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Related Concept Videos

Ellipses01:30

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest diameter,...
Eccentricity of an Ellipse01:27

Eccentricity of an Ellipse

An ellipse is a fundamental conic section defined by the constant sum of distances from any point on its curve to two fixed points, known as the foci. This geometric property can be physically demonstrated using a pencil, string, and two pins. By anchoring the string at both ends and maintaining it taut with a pencil, one can trace the outline of an ellipse.The shape and extent of the ellipse are determined by its eccentricity, e, defined as the ratio of the distance between the center and a...
Distance Corrections01:15

Distance Corrections

To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
Symmetry01:26

Symmetry

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
Detection of Black Holes01:10

Detection of Black Holes

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their closest cousins are neutron stars, which are composed almost entirely of neutrons packed against each other, making them extremely dense. A neutron star has the same mass as the Sun but its diameter is only a few kilometers. Therefore, the escape velocity from their surface is close to the speed of light.
Not until the 1960s, when the first neutron...

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Using an Automated Hirschberg Test App to Evaluate Ocular Alignment
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Published on: March 24, 2020

A split and merge based ellipse detector with self-correcting capability.

Alex Yong-Sang Chia1, Susanto Rahardja, Deepu Rajan

  • 1Institute for Infocomm Research, Singapore. ysachia@i2r.a-star.edu.sg

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|December 16, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new ellipse detection algorithm that uses edge following and arc grouping to find ellipses. The novel method excels in challenging conditions like noise and occlusion, significantly improving ellipse detection accuracy.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Pattern Recognition

Background:

  • Accurate ellipse detection is crucial for various computer vision tasks.
  • Existing ellipse detection methods struggle with image clutter, noise, and partial occlusion.

Purpose of the Study:

  • To propose a novel ellipse detector robust to challenging image conditions.
  • To improve the precision and recall of ellipse detection in complex scenarios.

Main Methods:

  • An edge-following approach to model edge connectivity with line segments.
  • Grouping disconnected elliptical-arcs to reconstruct full ellipses.
  • A feedback loop for self-correction and refinement of detected ellipses.

Main Results:

  • The proposed algorithm significantly outperforms existing methods on synthetic images.
  • High recall and precision scores achieved under clutter, noise, and occlusion.
  • Successful ellipse detection demonstrated on challenging real-world images.

Conclusions:

  • The novel ellipse detector offers a significant advancement in handling difficult ellipse detection scenarios.
  • The method shows superior performance compared to current state-of-the-art techniques.
  • This work provides a robust solution for detecting ellipses in complex and noisy images.