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Related Concept Videos

Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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An edge-adapting Laplacian kernel for nonlinear diffusion filters.

Mohammad Reza Hajiaboli1, M Omair Ahmad, Chunyan Wang

  • 1Center for Signal Processing and Communications, Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada. mohammad.hajiaboli@ieee.org

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|October 25, 2011
PubMed
Summary
This summary is machine-generated.

A new Laplacian kernel was developed for image processing, but caused artifacts. An improved, adaptive kernel was created to reduce edge distortion and enhance image quality in noisy images.

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Area of Science:

  • Image Processing
  • Computer Vision
  • Partial Differential Equations

Background:

  • Anisotropic diffusion is crucial for controlling image processing.
  • Existing Laplacian kernels can cause edge distortion and artifacts.

Purpose of the Study:

  • To develop a new Laplacian kernel with anisotropic behavior.
  • To address artifacts produced by initial kernel designs.
  • To improve nonlinear diffusion filters for noisy images.

Main Methods:

  • Developed a novel Laplacian kernel incorporating anisotropic behavior.
  • Analyzed artifact generation in the initial kernel.
  • Devised an analytical scheme for a spatially varying kernel.
  • Integrated the adaptive kernel into nonlinear diffusion filters.

Main Results:

  • The initial kernel reduced edge distortion but introduced artifacts.
  • The spatially varying kernel adapted to the diffusivity function.
  • The enhanced kernel demonstrated effectiveness in quantitative and qualitative evaluations.
  • Applied to noisy images, the kernel improved processing outcomes.

Conclusions:

  • The spatially varying Laplacian kernel effectively controls forward diffusion.
  • The adaptive kernel minimizes artifacts and edge distortion in image processing.
  • This approach enhances the performance of nonlinear diffusion filters on noisy images.