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Related Concept Videos

Singularity Functions for Shear01:26

Singularity Functions for Shear

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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Shear on the Horizontal Face of a Beam Element01:16

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To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's...
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Shear Diagram01:27

Shear Diagram

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In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
First, a free-body diagram of the beam is drawn, representing all the external forces and internal reactions acting on the beam. One can calculate the reaction forces at each support by employing the equilibrium equations of force and moment. The vertical component...
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Extraction: Advanced Methods00:56

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Metal ions can be separated from one another by complexation with organic ligands–the chelating agent– to form uncharged chelates. Here, the chelating agent must contain hydrophobic groups and behave as a weak acid, losing a proton to bind with the metal. Since most organic ligands used in this process are insoluble or undergo oxidation in the aqueous phase, the chelating agent is initially added to the organic phase and extracted into the aqueous phase. The metal-ligand complex is...
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Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
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Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm.

Héctor Andrade-Loarca1, Gitta Kutyniok1,2,3, Ozan Öktem4

  • 1Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany.

Proceedings. Mathematical, Physical, and Engineering Sciences
|December 28, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a hybrid method for semantic edge detection, combining shearlets and convolutional neural networks. The novel approach overcomes limitations in supervised learning and achieves high performance in image processing tasks like tomographic reconstruction.

Keywords:
deep learningfeature extractionharmonic analysismultiscale geometric analysis

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Area of Science:

  • Computer Vision
  • Image Processing
  • Machine Learning

Background:

  • Semantic edge detection is crucial for image analysis, extracting vital information from image edges.
  • Existing methods face challenges due to the distinct abstraction levels of edge detection and classification, known as the distracted supervision paradox.
  • This paradox limits the performance of purely supervised models in semantic edge detection.

Purpose of the Study:

  • To develop a novel hybrid method for semantic edge detection that overcomes the distracted supervision paradox.
  • To achieve high performance in semantic edge detection tasks.
  • To demonstrate the method's efficiency in terms of parameter count compared to data-driven approaches.

Main Methods:

  • A hybrid approach combining the model-based shearlet transform with a data-driven convolutional neural network (CNN).
  • Shearlets provide optimally sparse approximations for image models.
  • A specifically designed CNN is integrated with shearlet properties.

Main Results:

  • The proposed hybrid method successfully avoids the distracted supervision paradox.
  • Achieved high performance in semantic edge detection.
  • Demonstrated significantly fewer parameters compared to pure data-driven methods.
  • Outperformed previous methods in applications like tomographic reconstruction.

Conclusions:

  • The novel hybrid method offers a significant advancement in semantic edge detection.
  • This approach provides a more efficient and effective solution compared to existing methods.
  • Highlights the potential of hybrid methods in biomedical imaging and other fields.