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Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation and its Efficiency
Its generalization to the multidimensional geometric correlation in Clifford algebras has been proven a useful tool for color image processing, because it additionally contains information about a rotational misalignment.
Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q=2
We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain $\R^{p, q}$ taking values in Cl(p, q), p+q=2.
Quaternionic Fourier-Mellin Transform
The quaternionic Fourier Mellin transform (QFMT) applies to functions $f: \mathbb{R}^2 \rightarrow \mathbb{H}$, for which $|f|$ is summable over $\mathbb{R}_+^* \times \mathbb{S}^1$ under the measure $d\theta \frac{dr}{r}$.
Algebraic foundations of split hypercomplex nonlinear adaptive filtering
A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed.
Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions
The CR conditions mean that a complex $z$-derivative is independent of the direction.
OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions
We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions $f, g$.
Geometric operations implemented by conformal geometric algebra neural nodes
Geometric algebra is an optimal frame work for calculating with vectors.
Quaternion Fourier Transform on Quaternion Fields and Generalizations
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications.
Applications of Clifford's Geometric Algebra
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years.
