Classification Of Intersections Research Articles

Topological Classification and Determination of Non-Degenerate Intersections of Two Dupin Cyclides

The surface-surface intersection is a fundamental task in CAD/CAM. We present the classification and a full enumeration of the topology of all non-degenerate intersections of two Dupin cyclides. Inversion geometry is first used to transform the intersection of two Dupin cyclides to that of a cyclide and a torus. Then the topology of the intersection curve is reduced to the arrangements of the main circle of the torus and another pair of circles, which can be characterized by a simple algebraic sequence. Based on the classification and enumeration results, an efficient determination algorithm for the topology of two Dupin cyclides is also provided. • A classification of the non-degenerate intersections of two Dupin cyclides is given by a simple algebraic sequence. • A full enumeration of all non-degenerate intersections of two Dupin cyclides based on a simple algebraic sequence is provided. • An efficient and robust algorithm of determining the inter- section topology of two Dupin cyclides is provided.

Urban Intersection Classification: A Comparative Analysis.

Understanding the scene in front of a vehicle is crucial for self-driving vehicles and Advanced Driver Assistance Systems, and in urban scenarios, intersection areas are one of the most critical, concentrating between 20% to 25% of road fatalities. This research presents a thorough investigation on the detection and classification of urban intersections as seen from onboard front-facing cameras. Different methodologies aimed at classifying intersection geometries have been assessed to provide a comprehensive evaluation of state-of-the-art techniques based on Deep Neural Network (DNN) approaches, including single-frame approaches and temporal integration schemes. A detailed analysis of most popular datasets previously used for the application together with a comparison with ad hoc recorded sequences revealed that the performances strongly depend on the field of view of the camera rather than other characteristics or temporal-integrating techniques. Due to the scarcity of training data, a new dataset is created by performing data augmentation from real-world data through a Generative Adversarial Network (GAN) to increase generalizability as well as to test the influence of data quality. Despite being in the relatively early stages, mainly due to the lack of intersection datasets oriented to the problem, an extensive experimental activity has been performed to analyze the individual performance of each proposed systems.

Classification of Uncontrolled Intersections Using Hierarchical Clustering

This research helps define motorized level of service (MLOS) for different categories of uncontrolled intersections using mixed hierarchical clustering technique. Service and total delay has been considered for classifying MLOS and intersections, respectively. GPS is used to collect travel time and speed data for turning movements which are transformed to average delay values. Thirteen intersections from eight different cities in India form the dataset. Divisive followed by agglomerative clustering (DAC-HAC) algorithm is applied as a two-step process for obtaining the service and total delay ranges. Validation of clusters is performed based on Davies–Bouldin score, Calinski–Harabasz index and Silhouette gaps. Based on DAC-HAC, uncontrolled intersections are classified into six categories (Cat-I, II, III, IV, V and VI). Results indicate MLOS classes “D”, “E” and “F” have significantly higher service delay ranges as compared to Highway Capacity Manual “control” delay ranges indicating mixed traffic conditions. Most of the uncontrolled intersections under mixed traffic fall under Cat-IV, V and VI having higher total delay ranges (greater than 60 s/vehicle/approach). Finally, validation of the clustering results is done for geometric and roadside environmental features.

Varieties with nef diagonal

For a smooth projective variety [Formula: see text], we consider when the diagonal [Formula: see text] is nef as a cycle on [Formula: see text]. In particular, we give a classification of complete intersections and smooth del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for spherical varieties.

Analysis of intersections of trajectories of systems of linear fractional differential equations.

This article deals with trajectorial intersections in systems of linear fractional differential equations. We propose a classification of intersections of trajectories into three classes: (a) trajectories intersecting at the same time (IST), (b) trajectories intersecting at different times (IDT), and (c) self-intersections of a trajectory. We prove a generalization of the separation theorem for the case of linear fractional systems. This result proves the existence of the IST. Based on the presence of the IST, systems are further classified into two types, Type I and Type II systems, which are analyzed further for the IDT. Self-intersections in a fractional trajectory can be regular such as constant solution or limit-cycle behavior, or they can be irregular such as cusps or nodes. We give necessary and sufficient conditions for a trajectory to be regular.

Multi-Criteria Analysis of Pollution Caused by Auto Traffic in a Geographical Area Limited to Applicability for an Eco-Economy Environment

The pollution caused by road traffic is a significant problem for society in the 21st century. Climate change and mortality among the population, are increasingly influenced by increasing traffic in urban agglomerations. The present study aims at the multi-criteria analysis of the pollution caused by traffic at several busy intersections in the city of Sibiu, Romania. Classification of intersections was done using the Synchro Studio with Warrants software. Air pollutants, noise, and the number of vehicles in the traffic were taken into account. To analyze these criteria as a whole, the analytical hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) methods were used. A comparative study has been undertaken on the results obtained by applying the two multicriteria methods. The paper aims to provide solutions for the eco-economy of the future.

Building detection from orthophotos using binary feature classification

Building detection in orthophotos is crucial for various applications, such as urban planning and real-estate management. In order to realize accurate and fast building detection, a non-interactive approach based on binary feature classification is brought forward in this paper. The proposed approach includes two major stages, i.e., building area detection and building contours extraction. In the first stage, a sequence of intersections is obtained by superpixel segmentation in the subsampled orthophoto, and then building area is reserved roughly according to the classification of intersections. In the second stage, the sequence of intersections is updated by superpixel segmentation in the building area from original orthophoto, and then building contours is extracted in accordance with the classification of intersections likewise. The local feature of the intersections is descripted employing our extremely compact binary descriptor, and is classified using binary bag-of-features. Experiments show that benefiting from binary description and making full use of texture details and color channels, the proposed descriptor is not only computationally frugal, but also accurate. Experiments are also conducted on orthophotos with different roof colors, textures, shapes, sizes and orientations, and demonstrate that the proposed approach are capable of achieving desirable results.

COMPLETE INTERSECTIONS WITH S 1-ACTION

We give the diffeomorphism classification of complete intersections with S^1-symmetry in dimension less than or equal to 6. In particular, we show that a 6-dimensional complete intersection admits a smooth non-trivial S^1-action if and only if it is diffeomorphic to the complex projective space or the quadric. We also prove that in any odd complex dimension only finitely many complete intersections can carry a smooth effective action by a torus of rank $>1$.

A complete classification of equational classes of threshold functions included in clones

The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way.

Topological classification of non-degenerate intersections of two ring tori

We study the topological classification of all non-degenerate intersection curves of two arbitrary ring tori. Firstly, all topologically different types of such curves are enumerated. Secondly, an algebraic method is presented for determining the topological type of the non-degenerate intersection curve of two given ring tori. The method works by analyzing the real roots of two univariate quartic polynomials constructed from the two tori.

Collineation groups of the intersection of two classical unitals

AbstractKestenband proved in [12] that there are only seven pairwise non‐isomorphic Hermitian intersections in the desarguesian projective plane PG(2, q) of square order q. His classification is based on the study of the minimal polynomials of the matrices associated with the curves and leads to results of purely combinatorial nature: in fact, two Hermitian intersections from the same class might not be projectively equivalent in PG(2, q) and might have different collineation groups. The projective classification of Hermitian intersections in PG(2, q) is the main goal in this paper. It turns out that each of Kestenband's classes consists of projectively equivalent Hermitian intersections. A complete classification of the linear collineation groups preserving a Hermitian intersection is also given. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 445–459, 2001

LANDAU EQUATIONS AND ASYMPTOTIC OPERATION

The pinched/nonpinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities, for example due to linear denominators in non-covariant gauges, etc. As another application, the results of Euclidean asymptotic operation are extended to a class of quasi-Euclidean asymptotic regimes in Minkowski space.

Classification of p-branes, NUTs, waves and intersections

We give a full classification of the multi-charge supersymmetric p-brane solutions in the mass-less and massive maximal supergravities in dimensions D ⩾ 2 obtained from the toroidal reduction of eleven-dimensional supergravity. We derive simple universal rules for determining the fractions of supersymmetry that they preserve. By reversing the steps of dimensional reduction, the p-brane solutions become intersections of p-branes, NUTs and waves in D = 10 or D = 11. Having classified the lower-dimensional p-branes, this provides a classification of all the intersections in D = 10 and D = 11 where the harmonic functions depend on the space transverse to all the individual objects. We also discuss the structure of U-duality multiplets of p-brane solutions, and show how these translate into multiplets of harmonic and non-harmonic intersections.