Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

Bhatti, Uzair Aslam; Yu, Zhaoyuan; Yuan, Linwang; Zeeshan, Zeeshan; Nawaz, Saqib Ali; Bhatti, Mughair Aslam; Mehmood, Adeel; Ain, Qurat Ul; Luo, Wen

doi:10.1109/access.2020.3018544

Cited by 52 publications

(17 citation statements)

References 57 publications

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“…Geometric algebra presents a framework where operations are given as scalars, vectors and multivectors irrespective of the grade of the vectors. This unification and generalization is due to two main concepts in geometric algebra: geometric product and multivector [50,51]. To define the geometric product, we need first to introduce the outer product, also called the wedge product, operator of geometric algebra.…”

Section: Geometric Algebramentioning

confidence: 99%

Geometric algebra generation of molecular surfaces

Azzam

Wei

2022

J. R. Soc. Interface.

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Geometric algebra is a powerful framework that unifies mathematics and physics. Since its revival in the 1960s, it has attracted great attention and has been exploited in fields like physics, computer science and engineering. This work introduces a geometric algebra method for the molecular surface generation that uses the Clifford–Fourier transform (CFT) which is a generalization of the classical Fourier transform. Notably, the classical Fourier transform and CFT differ in the derivative property in R k for k even. This distinction is due to the non-commutativity of geometric product of pseudoscalars with multivectors and has significant consequences in applications. We use the CFT in R 3 to benefit from the derivative property in solving partial differential equations (PDEs). The CFT is used to solve the mode decomposition process in PDE transform. Two different initial cases are proposed to make the initial shapes in the present method. The proposed method is applied first to small molecules and proteins. To validate the method, the molecular surfaces generated are compared to surfaces of other definitions. Applications are considered to protein electrostatic surface potentials and solvation free energy. This work opens the door for further applications of geometric algebra and CFT in biological sciences.

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Section: Geometric Algebramentioning

confidence: 99%

Geometric algebra generation of molecular surfaces

Azzam

Wei

2022

J. R. Soc. Interface.

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“…Bhatti et al [52] provided a detailed review of GA in different fields of AI and computer vision regarding its applications and the current developments in geospatial research. The authors showed applications of the Clifford-Fourier transform and quaternion algebra in remote sensing image processing.…”

Section: H Geospatial Data Remote Sensing Gis Agriculturementioning

confidence: 99%

“…The recent reviews ''Applications of Clifford's Geometric Algebra'' by E. Hitzer, T. Nitta and Y. Kuroe [135], ''Geometric Algebra in Signal and Image Processing: A survey'' by R. Wang, K. Wang, W.Cao and X.Wang [233] and complementary ''A survey of quaternion neural networks'' by T. Parcollet, M. Morchid, M. and G. Linarés [194] are very useful to understand the progress in the area of geometric algebra. Bhatti et al [52] provide a detailed review of GA in different fields of AI and computer vision regarding its applications and the current developments in geospatial research. In our survey, we extend and complete these reviews discussing works in several areas of computer science and engineering from 1995 to 2020.…”

Section: Introductionmentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

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Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.INDEX TERMS Geometric algebra, Clifford algebra, quaternion algebra, screw theory, signal processing, electrical engineering and power systems, geometric and quantum computing, image processing, computer vision, graphic engineering, artificial intelligence, machine learning, neural networks, control engineering, robotics, biomedical engineering, and biotechnology.

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“…More and more people use computers to replace the manual work of target identification, tracking and measurement, and further do graphics and image information processing. In the current information age, image processing is not only widely used in aerospace [1][2][3] , remote sensing images [4] ,medical testing [5,6] , industrial testing [7] , etc. And it is a essential step in the process of building digital recognition models of certain features.…”

Section: Introductionmentioning

confidence: 99%

Traditional pattern enhancement based on improved singular value decomposition and gamma function in the frequency domain

Yan

Yuan

et al. 2023

Preprint

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Aiming at the problems of blurring and distortion of traditional patterns, an enhancement method to improve resolution and contrast is proposed.First, the discrete wavelet transform, stationary wavelet transform, and interpolation algorithm are used to obtain high-resolution images of traditional patterns. Then, the improved singular value matrix coefficients and the reconstructed gamma function are used to enhance the image contrast to obtain high-resolution and contrast-enhanced patterns. The experimental results show that the evaluation indexes such as mean square error, peak signal-to-noise ratio, and structural similarity corresponding to this method are improved compared with other comparison methods. It can effectively improve the quality of traditional patterns and is of great significance to the research on the restoration and protection of traditional patterns.

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Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

Cited by 52 publications

References 57 publications

Geometric algebra generation of molecular surfaces

Geometric algebra generation of molecular surfaces

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Traditional pattern enhancement based on improved singular value decomposition and gamma function in the frequency domain

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