This paper presents the detection of 3D pose of moving humans heads. The contribution of this work is the conjunction of an e ective preprocessing method and a strong estimation Kalman technique which uses less noise sensitive 3D line observations. The procedure involves the detection of the target face in any type of background using color histograms. To outline the face we use a minimization ...

Quaternions 1.1 Quaternions are a class of hypercomplex numbers with four real components [1]. By analogy with the complex numbers being representable as a sum of real and imaginary parts (z  a + bi), quaternions can also be written as a linear combination: q  a + bi + cj + dk, (1) where 1, i, j, k make a group and satisfy the noncommutative rules: i2  j2  k2  -1, ij  ji  k, jk  -kj ...

an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.

The paper lays the foundation for study of unimodular rows using Spin groups. We show that elementary orbits (of any length n≥3) are equivalent to on unit sphere. (This bijection is proved over all commutative rings.) In special case n=3, this leads an interpretation Vaserstein symbol addition, we introduce a new composition law operates certain subspaces underlying quadratic space (using multi...

Many quaternion numbers associated with Fibonacci and Lucas or even their generalizations have been defined widely discussed so far. In all the studies, coefficients of these quaternions selected from consecutive terms numbers. this study, we define other for usual quaternions. We also present some properties, including Binet's formulas d'Ocagne's identities, types quaternions.

Reasoning about the pose, i.e. position and orientation of objects is one of the cornerstones of robotic manipulation under uncertainty. In a number of joint research projects our group is developing a robotic perception system that perceives and models an unprepared kitchen scenario with many objects. Since no single sensor or measurement provides sufficient information, a technique is needed ...

Early in the development of computer graphics it was realized that projective geometry is suited quite well to represent points and transformations. Now, maybe another change of paradigm is lying ahead of us based on Geometric Algebra. If you already use quaternions or Lie algebra in additon to the well-known vector algebra, then you may already be familiar with some of the algebraic ideas that...