Application of Clifford algebra and quaternion representations to (3+1)D non-destructive testing
ORAL
Abstract
We study application of the Clifford algebra and the Grassmann algebra to image recognitions in $(3+1)D$ using quaternions.
Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees of freedom, similar to Cartan's supersymmetric model. The Clifford algebra ${mathcal A}_{3,1}$ is compared with ${mathcal A}_{2,1}$ and the model applied to the $(2+1)D$ non-destructive testing is extended.
We adopt the Riesz Wavelet transform for image recognition of non-destructive testing.
Comparison with the quaternion Fourier transfer of Hitzer and the tensor renormalization group approach to classical lattice models is also discussed.
Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees of freedom, similar to Cartan's supersymmetric model. The Clifford algebra ${mathcal A}_{3,1}$ is compared with ${mathcal A}_{2,1}$ and the model applied to the $(2+1)D$ non-destructive testing is extended.
We adopt the Riesz Wavelet transform for image recognition of non-destructive testing.
Comparison with the quaternion Fourier transfer of Hitzer and the tensor renormalization group approach to classical lattice models is also discussed.
* Nihon Sangyo Kagaku Kenkyujo grant in aid.
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Publication: arXiv:2310.10680
On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$
Presenters
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Sadataka Furui
Teikyo University
Authors
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Sadataka Furui
Teikyo University
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Serge Dos Santos
INSA val de Loire