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Analysis of the fractional hilbert transform
Applied Optics
|February 28, 2008
Summary
The fractional Hilbert transform enhances image edges selectively. This study analyzes a 1D fractional Hilbert transform of a rectangle function, explaining how selective edge enhancement occurs.
Area of Science:
- Image Processing
- Applied Mathematics
Background:
- The Hilbert transform is valuable for edge enhancement in image processing.
- A recent fractional Hilbert transform offers selective edge enhancement, but lacks explanation.
Purpose of the Study:
- To analyze the one-dimensional fractional Hilbert transform.
- To explain the phenomenon of selective edge enhancement.
Main Methods:
- Mathematical analysis of the one-dimensional fractional Hilbert transform.
- Application to a one-dimensional rectangle function.
Main Results:
- The analysis demonstrates how the fractional Hilbert transform selectively enhances edges.
- The output image shows controlled edge enhancement based on the transform's parameters.
Conclusions:
- The fractional Hilbert transform provides a mechanism for controllable edge enhancement in image processing.
- Understanding this phenomenon enables precise control over image feature highlighting.
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