Multivector Sparse Representation for Multispectral Images Using Geometric Algebra

Wang, Rui; Shen, Ming; Cao, Wenming

doi:10.1109/access.2019.2892822

Cited by 24 publications

(12 citation statements)

References 35 publications

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“…William K. Clifford introduced Geometric Algebra abbreviated as GA, also called Clifford Algebra, which provides such a coordinate-free framework to make the computation efficiently. It completes the constructions and modelings in a coordinate-free way and also has revealed wide applications especially when applying to computer vision tasks, such as multispectral images reconstruction or multispectral image denoising [72] and 3D geometrical shapes classification [73]. RGA-MLP [73]: Multilayer Perceptron (MLP) is an efficient feed-forward neural network, constituting one of the most common and popular classes of neural networks for image processing and pattern recognition.…”

Section: ) Geometric Algebra-based Methodsmentioning

confidence: 99%

A Comprehensive Survey on Geometric Deep Learning

et al. 2020

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Deep learning methods have achieved great success in analyzing traditional data such as texts, sounds, images and videos. More and more research works are carrying out to extend standard deep learning technologies to geometric data such as point cloud or voxel grid of 3D objects, real life networks such as social and citation network. Many methods have been proposed in the research area. In this work, we aim to provide a comprehensive survey of geometric deep learning and related methods. First, we introduce the relevant knowledge and history of geometric deep learning field as well as the theoretical background. In the method part, we review different graph network models for graphs and manifold data. Besides, practical applications of these methods, datasets currently available in different research area and the problems and challenges are also summarized. INDEX TERMS Convolutional neural networks, geometric deep learning, graph, manifold.

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Section: ) Geometric Algebra-based Methodsmentioning

confidence: 99%

A Comprehensive Survey on Geometric Deep Learning

et al. 2020

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“…(2) The sparse representation coefficients

and

of the column vectors can be calculated by GAOMP algorithm respectively in Wang et al (2019b) , which are described as follows…”

Section: Geometric Algebra Based Sparse Representation Based Multi-mo...mentioning

confidence: 99%

Multi-Modal Medical Image Fusion With Geometric Algebra Based Sparse Representation

Fang

Wang

et al. 2022

Front. Genet.

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Multi-modal medical image fusion can reduce information redundancy, increase the understandability of images and provide medical staff with more detailed pathological information. However, most of traditional methods usually treat the channels of multi-modal medical images as three independent grayscale images which ignore the correlation between the color channels and lead to color distortion, attenuation and other bad effects in the reconstructed image. In this paper, we propose a multi-modal medical image fusion algorithm with geometric algebra based sparse representation (GA-SR). Firstly, the multi-modal medical image is represented as a multi-vector, and the GA-SR model is introduced for multi-modal medical image fusion to avoid losing the correlation of channels. Secondly, the orthogonal matching pursuit algorithm based on geometric algebra (GAOMP) is introduced to obtain the sparse coefficient matrix. The K-means clustering singular value decomposition algorithm based on geometric algebra (K-GASVD) is introduced to obtain the geometric algebra dictionary, and update the sparse coefficient matrix and dictionary. Finally, we obtain the fused image by linear combination of the geometric algebra dictionary and the coefficient matrix. The experimental results demonstrate that the proposed algorithm outperforms existing methods in subjective and objective quality evaluation, and shows its effectiveness for multi-modal medical image fusion.

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“…Recently, the representation of color image as its GA form has attracted extensive attention [35], [36], which can process the spectral channels as a whole and maintain the inner-relationship of spectral channels successfully. The color image can be processed holistically when expressed as a multivector.…”

Section: Related Work a Geometric Algebramentioning

confidence: 99%

Multi-Focus Image Fusion Using Geometric Algebra Based Discrete Fourier Transform

Jiang

2020

IEEE Access

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For color image fusion, existing traditional algorithms regard each color image pixel as a scalar which may lose the relationships among spectral channels. In this paper, a novel multi-focus image fusion algorithm using geometric algebra based Discrete Fourier Transform (GA-DFT) is proposed. First, a novel Discrete Fourier Transform based on geometric algebra (GA) is provided. Second, the proposed algorithm represents the color image as a GA multivector by mapping the RGB channels into the GA space. Third, the variance is selected as a contrast measure to fuse the source images in GA space. The experimental results demonstrate that the proposed algorithm can achieve the comparable performance with its counterparts in terms of subjective quality evaluation, and outperform most of the traditional algorithms in terms of objective quality metrics, indicating good performance in image fusion applications.

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Multivector Sparse Representation for Multispectral Images Using Geometric Algebra

Cited by 24 publications

References 35 publications

A Comprehensive Survey on Geometric Deep Learning

A Comprehensive Survey on Geometric Deep Learning

Multi-Modal Medical Image Fusion With Geometric Algebra Based Sparse Representation

Multi-Focus Image Fusion Using Geometric Algebra Based Discrete Fourier Transform

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