We propose a general paradigm for generating optimal coordinate frame fields that may be exploited to annotate and display curves and surfaces. Parallel-transport framings, which work well for open curves, generally fail to have desirable properties for cyclic curves and for surfaces. We suggest that minimal quaternion measure provides an appropriate generalization of parallel transport. Our fu...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...

A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real-quaternion) stochastic time series representing two ‘remote’ complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great em...

Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel equalization and beamforming. With most recent developments in quaternion-valued signal processing, in this work, we fill the gap to solve the p...

The vicious random walker problem on a one dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site are prohibited. It is known that the probability distribution of N walkers after M steps can be written in a determinant form. Using an integration technique borrowed from the theory of random matric...

The real Ginibre ensemble refers to the family of n × n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as n→∞. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs...

Article history: Received 28 March 2017 Accepted 24 April 2017 Available online 26 April 2017 Editor: J. Hisano We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four “magical” Jordan algebras of 3 × 3 Hermitian matrices with real, comp...

The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. In this paper, we will develop efficient algorithms for QFT, QCV, and quater...

In this paper, we present an isomorphism between the ring of general polynomials over a division algebra D with center F and the group ring of the free monoid with [D : F ] variables over D. Using this isomorphism, we define the characteristic polynomial of any matrix over any division algebra, i.e., a general polynomial with one variable over the algebra whose roots are precisely the left eige...