clifford algebra, conformal geometric algebra