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PKCS: a polynomial kernel family with compact support for scale- space image processing.

Saeid Saryazdi1, Mohamed Cheriet

  • 1Shahid Bahonar University, Kerman, Iran. saryazdi@mail.uk.ac.ir

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 6, 2007
PubMed
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Researchers developed a new polynomial kernel with compact support, overcoming Gaussian kernel limitations in scale-space theory. This kernel approximates diffusion equations and aids in extracting handwritten data from noisy images.

Area of Science:

  • Computer Vision
  • Image Processing
  • Mathematical Imaging

Background:

  • The Gaussian kernel is fundamental in scale-space theory but has infinite support, posing implementation challenges.
  • Existing solutions involve approximating the Gaussian kernel or developing similar-property kernels.

Purpose of the Study:

  • To introduce a novel polynomial kernel family with compact support.
  • To address the practical implementation issues of the Gaussian kernel while retaining its beneficial properties.

Main Methods:

  • Derivation of a new polynomial kernel family from the Gaussian kernel.
  • Analysis of the kernel's properties, including its relation to the diffusion equation.
  • Demonstration of its application in handwritten data extraction.

Related Experiment Videos

Main Results:

  • The proposed polynomial kernel family offers compact support, resolving Gaussian kernel implementation drawbacks.
  • For specific parameters, the kernel approximates solutions to the diffusion equation.
  • The kernel satisfies fundamental linear scale-space theory constraints.

Conclusions:

  • The novel polynomial kernel provides a practical alternative to the Gaussian kernel in scale-space applications.
  • This kernel family preserves key Gaussian properties while enabling efficient computation.
  • Effective application demonstrated in noisy document image analysis for handwritten data extraction.