<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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<sup>−5</sup>.</p></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.

Implementation and Evaluation of Medical Imaging Techniques Based on Conformal Geometric Algebra

Department of Biomedicine, Neuroscience and Advanced Diagnostics (Bi.N.D.)

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard...

Implementation and Evaluation of Medical Imaging Techniques Based on Conformal Geometric Algebra

Published Online: Sep 29, 2020

Page range: 415 - 433

Received: Oct 14, 2019

Accepted: May 29, 2020

DOI: https://doi.org/10.34768/amcs-2020-0031

Keywords
medical image segmentation, medical image registration, computational geometry, Clifford algebra, conformal geometric algebra

© 2020 Silvia Franchini et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Implementation and Evaluation of Medical Imaging Techniques Based on Conformal Geometric Algebra

Published Online: Sep 29, 2020

Page range: 415 - 433

Received: Oct 14, 2019

Accepted: May 29, 2020

DOI: https://doi.org/10.34768/amcs-2020-0031

Keywordsmedical image segmentation, medical image registration, computational geometry, Clifford algebra, conformal geometric algebra

© 2020 Silvia Franchini et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
medical image segmentation, medical image registration, computational geometry, Clifford algebra, conformal geometric algebra