Understanding the representations of 3D scenes as encoded in multiple views taken by a camera from different vantage points is central to many tasks in image and video analysis. These tasks range from recovering the camera motion, 3D structure of the scene and detection and characterization of multiple motions in video. We will demonstrate that the natural representations of a 3D scene in 2D im...

We theoretically and experimentally analyze the process of adding sparse random links to a random wireless networks modeled as a random geometric graph. While this process has been previously proposed, we are the first to (i) theoretically consider sparse new-wiring (with asymptotically less than constant fraction of nodes allowed very small constant new wired edges), (ii) prove bounds for any ...

Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of ‘singularities’ such as boundaries, sharp features, and non-manifolds. A few of the current research in reconstruction have addressed handling some of these singularities, but a unified approach to handle them all is missing. In this paper we a...

by minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. this new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. in fact, bot...

Fluid flow in jointed rock mass with impermeable matrix is often controlled by joint properties, including aperture, orientation, spacing, persistence and etc. On the other hand, since the rock mass is made of heterogeneous and anisotropic natural materials, geometric properties of joints may have dispersed values. One of the most powerful methods for simulation of stochastic nature of geometri...

Geometric Dilution of Precision (GDOP) is a coefficient for constellations of Global Positioning System (GPS) satellites. These satellites are organized geometrically. Traditionally, GPS GDOP computation is based on the inversion matrix with complicated measurement equations. A new strategy for calculation of GPS GDOP is construction of time series problem; it employs machine learning and artif...

The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric da...

With the rise in prominence of high dimensional data, multivariate measures of center have become very important. In this paper we focus on one multivariate measure of center the geometric median, which is defined as the minimizer of the sum of distances to the data points. We study the quantitative robustness of the geometric median. Showing that for a non-degenerate distribution of N points, ...

The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. This paper investigates the action of a matrix on its core. Being closely related to ultimate periodicity of matrix powers, this study leads to new modifications and geometric characterizations of robust, orbit periodic and weakly stable matrices.