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

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 c...

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Bibliographic Details
Published inInternational journal of applied mathematics and computer science Vol. 30; no. 3; pp. 415 - 433
Main Authors Franchini, Silvia, Gentile, Antonio, Vassallo, Giorgio, Vitabile, Salvatore
Format Journal Article
LanguageEnglish
Published Zielona Góra Sciendo 01.09.2020
De Gruyter Poland
Subjects
Algorithms
Big Data
Clifford algebra
computational geometry
conformal geometric algebra
Image processing
Image reconstruction
Image segmentation
Imaging techniques
Linear algebra
Mathematical analysis
Matrix methods
medical image registration
medical image segmentation
Medical imaging
Operators (mathematics)
Registration
Three dimensional models
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Summary: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
ISSN:1641-876X
2083-8492
DOI:10.34768/amcs-2020-0031