Few-shot segmentation (FSS) aims to segment unseen classes given only a few annotated samples. Encouraging progress has been made for FSS by leveraging semantic features learned from base with sufficient training samples represent novel classes. The correlation-based methods lack the ability consider interaction of two subspace matching scores due inherent nature real-valued 2D convolutions. In...

In this article, we give some equality and basic theorems about quaternion numbers, and some special operations. the notation and terminology for this paper. In this paper z 1 , z 2 , z 3 , z 4 , z are quaternion numbers. The following propositions are true: (1) (z 1 · z 2) = (z 2 · z 1). (2) If z is a real number, then z + z 3 = (z) + (z 3) + 1 (z 3) · i + 2 (z 3) · j + 3 (z 3) · k. (4) If z i...

We give an explicit construction of the simply-connected compact real form of the Lie group of type E7, as a group of 28 × 28 matrices over quaternions, acting on a 28-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a 56dimensional real vector space, and thence to the finite quasi-simple groups of type E7. The sign problem...

The quaternion representation of colour is shown to be effective in the context of colour texture region segmentation in digital colour images. The advantage of using quaternion arithmetic is that a colour can be represented and analyzed as a single entity. A basis for the colour textures occurring in a given image is derived via quaternion principal component analysis of a training set of colo...

Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split two real nonlinear systems, we derive explicit formulas for computing x2+bx+c=0 quaternion

In this study, we develop a general method to solve the linear elliptic quaternionic matrix equations by means of real representation quaternion matrices. A pseudocode for our approach that provides solution is expressed. Moreover, apply well-known Slyvester and Kalman Yakubovich over algebra.

Let Hmxn be the set of all m x n matrices over real quaternion algebra. We call that A ? Hnxn is ?-Hermitian if = A?* where -?A*?,? {i,j,k},i,j,k are units. In this paper, we derive some solvability conditions and general solution to a system matrix equations. As an application, present necessary sufficient for existence systems also give expressions solutions these when they solvable. Some num...