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Related Concept Videos

Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...
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Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
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Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
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Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
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Maximizing the Directional Derivative

The directional derivative is a central concept in multivariable calculus that describes how a function changes at a given point when moving in a specified direction. This direction is represented by a unit vector, ensuring that only the orientation influences the rate of change. By varying the direction, different rates of change can be observed, demonstrating that the directional derivative depends strongly on the chosen direction.The directional derivative is computed using the gradient...
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Real-World Applications of Space Curves

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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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Continuous Full-Domain Highway Trajectory Tracking Based on Improved Deep-SORT and Inverse Covariance Intersection.

Zheye Tian1, Changhuizi Duan2, Shijie Gao1

  • 1Hebei Expressway Group Co., Ltd., Jingqin Branch, Qinhuangdao 066001, China.

Sensors (Basel, Switzerland)
|July 15, 2026
PubMed
Summary

This study introduces a real-time framework for continuous vehicle trajectory tracking on highways using radar-camera fusion. It achieves high accuracy in reconstructing full-domain trajectories, improving smart highway monitoring.

Keywords:
multisensor fusiontraffic engineeringtrajectory stitchingvehicle trajectory tracking

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A Protocol for Real-time 3D Single Particle Tracking
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A Protocol for Real-time 3D Single Particle Tracking
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A Protocol for Real-time 3D Single Particle Tracking

Published on: January 3, 2018

Area of Science:

  • Computer Vision
  • Robotics
  • Intelligent Transportation Systems

Background:

  • Single-sensor roadside perception for smart highway monitoring is limited by coverage, occlusion, and environmental factors.
  • Continuous vehicle trajectory tracking across multiple sensing domains is crucial but challenging.

Purpose of the Study:

  • To propose a real-time, full-domain highway trajectory tracking framework integrating radar-camera fusion, improved Deep-SORT, and inverse covariance intersection.
  • To enhance local multi-object tracking continuity and improve cross-domain association for seamless trajectory stitching.

Main Methods:

  • Developed a two-stage object-level and decision-level fusion model for local perception.
  • Improved Deep-SORT with CIoU matching and an occluded target tracking controller (OTTC).
  • Implemented a geometry-motion consistency stepwise calibration (GMCSC) and CATS-ICI for cross-domain association and trajectory stitching.

Main Results:

  • The local perception method achieved an Enhanced MOTA (EMOTA) of 92.35%.
  • The full-domain trajectory reconstruction achieved a 98.4% successful trajectory matching rate under high traffic density (452 vehicles/10 min).
  • Ablation studies confirmed the effectiveness of radar-camera fusion, CIoU, OTTC, GMCSC, CATS, and ICI.

Conclusions:

  • The proposed framework provides continuous and reliable full-domain vehicle trajectories for real-world highway monitoring.
  • The integration of advanced fusion and tracking techniques overcomes limitations of single-sensor systems.