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Image interpolation by two-dimensional parametric cubic convolution.

Jiazheng Shi1, Stephen E Reichenbach

  • 1Computer Science and Engineering Department, University of Nebraska, Lincoln 68588-0115, USA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 13, 2006
PubMed
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This study introduces novel nonseparable 2D cubic convolution kernels (2D-3PCC and 2D-5PCC) for improved image interpolation. These advanced kernels enhance interpolation fidelity, especially for images with aliasing, outperforming traditional methods.

Area of Science:

  • Image Processing
  • Computer Vision
  • Applied Mathematics

Background:

  • Traditional separable cubic convolution methods are limited by the statistical nonseparability of images.
  • Existing methods may not optimally handle the complex statistical properties inherent in real-world images.

Purpose of the Study:

  • To develop and evaluate novel nonseparable 2D cubic convolution kernels for image interpolation.
  • To investigate kernels that address the statistical nonseparability of images.
  • To provide a practical method for adaptive interpolation based on image characteristics.

Main Methods:

  • Derivation of two new nonseparable 2D cubic convolution kernels: 2D-3PCC (3 parameters) and 2D-5PCC (5 parameters).
  • Development of a closed-form solution for optimizing kernel parameters using scene autocorrelation (power spectrum).

Related Experiment Videos

  • Quantitative fidelity analyses and visual experiments comparing new methods against popular interpolation techniques.

    • Main Results:

    • The proposed 2D-3PCC and 2D-5PCC kernels demonstrate superior interpolation fidelity, particularly for images containing aliased components.
    • A closed-form solution enables adaptive interpolation by optimizing kernel parameters based on local image autocorrelation.
    • New methods achieve results comparable to popular methods for images with minimal aliasing.

    Conclusions:

    • Nonseparable 2D cubic convolution kernels offer significant advantages in image interpolation accuracy.
    • The developed methods are computationally efficient due to low-order polynomials and small spatial support.
    • This work provides a robust framework for adaptive and high-fidelity image interpolation.