Epipolar geometry is the geometry situation of two cameras depicting the same scene. For un-calibrated cameras epipolar geometry is compactly described by the fundamental matrix. Estimation of the fundamental matrix is trivial if we have a set of corresponding points in the two images. Corresponding points are often found using e.g. the Harris interest point detector, but there are several adva...

The 3-dimensional coherence matrix is interpreted by emphasising its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the moment of inertia of the ensemble (and the corresponding ellipsoid), and a real axial vector, corresponding to the mean angular momentum of the ensemble. This vec...

In this paper we first construct the non-split extension $overline{G}= 2^{6} {^{cdot}}Sp(6,2)$ as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique, inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory. There are two inerti...

The 3 × 3 local mass matrix fully characterizes a pair of colliding “rigid” bodies for many purposes. We prove here that arbitrary 3 × 3, symmetric positive definite matrices have physical realizations as local mass matrices for collisions of two bodies with finite dimensions and inertia. General collision models thus must be able to handle all such matrices.

In this report, we discuss adaptive control of a space robot system with an attitude controlled base on which the robot is attached. We at first derive the system kinematic and dynamic equations based on Lagrangian dynamics and linear momentum conservation law. Using the dynamic model developed, we discuss the problem of linear parameterization in t m s of dynamic parameters, and have found tha...

In this paper, we propose a structured bisection method with adaptive randomized sampling for finding selected or all of the eigenvalues of certain real symmetric matrices A. For A with a low-rank property, we construct a hierarchically semiseparable (HSS) approximation and show how to quickly evaluate and update its inertia in the bisection method. Unlike some existing randomized HSS construct...