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Related Concept Videos

Rotation of Asymmetric Top01:11

Rotation of Asymmetric Top

By definition, a spherically symmetric body has the same moment of inertia about any axis passing through its center of mass. This situation changes if there is no spherical symmetry. Since most rigid bodies are not spherically symmetric, these require special treatment.
The relationship between the angular momentum of any rigid body and its angular velocity, both of which are vectors, involves the moment of inertia. The moment of inertia is a scalar quantity only for spherically symmetric...
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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...
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

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Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.

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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
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Hierarchical shape description via the multiresolution symmetric axis transform.

S M Pizer1, W R Oliver, S H Bloomberg

  • 1Department of Computer Science and the Department of Radiology, University of North Carolina, Chapel Hill, NC 27514.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for generating hierarchical shape descriptions using symmetric axis sequences. This figure-based approach offers natural segmentation and noise insensitivity for 2D and 3D object representation.

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Area of Science:

  • Computer Vision
  • Image Analysis
  • Computational Geometry

Background:

  • Traditional shape descriptions often rely on object boundaries, which can be sensitive to noise and segmentation issues.
  • Figure-based descriptions offer an alternative perspective, focusing on the internal structure of shapes.
  • Hierarchical representations are valuable for capturing multi-scale features in complex objects.

Purpose of the Study:

  • To propose a new method for creating hierarchical shape descriptions.
  • To develop a figure-oriented approach that is robust to noise.
  • To explore the generation of shape hierarchies based on symmetric axes.

Main Methods:

  • Generating shape descriptions as a hierarchy of simple symmetric axis sequences.
  • Inducing scale and parent-child relationships by analyzing symmetric axes under successive resolution reduction.
  • Developing methods for resolution reduction and computer implementation of the described approach.

Main Results:

  • The proposed method produces a figure-oriented shape description, rather than a boundary-oriented one.
  • The resulting hierarchical description has natural segments and demonstrates insensitivity to noise.
  • The approach is applicable to both two-dimensional (2D) and three-dimensional (3D) shapes.

Conclusions:

  • The symmetric axis-based hierarchical method provides a robust and natural way to describe shapes.
  • This figure-based representation overcomes limitations of boundary-based methods, particularly in noisy data.
  • The approach offers a foundation for advanced shape analysis and recognition tasks.