Conjugate Points Research Articles

Special Classes of Terrestrial Gamma Ray Flashes From RHESSI

AbstractWe report on three classes of terrestrial gamma ray flashes (TGFs) from the (RHESSI) satellite. The first class drives the detectors into paralysis, being observed usually through a few counts on the rising edge and the later tail of Comptonized photons. These events—and any bright TGF—reveal their true luminosity more clearly via their Compton tail than via the main peak, since the former is unaffected by the unknown beaming pattern of the unscattered radiation, and Comptonization mostly isotropizes the flux. This technique could be applied to TGFs from any mission. The second class is more than usually bright and long in duration. When the magnetic field at the conjugate point is stronger than at the nearby footpoint, we find that 4 out of 11 such events show a significant signal at the time expected for a relativistic electron beam to make a round trip to the opposite footpoint and back. We conclude that a large fraction of TGFs lasting more than a few hundred microseconds may include counts due to the upward moving secondary particle beam ejected from the atmosphere. Finally, using a new search algorithm to find short TGFs in RHESSI, we see that these tend to occur more often over the oceans than land, relative to longer‐duration events. In the feedback model of TGF production, this suggests a higher thunderstorm potential, since more feedback per avalanche implies fewer “generations” of avalanches needed to complete the TGF discharge.

Entangled dynamos and Joule heating in the Earth's ionosphere

Abstract. The Earth's neutral atmosphere is the driver of the well-known solar quiet (Sq) and other magnetic variations observed for more than 100 years. Yet the understanding of how the neutral wind can accomplish a dynamo effect has been incomplete. A new viable model is presented where a dynamo effect is obtained only in the case of winds perpendicular to the magnetic field B that do not map along B. Winds where u×B is constant have no effect. We identify Sq as being driven by wind differences at magnetically conjugate points and not by a neutral wind per se. The view of two different but entangled dynamos is favoured, with some conceptual analogy to quantum mechanical states. Because of the large preponderance of the neutral gas mass over the ionized component in the Earth's ionosphere, the dominant effect of the plasma adjusting to the winds is Joule heating. The amount of global Joule heating power from Sq is estimated, with uncertainties, to be much lower than Joule heating from ionosphere–magnetosphere coupling at high latitudes in periods of strong geomagnetic activity. However, on average both contributions could be relatively comparable. The global contribution of heating by ionizing solar radiation in the same height range should be 2–3 orders of magnitude larger.

A Double Epipolar Resampling Approach to Reliable Conjugate Point Extraction for Accurate Kompsat-3/3A Stereo Data Processing

Kompsat-3/3A provides along-track and across-track stereo data for accurate three-dimensional (3D) topographic mapping. Stereo data preprocessing involves conjugate point extraction and acquisition of ground control points (GCPs), rational polynomial coefficient (RPC) bias compensation, and epipolar image resampling. Applications where absolute positional accuracy is not a top priority do not require GCPs, but require precise conjugate points from stereo images for subsequent RPC bias compensation, i.e., relative orientation. Conjugate points are extracted between the original stereo data using image-matching methods by a proper outlier removal process. Inaccurate matching results and potential outliers produce geometric inconsistency in the stereo data. Hence, the reliability of conjugate point extraction must be improved. For this purpose, we proposed to apply the coarse epipolar resampling using raw RPCs before the conjugate point matching. We expect epipolar images with even inaccurate RPCs to show better stereo similarity than the original images, providing better conjugate point extraction. To this end, we carried out the quantitative analysis of the conjugate point extraction performance by comparing the proposed approach using the coarsely epipolar resampled images to the traditional approach using the original stereo images. We tested along-track Kompsat-3 stereo and across-track Kompsat-3A stereo data with four well-known image-matching methods: phase correlation (PC), mutual information (MI), speeded up robust features (SURF), and Harris detector combined with fast retina keypoint (FREAK) descriptor (i.e., Harris). These matching methods were applied to the original stereo images and coarsely resampled epipolar images, and the conjugate point extraction performance was investigated. Experimental results showed that the coarse epipolar image approach was very helpful for accurate conjugate point extraction, realizing highly accurate RPC refinement and sub-pixel y-parallax through fine epipolar image resampling, which was not achievable through the traditional approach. MI and PC provided the most stable results for both along-track and across-track test data with larger patch sizes of more than 400 pixels.

AUTOMATIC EVALUATION OF THE INITIAL GEOPOSITIONING ACCURACY FOR LARGE AREA PLANETARY REMOTE SENSING IMAGES

Abstract. The photogrammetric processing of large area planetary remote sensing images is still a very challenging work. In addition to the lack of ground control data and poor tie points extraction, the insufficient knowledge of the initial geopositioning accuracy of the planetary images also increases the difficulty of processing. This paper presents an automatic evaluation method of the initial geopositioning accuracy for large area planetary remote sensing images. The accuracy evaluation method was conducted through image matching on approximate orthophotos derived using coarse resolution digital elevation model (DEM). To improve the orthophotos generation efficiency of linear pushbroom images, a fast ground-to-image transformation algorithm and multi-threaded parallel computing are adopted. The classical normalized cross correlation (NCC) and pyramid matching schemes are used to perform image matching between overlapping orthophotos. Because the conjugate points on orthophotos contain geographic coordinates, we can derive the statistics information (e.g., maximum errors, mean errors and standard deviation) about the geopositioning accuracy of the planetary images. Although it’s actually an evaluation result of relative accuracy, the quantitative geopositioning accuracy information of stereopairs can be used to (1) specify the search window size and the starting position of conjugate points for tie points extraction; (2) set the weight value of bundle adjustment; and (3) identify images with abnormal geopositioning accuracy. Tens of Mars Express (MEX) High Resolution Stereo Camera (HRSC) images were used to conduct the test. The experimental results demonstrate that the proposed method shows high computational efficiency and automation degree. The automatic evaluation of the initial geopositioning accuracy of the planetary images is helpful to produce large area planetary mapping products.

Алгоритмический комплекс для решения задач с квадриками с применением мнимых геометрических образов

The paper is devoted to the consideration of a number of issues related to the creation of an algorithmic complex designed to solve positional and metric problems with quadrics on a projection model . A feature of the complex is the active use of geometric schemes and algorithms involving imaginary geometric images. In the paper has been presented a detailed description of constructive geometric algorithms for constructing of conics, quadrics and associated geometric images in a system of constructive geometric modeling – Simplex. All the discussed algorithms are available for independent repetition by the reader. In the paper have been presented and implemented algorithms for constructing conic from a point, a polar, and three points; constructing conic from two pairs of complex conjugate points and one real point; determination of a point on a quadric’s surface; setting a quadric by nine points in three-dimensional space. A new alternative frame of the quadric has been considered, based on which have been solved problems of constructing a tangent and a normal to the quadric, finding an intersection line of an arbitrary plane with the quadric, and performing polar and inverse transformations with respect to the quadric. Have been proposed algorithms for constructing an autopolar tetrahedron with respect to the quadric, and for constructing a conic from an autopolar triangle and two points. Have been considered problems of determining a collinear transformation in three-dimensional space and control the quadric through it. The implementation of the algorithms considered in the paper allowed conclude that there is an urgent need to develop tools for modeling imaginary conics, without which the complex of solving problems with quadrics cannot be taken for the complete one.

Local Universality for Zeros and Critical Points of Monochromatic Random Waves

This paper concerns the asymptotic behavior of zeros and critical points for monochromatic random waves $$\phi _\lambda $$ of frequency $$\lambda $$ on a compact, smooth, Riemannian manifold (M, g) as $$\lambda \rightarrow \infty .$$ We prove global variance estimates for the measures of integration over the zeros and critical points of $$\phi _\lambda .$$ These global estimates hold for a wide class of manifolds—for example when (M, g) has no conjugate points—and rely on new local variance estimates on zeros and critical points of $$\phi _\lambda $$ in balls of radius $$\approx \lambda ^{-1}$$ around a fixed point. Our local results hold under conditions about the structure of geodesics that are generic in the space of all metrics on M.

AUTOMATIC GEOREFERNCING OF CLOSE-RANGE FAÇADE IMAGES ACQUIRED IN AN NARROW AND LONG ALLEYWAY USING RTK DRONE IMAGES

Abstract. The city of Seoul has selected Sewoon market building and its surrounding district as part of the urban regeneration zone, and currently has been promoting the project. To monitor results of the project regularly, the city has been trying to utilize a 3 dimension model of the area. In the case of buildings placed in narrow alleyways in the district, however, it is limited to generate 3D model of the buildings due to some factors. Therefore, in this study, a 3D model of façade of the building was created, using a RTK drone and action camera only. First method is to estimate of location of conjugate points using Structure from Motion, after setting conjugate points between images of the drone. Second method is to georeference action camera images by setting drone images as the reference images itself without the process of estimating location of the conjugate points. As a result of preliminary experiments to verify the two methods, the error of each method did not exceed a maximum of 0.030 m. Based on the result, we created 3D models of façade of the building in the alleyway, which is located at the intersection of Donhwamoon-ro 2 gil and Jong-ro 24 gil, and calculated absolute distance between the models. And the comparison showed that the difference was about 0.010 m on average.

The Comparison of Responses to Geomagnetic Activity Changes of foF2 Predicted by IRI with Observations at Magnetic Conjugate Points for Middle and High Latitudes

In this study, the response to geomagnetic storms of the ionospheric F2 layer critical frequency (foF2) was investigated at the magnetic conjugate points. The hourly foF2 data observed at the magnetic conjugate points of middle and high latitudes for the geomagnetic stormy days around both of 1976 and foF2 data received from IRI-2016 Model for same points were used. The foF2 data observed in magnetic conjugate points and received from IRI Model were examined using the superposed epoch analysis method and the results obtained were compared. From the results of analysis, it was observed that the foF2 data observed at magnetic conjugate points and received from IRI Model simultaneously respond to geomagnetic activity changes for both the middle latitudes and the high latitudes.

Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points

We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points

Bifurcation problems for second order systems

In this paper, we consider the following linear system of second order differential equations (0.1)u′′+A(t)u=0,0≤t<∞where, for each t, A(t) is an n×n matrix with real components, and positive with respect to the usual cone K in Rn. Conditions are provided in order that the first conjugate point T of t=0, i.e. the smallest T such that the above equation has a nontrivial solution u:[0,T]→K satisfying the boundary conditions u(0)=0=u(T)will be a bifurcation point for higher order perturbations of the equation. The paper is mainly motivated by results in Ahmad and Lazer (1997, 1980); Ahmad and Salazar (1981) and Schmitt (1975); Schmitt and Smith (1978). Some additional new consequences are discussed.

Approximation of the exit probability of a stable Markov modulated constrained random walk

Let X be the constrained random walk on \({\mathbb {Z}}_+^2\) having increments (1, 0), \((-\,1,1)\), \((0,-\,1)\) with jump probabilities \(\lambda (M_k)\), \(\mu _1(M_k)\), and \(\mu _2(M_k)\) where M is an irreducible aperiodic finite state Markov chain. The process X represents the lengths of two tandem queues with arrival rate \(\lambda (M_k)\), and service rates \(\mu _1(M_k)\), and \(\mu _2(M_k)\); the process M represents the random environment within which the system operates. We assume that the average arrival rate with respect to the stationary measure of M is less than the average service rates, i.e., X is assumed stable. Let \(\tau _n\) be the first time when the sum of the components of X equals n for the first time. Let Y be the random walk on \({{\mathbb {Z}}} \times {{\mathbb {Z}}}_+\) having increments \((-\,1,0)\), (1, 1), \((0,-\,1)\) with probabilities \(\lambda (M_k)\), \(\mu _1(M_k)\), and \(\mu _2(M_k)\). Supposing that the queues share a joint buffer of size n, \(p_n =P_{(x_n,m)}(\tau _n < \tau _0)\) is the probability that this buffer overflows during a busy cycle of the system. To the best of our knowledge, the only methods currently available for the approximation of \(p_n\) are classical large deviations analysis giving the exponential decay rate of \(p_n\) and rare event simulation. Let \(\tau \) be the first time the components of Y are equal. For \(x \in {{\mathbb {R}}}_+^2\), \(x(1) + x(2) < 1\), \(x(1) > 0\), and \(x_n = \lfloor nx \rfloor \), we show that \(P_{(n-x_n(1),x_n(2),m)}( \tau < \infty )\) approximates \(P_{(x_n,m)}(\tau _n < \tau _0)\) with exponentially vanishing relative error as \(n\rightarrow \infty \). For the analysis we define a characteristic matrix in terms of the jump probabilities of (X, M). The 0-level set of the characteristic polynomial of this matrix defines the characteristic surface; conjugate points on this surface and the associated eigenvectors of the characteristic matrix are used to define (sub/super) harmonic functions which play a fundamental role both in our analysis and the computation/approximation of \(P_{(y,m)}(\tau < \infty )\).

Positional Accuracy Assessment of Lidar Point Cloud from NAIP/3DEP Pilot Project

The Leica Geosystems CountryMapper hybrid system has the potential to collect data that satisfy the U.S. Geological Survey (USGS) National Geospatial Program (NGP) and 3D Elevation Program (3DEP) and the U.S. Department of Agriculture (USDA) National Agriculture Imagery Program (NAIP) requirements in a single collection. This research will help 3DEP determine if this sensor has the potential to meet current and future 3DEP topographic lidar collection requirements. We performed an accuracy analysis and assessment on the lidar point cloud produced from CountryMapper. The boresighting calibration and co-registration by georeferencing correction based on ground control points are assumed to be performed by the data provider. The scope of the accuracy assessment is to apply the following variety of ways to measure the accuracy of the delivered point cloud to obtain the error statistics. Intraswath uncertainty from a flat surface was computed to evaluate the point cloud precision. Intraswath difference between opposite scan directions and the interswath overlap difference were evaluated to find boresighting or any systematic errors. Absolute vertical accuracy over vegetated and non-vegetated areas were also assessed. Both horizontal and vertical absolute errors were assessed using the 3D absolute error analysis methodology of comparing conjugate points derived from geometric features. A three-plane feature makes a single unique intersection point. Intersection points were computed from ground-based lidar and airborne lidar point clouds for comparison. The difference between two intersection points form one error vector. The geometric feature-based error analysis was applied to intraswath, interswath, and absolute error analysis. The CountryMapper pilot data appear to satisfy the accuracy requirements suggested by the USGS lidar specification, based upon the error analysis results. The focus of this research was to demonstrate various conventional accuracy measures and novel 3D accuracy techniques using two different error computation methods on the CountryMapper airborne lidar point cloud.

Central splitting of manifolds with no conjugate points

Each compact Riemannian manifold with no conjugate points admits a family of functions whose integrals vanish exactly when central Busemann functions split linearly. These functions vanish when all central Busemann functions are sub- or superharmonic. When central Busemann functions are convex or concave, they must be totally geodesic. These yield generalizations of the splitting theorems of O'Sullivan and Eberlein for manifolds with no focal points and, respectively, nonpositive curvature.

Spectral flow, Brouwer degree and Hill's determinant formula

In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This invariant was defined in terms of a suspension of a complexified family of linear second order Dirichlet boundary value problems.In this paper, starting from this result, we generalize this invariant to a general self-adjoint Morse-Sturm system and we prove a new spectral flow formula. Finally we discuss the relation between this spectral flow formula and the Hill's determinant formula and we apply this invariant for detecting instability of periodic orbits of a Hamiltonian system.

Generalization of functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points

In this paper, by using convolution we generalize the class of analytic functions of bounded Mocanu variation with respect to 2k-symmetric conjugate points and study some of its basic properties. Our results generalize many research works in the literature.

Geodesic ray transform with matrix weights for piecewise constant functions

We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.

Extensions maximales et classification des tores lorentziens munis d’un champ de Killing

We study the simply connected inextendable Lorentzian surfaces admitting a Killing vector field. We construct a natural family of such surfaces, that we call extensions. They are characterized by a condition of symmetry, the reflexivity, and a by a rather weak completeness assumption, the absence of saddles at infinity. Considering these surfaces as model spaces, we study their minimal quotients, divisible open sets and conjugate points. We show uniformisation results (by an open subset of one of these universal extensions, which is uniquely determined) in the following cases: compact surfaces and analytical surfaces. It allows us to give a classification of Lorentzian tori and Klein bottles with a Killing vector field.

Subclasses of analytic functions with respect to symmetric and conjugate points bounded by conical domain

The main objective of this present investigation is to derive the Fekete Szeg$\ddot{o}$ inequality for the function belongs to the defined class in the open unit disk with respect to symmetric and conjugate points bounded by conical region. As a special consequences of our result, we extracted some interesting results through corollaries.

An Improved Method of Refining Relative Orientation in Global Structure from Motion with a Focus on Repetitive Structure and Very Short Baselines

Recently, global structure from motion has successfully gained many followers, mainly because of its computational speed. Most of these global methods take the parameters of relative orientation (ROs ) as input and then perform averaging operations. Therefore, eliminating incorrect ROs is of great significance for improving the robustness of global structure from motion. In this article, we propose a method to eliminate wrong ROs which have resulted from repetitive structure and very short baselines. We present two corresponding criteria that indicate the quality of ROs. Repetitive structure is detected based on counts of conjugate points of the various image pairs, while very short baselines are found by inspecting the intersection angles of corresponding image rays. By analyzing these two criteria, we detect and eliminate incorrect ROs. As correct ROs of image pairs with a longer baseline nearly parallel to both viewing directions can be valuable, a method to identify and keep these ROs is also part of our approach. We demonstrate the new method on various data sets, including public benchmarks as well as close-range images and images from unmanned aerial vehicles, by inserting our refined ROs into a global structure-from-motion pipeline. The experiments show that compared to other methods, we can generate the best results.

Regularity and Conjugacy for Constrained Variational Problems

For problems in the calculus of variations involving equality and inequality mixed constraints we characterize, in terms of an extended notion of conjugate points, the sign of a quadratic form which corresponds to the second variation of the integral to be minimized. Second order necessary conditions are then derived assuming the well-known constraint qualification of regularity in the sense that, with respect to the set of mixed constraints, both the tangent cone and the set of tangential constraints coincide.