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Related Experiment Videos

Adaptive image resizing based on continuous-domain stochastic modeling.

Hagai Kirshner, Aurélien Bourquard, John Paul Ward

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |November 16, 2013
    PubMed
    Summary
    This summary is machine-generated.

    Related Concept Videos

    Sampling Continuous Time Signal01:11

    Sampling Continuous Time Signal

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    In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
    In the...
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    This study presents an adaptive continuous-domain image modeling approach using Sobolev spaces and stochastic auto-regressive models. It enhances image processing tasks like interpolation by improving robustness to non-Gaussian processes.

    Area of Science:

    • Computer Vision
    • Image Processing
    • Mathematical Modeling

    Background:

    • Traditional image modeling often assumes discrete data, limiting continuous-domain analysis.
    • Sobolev spaces provide a framework for representing smooth functions, applicable to continuous images.
    • Stochastic auto-regressive models are effective for image texture and data modeling.

    Purpose of the Study:

    • To introduce an adaptive continuous-domain modeling approach for texture and natural images.
    • To link Sobolev spaces with stochastic auto-regressive models for optimal parameter selection.
    • To develop robust estimators for non-Gaussian processes in image modeling.

    Main Methods:

    • Embedding continuous-domain images in parameterized Sobolev spaces.
    • Establishing a link between Sobolev spaces and stochastic auto-regressive models.

    Related Experiment Videos

  • Utilizing exact continuous-to-discrete mapping based on symmetric exponential splines.
  • Maximizing approximated Gaussian likelihood and deriving a robust auto-correlation based estimator.

    • Main Results:

    • Optimal Sobolev parameters are chosen from pixel values using the established link.
    • The auto-correlation criterion demonstrates superior performance with non-Gaussian processes and model mismatch.
    • Multiple initialization values help overcome local minima in fitting criteria.

    Conclusions:

    • The auto-correlation function is crucial for adaptive image interpolation and modeling.
    • The proposed adaptive continuous-domain approach enhances image processing capabilities.
    • This methodology shows promise for broader applications in image processing.