Information Sciences, ISSN 0020-0255, 10/2014, Volume 281, pp. 559 - 572

Feature analysis plays an important role in many multispectral image applications and scale invariant feature transform (SIFT) has been successfully applied...

Geometric algebra | Feature extraction | Multispectral image | SIFT | CLIFFORD | DISCRIMINANT-ANALYSIS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CLASSIFICATION | REGISTRATION | Analysis | Algebra | Algorithms | Transforms | Images | Invariants | Image detection | Genetic algorithms

Geometric algebra | Feature extraction | Multispectral image | SIFT | CLIFFORD | DISCRIMINANT-ANALYSIS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CLASSIFICATION | REGISTRATION | Analysis | Algebra | Algorithms | Transforms | Images | Invariants | Image detection | Genetic algorithms

Journal Article

Proceedings of the IEEE, ISSN 0018-9219, 09/2014, Volume 102, Issue 9, pp. 1340 - 1363

In this paper, we explicate the suggested benefits of Clifford's geometric algebra (GA) when applied to the field of electrical engineering. Engineers are...

Geometry | Algebra | Quaternions | Magnetic separation | electromagnetism | geometric algebra (GA) | relativity | Mathematics | Clifford algebra | Maxwell's equations | Doppler effect | Electric fields | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Learning curves | Problem solving | Electronics | Representations | Cases (containers)

Geometry | Algebra | Quaternions | Magnetic separation | electromagnetism | geometric algebra (GA) | relativity | Mathematics | Clifford algebra | Maxwell's equations | Doppler effect | Electric fields | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Learning curves | Problem solving | Electronics | Representations | Cases (containers)

Journal Article

2003, Graduate texts in mathematics, ISBN 0387401229, Volume 222, 453

eBook

IEEE Signal Processing Letters, ISSN 1070-9908, 06/2016, Volume 23, Issue 6, pp. 858 - 862

This letter exploits geometric (Clifford) algebra (GA) theory to devise and introduce a new adaptive filtering strategy. From a least-squares cost function,...

Adaptive Filters | Three-dimensional displays | Algebra | Geometric Algebra | Quaternions | Rotors | Estimation | 3D Registration | Calculus | Point Cloud Alignment | Standards | 3-D registration | point cloud alignment | geometric algebra (GA) | REGISTRATION | adaptive filters (AFs) | GRADIENT OPERATOR | QUATERNION | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Mathematical analysis | Adaptive filters | Estimating | Cost function | Three dimensional

Adaptive Filters | Three-dimensional displays | Algebra | Geometric Algebra | Quaternions | Rotors | Estimation | 3D Registration | Calculus | Point Cloud Alignment | Standards | 3-D registration | point cloud alignment | geometric algebra (GA) | REGISTRATION | adaptive filters (AFs) | GRADIENT OPERATOR | QUATERNION | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Mathematical analysis | Adaptive filters | Estimating | Cost function | Three dimensional

Journal Article

Microprocessors and Microsystems, ISSN 0141-9331, 03/2019, Volume 65, pp. 180 - 195

In modern days multi-dimensional signal processing has appeared as a trendy research area, including hyper-spectral image/video processing. It involves...

Dimensional customization | Parallelism | Geometric algebra (GA) | VLSI architecture design | Modular GA co-processor | PQC-ALU | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMPLEMENTATION | GEOMETRIC-ALGEBRA | ENGINEERING, ELECTRICAL & ELECTRONIC | COPROCESSOR | COMPUTER SCIENCE, THEORY & METHODS | VLSI | Image processing | Digital electronics | Very large scale integration | Real time | Integrated circuits | Pipelining (computers) | Algebra | Algorithms | Microprocessors | Mathematical analysis | Video | Signal processing | Hardware

Dimensional customization | Parallelism | Geometric algebra (GA) | VLSI architecture design | Modular GA co-processor | PQC-ALU | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMPLEMENTATION | GEOMETRIC-ALGEBRA | ENGINEERING, ELECTRICAL & ELECTRONIC | COPROCESSOR | COMPUTER SCIENCE, THEORY & METHODS | VLSI | Image processing | Digital electronics | Very large scale integration | Real time | Integrated circuits | Pipelining (computers) | Algebra | Algorithms | Microprocessors | Mathematical analysis | Video | Signal processing | Hardware

Journal Article

Pattern Recognition Letters, ISSN 0167-8655, 11/2019, Volume 127, pp. 11 - 17

•Speeded-up robust features algorithm is reformulated based on geometric algebra to deal with multispectral images.•A new Hessian matrix based on geometric...

Multispectral image | Speeded-Up robust features (SURF) | Geometric algebra (GA) | Interest points | CLIFFORD ALGEBRAS | SIFT | FUSION | REGISTRATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Image registration | Pyramids | Algorithms | Mathematical analysis | Feature extraction | Robustness | Pattern recognition | Object recognition | Hessian matrices | Image reconstruction | Image classification

Multispectral image | Speeded-Up robust features (SURF) | Geometric algebra (GA) | Interest points | CLIFFORD ALGEBRAS | SIFT | FUSION | REGISTRATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Image registration | Pyramids | Algorithms | Mathematical analysis | Feature extraction | Robustness | Pattern recognition | Object recognition | Hessian matrices | Image reconstruction | Image classification

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 07/2019, Volume 67, Issue 14, pp. 3649 - 3662

This paper reformulates adaptive filters (AFs) in the framework of geometric algebra (GA), developing a complete study of the resulting geometric-algebra...

Three-dimensional displays | Quaternions | geometric algebra | Adaptive filtering | Cost function | Calculus | Matrices | Standards

Three-dimensional displays | Quaternions | geometric algebra | Adaptive filtering | Cost function | Calculus | Matrices | Standards

Journal Article

Memetic Computing, ISSN 1865-9284, 9/2017, Volume 9, Issue 3, pp. 231 - 244

This paper presents panoramic unmanned aerial vehicle (UAV) image stitching techniques based on an optimal Scale Invariant Feature Transform (SIFT) method. The...

Engineering | Control, Robotics, Mechatronics | Complex Systems | Appl.Mathematics/Computational Methods of Engineering | Artificial Intelligence (incl. Robotics) | Panoramic UAV images | Adaptive threshold value | Geometric algebra (GA) | RANSAC (random sample consensus) | Applications of Mathematics | Good distinctiveness and robustness | Bioinformatics | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | OPTIMIZATION | REGISTRATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | FEATURES

Engineering | Control, Robotics, Mechatronics | Complex Systems | Appl.Mathematics/Computational Methods of Engineering | Artificial Intelligence (incl. Robotics) | Panoramic UAV images | Adaptive threshold value | Geometric algebra (GA) | RANSAC (random sample consensus) | Applications of Mathematics | Good distinctiveness and robustness | Bioinformatics | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | OPTIMIZATION | REGISTRATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | FEATURES

Journal Article

IEEE Access, ISSN 2169-3536, 2019, Volume 7, pp. 71235 - 71244

Feature extraction, including feature detection and description, plays an important role in many computer vision applications. The feature extraction for...

Computer vision | Algebra | geometric algebra (GA) | Feature extraction | Robustness | Real-time systems | Oriented fast and rotated brief (ORB) | multispectral images | Genetic algorithms | Manganese | feature extraction | PART | COMPUTER SCIENCE, INFORMATION SYSTEMS | REGISTRATION | MODEL | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC

Computer vision | Algebra | geometric algebra (GA) | Feature extraction | Robustness | Real-time systems | Oriented fast and rotated brief (ORB) | multispectral images | Genetic algorithms | Manganese | feature extraction | PART | COMPUTER SCIENCE, INFORMATION SYSTEMS | REGISTRATION | MODEL | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 03/2017, Volume 470, pp. 154 - 196

The art of quantum algorithm design is highly nontrivial. Grover’s search algorithm constitutes a masterpiece of quantum computational software. In this...

Riemannian geometry | Quantum algorithms | Geometric Clifford algebras | Probability theory | Quantum mechanics | FISHER INFORMATION | ENERGY | SPACETIME ALGEBRA | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | IMPLEMENTATION | SEARCH ALGORITHM | ENTROPIC ANALYSIS | STATISTICAL DISTANCE | ERROR-CORRECTION | MATHEMATICAL LANGUAGE | Atoms | Algebra | Algorithms | Quantum theory | Physics - Quantum Physics

Riemannian geometry | Quantum algorithms | Geometric Clifford algebras | Probability theory | Quantum mechanics | FISHER INFORMATION | ENERGY | SPACETIME ALGEBRA | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | IMPLEMENTATION | SEARCH ALGORITHM | ENTROPIC ANALYSIS | STATISTICAL DISTANCE | ERROR-CORRECTION | MATHEMATICAL LANGUAGE | Atoms | Algebra | Algorithms | Quantum theory | Physics - Quantum Physics

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 9/2019, Volume 29, Issue 4, pp. 1 - 41

We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we...

Secondary 83Dxx | 83Cxx | Theoretical, Mathematical and Computational Physics | Gravitational waves | Relativity | General relativity | 83C35 | Geometric algebra | 83C40 | Physics | Mathematical Methods in Physics | 15A66 | Clifford algebra | Primary 83-XX | Applications of Mathematics | Physics, general | MATHEMATICS, APPLIED | MEMORY | PHYSICS, MATHEMATICAL | Physicists | Algebra | Gravity

Secondary 83Dxx | 83Cxx | Theoretical, Mathematical and Computational Physics | Gravitational waves | Relativity | General relativity | 83C35 | Geometric algebra | 83C40 | Physics | Mathematical Methods in Physics | 15A66 | Clifford algebra | Primary 83-XX | Applications of Mathematics | Physics, general | MATHEMATICS, APPLIED | MEMORY | PHYSICS, MATHEMATICAL | Physicists | Algebra | Gravity

Journal Article

2003, ISBN 0521480221, Volume 9780521480222, 592

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to...

Electronic commerce | Information storage and retrieval systems | Congresses

Electronic commerce | Information storage and retrieval systems | Congresses

Book

IEEE Access, ISSN 2169-3536, 2018, Volume 6, pp. 56575 - 56586

Spatiotemporal interest points (STIPs) are often extracted for action recognition in videos. But most of the current interest point detection methods are not...

Optical fibers | Action recognition | Three-dimensional displays | Algebra | multi-scale space | geometric algebra (GA) | multi-channel video | Detectors | Color | Feature extraction | Videos | spatio-temporal interest points (STIPs) | SIFT | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC

Optical fibers | Action recognition | Three-dimensional displays | Algebra | multi-scale space | geometric algebra (GA) | multi-channel video | Detectors | Color | Feature extraction | Videos | spatio-temporal interest points (STIPs) | SIFT | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Journal of Automated Reasoning, ISSN 0168-7433, 10/2019, Volume 63, Issue 3, pp. 787 - 808

Although the theories of geometric algebra (GA) are widely applied in engineering design and analysis, the studies on their formalization have been scarcely...

Metrics | Artificial Intelligence | Computer Science | Multivectors | Geometric algebra | Formalization | HOL Light | Symbolic and Algebraic Manipulation | Mathematical Logic and Foundations | Mathematical Logic and Formal Languages | CLIFFORD | ROBOTS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Analysis | Algebra | Design engineering

Metrics | Artificial Intelligence | Computer Science | Multivectors | Geometric algebra | Formalization | HOL Light | Symbolic and Algebraic Manipulation | Mathematical Logic and Foundations | Mathematical Logic and Formal Languages | CLIFFORD | ROBOTS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Analysis | Algebra | Design engineering

Journal Article

Electronics, ISSN 2079-9292, 01/2015, Volume 4, Issue 1, pp. 94 - 117

This paper describes advancement in color edge detection, using a dedicated Geometric Algebra (GA) co-processor implemented on an Application Specific...

Geometric algebra | Color edge detection | Geometric algebra hardware | SUPPORT | geometric algebra | geometric algebra hardware | VECTOR-FIELDS | COPROCESSOR | color edge detection | QUATERNION | ENGINEERING, ELECTRICAL & ELECTRONIC | Algebra | Algorithms | Images | Color | Hardware | Edge detection | Channels | Genetic algorithms

Geometric algebra | Color edge detection | Geometric algebra hardware | SUPPORT | geometric algebra | geometric algebra hardware | VECTOR-FIELDS | COPROCESSOR | color edge detection | QUATERNION | ENGINEERING, ELECTRICAL & ELECTRONIC | Algebra | Algorithms | Images | Color | Hardware | Edge detection | Channels | Genetic algorithms

Journal Article

IEEE Access, ISSN 2169-3536, 2019, Volume 7, pp. 12755 - 12767

Multispectral images can provide more faithful representations for real scenes than the traditional images and improve the performance of image restoration...

K-GASVD | Dictionaries | Algebra | Image color analysis | Multivector | geometric algebra (GA) | Color | multispectral images | dictionary learning | Task analysis | Image reconstruction | sparse representation | FUSION | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | TRANSFORM | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC

K-GASVD | Dictionaries | Algebra | Image color analysis | Multivector | geometric algebra (GA) | Color | multispectral images | dictionary learning | Task analysis | Image reconstruction | sparse representation | FUSION | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | TRANSFORM | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Computers, Environment and Urban Systems, ISSN 0198-9715, 09/2016, Volume 59, pp. 208 - 219

Integrating dynamic analysis models into geographic information system (GIS)-based evacuation simulations is important yet complex. Different models must be...

GIS | Geometric algebra | Model integration | Evacuation | Spatiotemporal analysis | ROUTES | INFORMATION | MODEL | COMPUTATION | ENVIRONMENTAL STUDIES | EXPOSURE | GEOGRAPHY | Case studies | Evacuation of civilians | Algebra | Analysis | Geospatial data | Yuan (China)

GIS | Geometric algebra | Model integration | Evacuation | Spatiotemporal analysis | ROUTES | INFORMATION | MODEL | COMPUTATION | ENVIRONMENTAL STUDIES | EXPOSURE | GEOGRAPHY | Case studies | Evacuation of civilians | Algebra | Analysis | Geospatial data | Yuan (China)

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 11/2019, Volume 29, Issue 5, pp. 1 - 34

This paper has two objectives. The first is to explore the form and action of raising and lowering operators expressed in geometric algebra (GA). The second is...

Theoretical, Mathematical and Computational Physics | Electroweak | Ladder operators | Geometric algebra | 4+1 dimensions | Compound bivector generators | Physics | Projectors | Mathematical Methods in Physics | Hestenes–Dirac equation | Chirality | Particle physics | Lie groups | Applications of Mathematics | Physics, general | Lie algebra | Standard Model | MATHEMATICS, APPLIED | Hestenes-Dirac equation | PHYSICS, MATHEMATICAL | Analysis | Algebra

Theoretical, Mathematical and Computational Physics | Electroweak | Ladder operators | Geometric algebra | 4+1 dimensions | Compound bivector generators | Physics | Projectors | Mathematical Methods in Physics | Hestenes–Dirac equation | Chirality | Particle physics | Lie groups | Applications of Mathematics | Physics, general | Lie algebra | Standard Model | MATHEMATICS, APPLIED | Hestenes-Dirac equation | PHYSICS, MATHEMATICAL | Analysis | Algebra

Journal Article

Mechanism and Machine Theory, ISSN 0094-114X, 10/2017, Volume 116, pp. 273 - 293

• The motions, constraints and their relations are represented in a concise form by employing the characterized geometric elements with CGA.• The mobility of...

Parallel mechanism | Geometric algebra | Mobility | Singularity | Constraint | Kinematics | WORKSPACE | ENGINEERING, MECHANICAL | Computer programming | Analysis | Algebra

Parallel mechanism | Geometric algebra | Mobility | Singularity | Constraint | Kinematics | WORKSPACE | ENGINEERING, MECHANICAL | Computer programming | Analysis | Algebra

Journal Article