AHCI RESEARCH GROUP
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Papers published in international journals,
proceedings of conferences, workshops and books.
OUR RESEARCH
Scientific Publications
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2021
Franchini, Silvia; Vitabile, Salvatore
Geometric Calculus Applications to Medical Imaging: Status and Perspectives Proceedings Article
In: Xambó-Descamps, Sebasti`a (Ed.): Systems, Patterns and Data Engineering with Geometric Calculi, pp. 31–46, Springer International Publishing, Cham, 2021, ISBN: 978-3-030-74486-1.
Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Deep learning, Geometric algebra, Geometric Calculus, Medical image classification, Medical image registration, Medical image segmentation, Medical Imaging, radiomics
@inproceedings{franchiniGeometricCalculusApplications2021,
title = {Geometric Calculus Applications to Medical Imaging: Status and Perspectives},
author = { Silvia Franchini and Salvatore Vitabile},
editor = { Sebasti{`a} {Xambó-Descamps}},
doi = {10.1007/978-3-030-74486-1_3},
isbn = {978-3-030-74486-1},
year = {2021},
date = {2021-01-01},
booktitle = {Systems, Patterns and Data Engineering with Geometric Calculi},
pages = {31--46},
publisher = {Springer International Publishing},
address = {Cham},
series = {SEMA SIMAI Springer Series},
abstract = {Medical imaging data coming from different acquisition modalities requires automatic tools to extract useful information and support clinicians in the formulation of accurate diagnoses. Geometric Calculus (GC) offers a powerful mathematical and computational model for the development of effective medical imaging algorithms. The practical use of GC-based methods in medical imaging requires fast and efficient implementations to meet real-time processing constraints as well as accuracy and robustness requirements. The purpose of this article is to present the state of the art of the GC-based techniques for medical image analysis and processing. The use of GC-based paradigms in Radiomics and Deep Learning, i.e. a comprehensive quantification of tumor phenotypes by applying a large number of quantitative image features and its classification, is also outlined.},
keywords = {3D modeling, Clifford algebra, Deep learning, Geometric algebra, Geometric Calculus, Medical image classification, Medical image registration, Medical image segmentation, Medical Imaging, radiomics},
pubstate = {published},
tppubtype = {inproceedings}
}
Franchini, Silvia; Vitabile, Salvatore
Geometric Calculus Applications to Medical Imaging: Status and Perspectives Proceedings Article
In: Xambó-Descamps, Sebastià (Ed.): Systems, Patterns and Data Engineering with Geometric Calculi, pp. 31–46, Springer International Publishing, Cham, 2021, ISBN: 978-3-030-74486-1.
Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Deep learning, Geometric algebra, Geometric Calculus, Medical image classification, Medical image registration, Medical image segmentation, Medical Imaging, radiomics
@inproceedings{franchini_geometric_2021,
title = {Geometric Calculus Applications to Medical Imaging: Status and Perspectives},
author = {Silvia Franchini and Salvatore Vitabile},
editor = {Sebastià Xambó-Descamps},
doi = {10.1007/978-3-030-74486-1_3},
isbn = {978-3-030-74486-1},
year = {2021},
date = {2021-01-01},
booktitle = {Systems, Patterns and Data Engineering with Geometric Calculi},
pages = {31–46},
publisher = {Springer International Publishing},
address = {Cham},
series = {SEMA SIMAI Springer Series},
abstract = {Medical imaging data coming from different acquisition modalities requires automatic tools to extract useful information and support clinicians in the formulation of accurate diagnoses. Geometric Calculus (GC) offers a powerful mathematical and computational model for the development of effective medical imaging algorithms. The practical use of GC-based methods in medical imaging requires fast and efficient implementations to meet real-time processing constraints as well as accuracy and robustness requirements. The purpose of this article is to present the state of the art of the GC-based techniques for medical image analysis and processing. The use of GC-based paradigms in Radiomics and Deep Learning, i.e. a comprehensive quantification of tumor phenotypes by applying a large number of quantitative image features and its classification, is also outlined.},
keywords = {3D modeling, Clifford algebra, Deep learning, Geometric algebra, Geometric Calculus, Medical image classification, Medical image registration, Medical image segmentation, Medical Imaging, radiomics},
pubstate = {published},
tppubtype = {inproceedings}
}
2020
Franchini, Silvia; Gentile, Antonio; Vassallo, Giorgio; Vitabile, Salvatore
Implementation and Evaluation of Medical Imaging Techniques Based on Conformal Geometric Algebra Journal Article
In: International Journal of Applied Mathematics and Computer Science, vol. 30, no. 3, pp. 415–433, 2020, ISSN: 1641-876X.
Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Geometric algebra, Medical image registration, Medical image segmentation, Medical Imaging
@article{franchiniImplementationEvaluationMedical2020,
title = {Implementation and Evaluation of Medical Imaging Techniques Based on Conformal Geometric Algebra},
author = { Silvia Franchini and Antonio Gentile and Giorgio Vassallo and Salvatore Vitabile},
doi = {10.34768/amcs-2020-0031},
issn = {1641-876X},
year = {2020},
date = {2020-01-01},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {30},
number = {3},
pages = {415--433},
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. textcopyright 2020 Sciendo. All rights reserved.},
keywords = {3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Geometric algebra, Medical image registration, Medical image segmentation, Medical Imaging},
pubstate = {published},
tppubtype = {article}
}
Scianna, Andrea; Gaglio, Giuseppe Fulvio; Grima, Reuben; Guardia, Marcello La
THE VIRTUALIZATION of CH for HISTORICAL RECONSTRUCTION: The AR FRUITION of the FOUNTAIN of ST. GEORGE SQUARE in VALLETTA (MALTA) Proceedings Article
In: K., Morley J. Ellul C. Wong (Ed.): International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives, pp. 143–149, International Society for Photogrammetry and Remote Sensing, 2020, (Issue: 4/W1).
Abstract | Links | BibTeX | Tags: 3D modeling, 3D Modelling, Archaeological Site, Augmented Reality, Complex environments, Cultural heritage, Cultural heritages, Data visualization, Digital Photogrammetry, Fountains, Historical Reconstruction, Sensor sensitivity, Surveying instruments, Technological tools, Terrestrial Laser Scanners, Virtualization
@inproceedings{scianna_virtualization_2020,
title = {THE VIRTUALIZATION of CH for HISTORICAL RECONSTRUCTION: The AR FRUITION of the FOUNTAIN of ST. GEORGE SQUARE in VALLETTA (MALTA)},
author = {Andrea Scianna and Giuseppe Fulvio Gaglio and Reuben Grima and Marcello La Guardia},
editor = {Morley J. Ellul C. Wong K.},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85092158237&doi=10.5194%2fisprs-archives-XLIV-4-W1-2020-143-2020&partnerID=40&md5=78e65721658fcbc025994f2404040e59},
doi = {10.5194/isprs-archives-XLIV-4-W1-2020-143-2020},
year = {2020},
date = {2020-01-01},
booktitle = {International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives},
volume = {44},
pages = {143–149},
publisher = {International Society for Photogrammetry and Remote Sensing},
abstract = {Improving accessibility to Cultural Heritage (CH) is an increasingly urgent challenge today. It is not only a matter of physical inaccessibility but also temporal, considering that part of CH now lost. Fortunately, the most modern technological tools are helping to break down both space and time barriers. In facts, recent advances in representation, 3D modelling and survey methodologies opened new scenarios for valorization and conservation of CH. In particular, the improvement of quality in resolution and sensor sensitivity of cameras allowed to achieve the right level of 3D reconstruction through digital photogrammetry procedures. In the same field, terrestrial laser scanners (TLS) allowed acquiring dense point clouds of complex environments with a millimetric level of accuracy. At the same time, the application of Augmented Reality (AR) and Virtual Reality (VR) technologies is an excellent solution for improving the accessibility to monuments, museums and archaeological sites. It is possible to share new levels of information about CH, in space and time, for touristic, managerial and scientific aims. This work is focused on the virtualization of CH, considering the study case of the fountain of Wignacourt, today present in St. Philip Garden in Floriana and initially located in Valletta (Malta). The application presented allows the virtual fruition of the monument placed in its original location, St. George Square. A simplified plant of the square will enable tourists to make a temporal journey in the past with their mobile device. The work is part of the Interreg Italia-Malta European project named I-Access, dedicated to the improvement of CH accessibility. It focuses the attention to the experimentation of new specific procedures in Geomatics necessary to solve big data issues of complex environment visualization. © Authors 2020.},
note = {Issue: 4/W1},
keywords = {3D modeling, 3D Modelling, Archaeological Site, Augmented Reality, Complex environments, Cultural heritage, Cultural heritages, Data visualization, Digital Photogrammetry, Fountains, Historical Reconstruction, Sensor sensitivity, Surveying instruments, Technological tools, Terrestrial Laser Scanners, Virtualization},
pubstate = {published},
tppubtype = {inproceedings}
}
Scianna, Andrea; Gaglio, Giuseppe Fulvio; Guardia, Marcello La
DIGITAL PHOTOGRAMMETRY, TLS SURVEY and 3D MODELLING for VR and AR APPLICATIONS in CH Proceedings Article
In: N., Lafarge F. Mallet C. Paparoditis (Ed.): International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives, pp. 901–909, International Society for Photogrammetry and Remote Sensing, 2020, (Issue: B2).
Abstract | Links | BibTeX | Tags: 3D model reconstruction, 3D modeling, 3D Modelling, Antennas, Augmented Reality, Digital Photogrammetry, Geometric information, Global Navigation Satellite Systems, Global positioning system, Ground control points, Image Reconstruction, Mini unmanned aerial vehicles, Photogrammetry, Rock mechanics, Surveying instruments, Surveys, Terrestrial Laser Scanners, Three dimensional computer graphics, Unmanned Aerial Vehicles, Unmanned aerial vehicles (UAV), Virtual Reality, Virtual representations
@inproceedings{scianna_digital_2020,
title = {DIGITAL PHOTOGRAMMETRY, TLS SURVEY and 3D MODELLING for VR and AR APPLICATIONS in CH},
author = {Andrea Scianna and Giuseppe Fulvio Gaglio and Marcello La Guardia},
editor = {Lafarge F. Mallet C. Paparoditis N.},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85091094351&doi=10.5194%2fisprs-archives-XLIII-B2-2020-901-2020&partnerID=40&md5=02cb4e9119a689d19125360cf3c388de},
doi = {10.5194/isprs-archives-XLIII-B2-2020-901-2020},
year = {2020},
date = {2020-01-01},
booktitle = {International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives},
volume = {43},
pages = {901–909},
publisher = {International Society for Photogrammetry and Remote Sensing},
abstract = {The world of valorization of Cultural Heritage is even more focused on the virtual representation and reconstructions of digital 3D models of monuments and archaeological sites. In this scenario the quality and the performances offered by the virtual reality (VR) and augmented reality (AR) navigation take primary importance, improving the accessibility of cultural sites where the real access is not allowed for natural conditions or human possibilities. The creation of a virtual environment useful for these purposes requires a specific workflow to follow, combining different strategies in the fields of survey, 3D modelling and virtual navigation. In this work a specific case of study has been analyzed as a practical example, the church of ĝ€ San Giorgio dei Genovesi', settled in the Historic Centre of Palermo (Italy). The acquisition of geometric information has been obtained with the integration of Terrestrial Laser Scanner (TLS) technologies and the photogrammetric reconstruction from mini Unmanned Aerial Vehicle (UAV) equipment. The obtained point cloud has been georeferred considering a network of Ground Control Points (GCP) acquired by a Global Navigation Satellite System (GNSS) receiver. The final point cloud has been processed and properly simplified through 3D modelling procedures, to obtain a realistic and light 3D model reconstruction. The model has hence employed into a VR WEB navigation system and will be used for AR outdoor application in the future, allowing to obtain different solutions for empowering the accessibility of the cultural good. The strategy of 3D CH model reconstruction, followed in this work, could be considered a reference methodology for the development of VR gaming applications finalized to CH valorization and AR applications, applied to museums or touristic paths in historical centres. © 2020 International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives.},
note = {Issue: B2},
keywords = {3D model reconstruction, 3D modeling, 3D Modelling, Antennas, Augmented Reality, Digital Photogrammetry, Geometric information, Global Navigation Satellite Systems, Global positioning system, Ground control points, Image Reconstruction, Mini unmanned aerial vehicles, Photogrammetry, Rock mechanics, Surveying instruments, Surveys, Terrestrial Laser Scanners, Three dimensional computer graphics, Unmanned Aerial Vehicles, Unmanned aerial vehicles (UAV), Virtual Reality, Virtual representations},
pubstate = {published},
tppubtype = {inproceedings}
}
Franchini, Silvia; Gentile, Antonio; Vassallo, Giorgio; Vitabile, Salvatore
Implementation and evaluation of medical imaging techniques based on conformal geometric algebra Journal Article
In: International Journal of Applied Mathematics and Computer Science, vol. 30, no. 3, pp. 415–433, 2020, ISSN: 1641-876X.
Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Geometric algebra, Medical image registration, Medical image segmentation, Medical Imaging
@article{franchini_implementation_2020,
title = {Implementation and evaluation of medical imaging techniques based on conformal geometric algebra},
author = {Silvia Franchini and Antonio Gentile and Giorgio Vassallo and Salvatore Vitabile},
doi = {10.34768/amcs-2020-0031},
issn = {1641-876X},
year = {2020},
date = {2020-01-01},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {30},
number = {3},
pages = {415–433},
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. © 2020 Sciendo. All rights reserved.},
keywords = {3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Geometric algebra, Medical image registration, Medical image segmentation, Medical Imaging},
pubstate = {published},
tppubtype = {article}
}
2019
Scianna, Andrea; Gaglio, Giuseppe Fulvio; Guardia, Marcello
Augmented reality for cultural heritage: The rebirth of a historical square Proceedings Article
In: P., Macher H. Murtiyoso A. Grussenmeyer (Ed.): International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives, pp. 303–308, International Society for Photogrammetry and Remote Sensing, 2019, (Issue: 2/W17).
Abstract | Links | BibTeX | Tags: 3-D printing, 3D model reconstruction, 3D modeling, 3D Modelling, 3D printers, 3D Printing, Augmented Reality, Cultural heritage, Cultural heritages, Data acquisition, Data handling, Image Reconstruction, Mobile Applications, Photogrammetry, Rapid prototyping, Rapid prototyping technology, Repair, Reverse engineering, Reverse engineering techniques, Surveying instruments, Terrestrial Laser Scanners, Thallium, Three dimensional computer graphics, Virtual heritage, Visualization
@inproceedings{scianna_augmented_2019,
title = {Augmented reality for cultural heritage: The rebirth of a historical square},
author = {Andrea Scianna and Giuseppe Fulvio Gaglio and Marcello Guardia},
editor = {Macher H. Murtiyoso A. Grussenmeyer P.},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85078130517&doi=10.5194%2fisprs-archives-XLII-2-W17-303-2019&partnerID=40&md5=7c28c9b8bf88d7a1af810aeca9c2cff9},
doi = {10.5194/isprs-archives-XLII-2-W17-303-2019},
year = {2019},
date = {2019-01-01},
booktitle = {International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences - ISPRS Archives},
volume = {42},
pages = {303–308},
publisher = {International Society for Photogrammetry and Remote Sensing},
abstract = {The case study, faced in this paper, arises in the context of Interreg Italia-Malta European project named I-Access, dedicated to the improvement of accessibility to Cultural Heritage (CH). Accessibility considered not only as the demolition of physical architectural barriers, but also as the possibility of fruition of CH through technological tools that can increase its perception and knowledge. Last achievements in photogrammetry and terrestrial laser scanner (TLS) technology offered new methods of data acquisition in the field of CH, giving the possibility of monitoring and processing big data, in the form of point clouds. Ever in this field, reverse engineering techniques and computer graphics are even more used for involving visitors to discover CH, with navigation into 3D reconstructions, empowering the real visualization adding further 3D information through the Augmented Reality (AR). At the same time, recent advances on rapid prototyping technologies grant the automated 3D printing of scaled 3D model reconstructions of real CH elements allowing the tactile fruition of visitors that suffer from visual defects and the connection with 3D AR visualizations. The presented work shows how these technologies could revive an historical square, the Piazza Garraffo in Palermo (Italy), with the virtual insertion of its baroque fountain, originally placed there. The final products of this work are an indoor and an outdoor AR mobile application, that allow the visualization of the historical original asset of the square. This study case shows how the mixing of AR and the rapid prototyping technologies could be useful for the improvement of the fruition of CH. This work could be considered a multidisciplinary experimentation, where different technologies, today still in development, contribute to the same goal aimed at improving the accessibility of the monument for enhancing the fruition of CH. © Authors 2019. CC BY 4.0 License},
note = {Issue: 2/W17},
keywords = {3-D printing, 3D model reconstruction, 3D modeling, 3D Modelling, 3D printers, 3D Printing, Augmented Reality, Cultural heritage, Cultural heritages, Data acquisition, Data handling, Image Reconstruction, Mobile Applications, Photogrammetry, Rapid prototyping, Rapid prototyping technology, Repair, Reverse engineering, Reverse engineering techniques, Surveying instruments, Terrestrial Laser Scanners, Thallium, Three dimensional computer graphics, Virtual heritage, Visualization},
pubstate = {published},
tppubtype = {inproceedings}
}
2015
Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore
ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing Journal Article
In: IEEE Transactions on Computers, vol. 64, no. 4, pp. 955–970, 2015, ISSN: 0018-9340.
Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Embedded coprocessors, Field Programmable Gate Arrays, FPGA prototyping, Geometric algebra, Growing Neural Gas, iterative closest point (ICP), marching spheres, Medical image registration, Medical Imaging, Segmentation, systems-on-programmable-chip, thin-plate spline robust point matching (TPS-RPM), Volume registration
@article{franchiniConformalALUConformalGeometric2015,
title = {ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing},
author = { Silvia Franchini and Antonio Gentile and Filippo Sorbello and Giorgio Vassallo and Salvatore Vitabile},
doi = {10.1109/TC.2014.2315652},
issn = {0018-9340},
year = {2015},
date = {2015-01-01},
journal = {IEEE Transactions on Computers},
volume = {64},
number = {4},
pages = {955--970},
abstract = {Medical imaging involves important computational geometric problems, such as image segmentation and analysis, shape approximation, three-dimensional (3D) modeling, and registration of volumetric data. In the last few years, Conformal Geometric Algebra (CGA), based on five-dimensional (5D) Clifford Algebra, is emerging as a new paradigm that offers simple and universal operators for the representation and solution of complex geometric problems. However, the widespread use of CGA has been so far hindered by its high dimensionality and computational complexity. This paper proposes a simplified formulation of the conformal geometric operations (reflections, rotations, translations, and uniform scaling) aimed at a parallel hardware implementation. A specialized coprocessing architecture (ConformalALU) that offers direct hardware support to the new CGA operators, is also presented. The ConformalALU has been prototyped as a complete System-on-Programmable-Chip (SoPC) on the Xilinx ML507 FPGA board, containing a Virtex-5 FPGA device. Experimental results show average speedups of one order of magnitude for CGA rotations, translations, and dilations with respect to the geometric algebra software library Gaigen running on the general-purpose PowerPC processor embedded in the target FPGA device. A suite of medical imaging applications, including segmentation, 3D modeling and registration of medical data, has been used as testbench to evaluate the coprocessor effectiveness. textcopyright 2015 IEEE.},
keywords = {3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Embedded coprocessors, Field Programmable Gate Arrays, FPGA prototyping, Geometric algebra, Growing Neural Gas, iterative closest point (ICP), marching spheres, Medical image registration, Medical Imaging, Segmentation, systems-on-programmable-chip, thin-plate spline robust point matching (TPS-RPM), Volume registration},
pubstate = {published},
tppubtype = {article}
}
Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore
ConformalALU: A conformal geometric algebra coprocessor for medical image processing Journal Article
In: IEEE Transactions on Computers, vol. 64, no. 4, pp. 955–970, 2015, ISSN: 0018-9340.
Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Embedded coprocessors, Field Programmable Gate Arrays, FPGA prototyping, Geometric algebra, Growing Neural Gas, iterative closest point (ICP), marching spheres, Medical image registration, Medical Imaging, Segmentation, systems-on-programmable-chip, thin-plate spline robust point matching (TPS-RPM), Volume registration
@article{franchini_conformalalu_2015,
title = {ConformalALU: A conformal geometric algebra coprocessor for medical image processing},
author = {Silvia Franchini and Antonio Gentile and Filippo Sorbello and Giorgio Vassallo and Salvatore Vitabile},
doi = {10.1109/TC.2014.2315652},
issn = {0018-9340},
year = {2015},
date = {2015-01-01},
journal = {IEEE Transactions on Computers},
volume = {64},
number = {4},
pages = {955–970},
abstract = {Medical imaging involves important computational geometric problems, such as image segmentation and analysis, shape approximation, three-dimensional (3D) modeling, and registration of volumetric data. In the last few years, Conformal Geometric Algebra (CGA), based on five-dimensional (5D) Clifford Algebra, is emerging as a new paradigm that offers simple and universal operators for the representation and solution of complex geometric problems. However, the widespread use of CGA has been so far hindered by its high dimensionality and computational complexity. This paper proposes a simplified formulation of the conformal geometric operations (reflections, rotations, translations, and uniform scaling) aimed at a parallel hardware implementation. A specialized coprocessing architecture (ConformalALU) that offers direct hardware support to the new CGA operators, is also presented. The ConformalALU has been prototyped as a complete System-on-Programmable-Chip (SoPC) on the Xilinx ML507 FPGA board, containing a Virtex-5 FPGA device. Experimental results show average speedups of one order of magnitude for CGA rotations, translations, and dilations with respect to the geometric algebra software library Gaigen running on the general-purpose PowerPC processor embedded in the target FPGA device. A suite of medical imaging applications, including segmentation, 3D modeling and registration of medical data, has been used as testbench to evaluate the coprocessor effectiveness. © 2015 IEEE.},
keywords = {3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Embedded coprocessors, Field Programmable Gate Arrays, FPGA prototyping, Geometric algebra, Growing Neural Gas, iterative closest point (ICP), marching spheres, Medical image registration, Medical Imaging, Segmentation, systems-on-programmable-chip, thin-plate spline robust point matching (TPS-RPM), Volume registration},
pubstate = {published},
tppubtype = {article}
}