If γ(t) is a unit speed geodesic on a manifold M and J(t) is a non-trivial perpendicular Jacobi field along γ such that J(t0) = 0 and (||J ||2)′(t1) = 0 for some t0 < t1, then the geodesic that is tangent to J(t1) at γ(t1) is said to have a focal point at γ(t0). If this does not happen for any times t0 < t1 and any non-trivial perpendicular Jacobi field J , then we say that there are no focal p...

We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to plane. It is shown that affine scene structure may then be determined from the image, without knowl...

This paper continues the study of the global dynamic properties specific to maps of the plane characterized by the presence of a denominator that vanishes in a one-dimensional submanifold. After two previous papers by the same authors, where the definitions of new kinds of singularities, called focal points and prefocal sets, are given, as well as the particular structures of the basins and the...

We analyze a large, detailed operational data set from a restaurant chain to shed new light on how workload (defined as the hourly average number of diners assigned to a server) affects servers’ performance (measured as hourly sales). We use an exogenous shock implementation of a labor scheduling software to disentangle the endogeneity between demand and supply in this setting. We find that whe...

This paper presents a novel technique for the estimation of the height of an object using a single camera view. In the proposed method, the only information required is the knowledge about the pose of the camera with respect to the world (i.e., height and pitch angle of the camera with respect to the ground) and a vanishing point. In the developed theory, the focal length may also be known, but...

Abstract The reflector on an impulse radiating antennas (IRAs) is normally designed to be paraboloidal in shape, and are oriented so that the electrical feed point of the TEM feed line coincides with the focal point of the paraboloid. In many practical cases, the feed point and focal points are not exactly aligned, producing some defocus of the reflector. There are two types of defocus that can...

In single photon emission computed tomography (SPECT), a varying-focal-length cone-beam collimator can be used to reduce the truncation problem and to maintain sensitivity when imaging the organ of interest. The collimator is constructed so that the collimator holes focus to a circular symmetric, spatially varying, focal point function. The focal length increases radially from the shortest foca...

This paper focuses on automatic focal length estimation. In several vision applications one can assume that the utilized cameras are semi-calibrated, which means that all the intrinsic camera parameters but the focal length (aspect ratio, principal point, and skew) are known. In this case the camera calibration procedure reduces to the computation of the focal length(s). The main contribution o...

We consider a Riemannian manifold (M, g) and a codimension one distribution ∆ ⊂ TM on M which is the orthogonal of a unit vector field Y onM. We do not make any nonintegrability assumption on ∆. The aim of the paper is to develop a Morse Theory for the sub-Riemannian action functional E on the space of horizontal curves, i.e. everywhere tangent to the distribution ∆. We consider the case of hor...

The rapid development of educational technologies, combined with the Internet boom at a worldwide level, gives rise to favorable conditions for the establishment of a new model of university training. The first part of this work will give a description of the major components of the new virtual university. The second part will attempt a critical approach of the sense of virtual university from ...