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Related Concept Videos

Graphs of Polar Equations01:17

Graphs of Polar Equations

88
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
88
Polar Equations of Conics01:29

Polar Equations of Conics

57
A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can describe any...
57
Polar Coordinates01:24

Polar Coordinates

67
The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ), where r is the radial distance from a fixed...
67
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

18.1K
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
18.1K
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

660
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
660
Spherical Coordinates01:23

Spherical Coordinates

13.2K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
13.2K

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Related Experiment Video

Updated: Nov 15, 2025

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
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Unsupervised Classification of Polarimetric SAR Image Based on Geodesic Distance and Non-Gaussian Distribution

Junrong Qu1,2,3, Xiaolan Qiu1,2, Chibiao Ding1,2

  • 1Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China.

Sensors (Basel, Switzerland)
|March 6, 2021
PubMed
Summary

This study introduces an unsupervised method for Polarimetric Synthetic Aperture Radar (PolSAR) image classification using geodesic distance and K-Wishart distribution. The approach effectively categorizes scattering types for improved PolSAR image interpretation.

Keywords:
K-Wishart classifierclassificationgeodesic distancepolarimetric SAR

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Area of Science:

  • Remote Sensing
  • Geophysics
  • Computer Vision

Background:

  • Polarimetric Synthetic Aperture Radar (PolSAR) image classification is crucial for interpreting complex terrain.
  • Existing unsupervised methods often struggle with nuanced scattering variations.
  • Accurate classification aids in environmental monitoring and resource management.

Discussion:

  • A novel unsupervised classification method for PolSAR images is proposed, leveraging geodesic distance and K-Wishart distribution.
  • The method defines scattering similarity using geodesic distance between Kennaugh matrices for initial segmentation.
  • Further sub-classification within primary scattering categories (surface, double-bounce, volume) is achieved using K-distribution's shape parameter (α) to capture heterogeneity.

Key Insights:

  • The proposed method achieves effective initial segmentation into surface, double-bounce, and random volume scattering categories.
  • Incorporation of K-distribution's shape parameter allows for detailed sub-classification based on scattering heterogeneity.
  • Iterative application of the K-Wishart maximum likelihood classifier refines results and enhances classification accuracy.

Outlook:

  • The method demonstrates superior performance across diverse PolSAR datasets (AIRSAR, ESAR, GaoFen-3) with varying resolutions and terrains.
  • This unsupervised approach offers a robust alternative for PolSAR image interpretation, particularly where labeled data is scarce.
  • Future work could explore adaptive parameter selection and integration with deep learning architectures for further advancements.