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The design of two-dimensional gradient estimators based on one-dimensional operators
M Azaria1, I Vitsnudel, Y Y Zeevi
1Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa.
Summary
A new computational method extends one-dimensional (1-D) gradient estimators to two dimensions (2-D) for image processing. This simpler 1-D design approach also allows for higher-order derivative estimators.
Area of Science:
- Image Processing
- Computational Mathematics
Background:
- Two-dimensional (2-D) gradient estimators are essential tools in image processing.
- Existing methods for 2-D gradient estimation can be complex in design.
Purpose of the Study:
- To present a computational procedure for extending one-dimensional (1-D) gradient estimators to two dimensions (2-D).
- To offer a simpler alternative to existing 2-D surface fitting methods.
Main Methods:
- A computational procedure is detailed for adapting 1-D gradient estimators to a 2-D context.
- The proposed method is shown to be equivalent to surface fitting but with a simplified 1-D design.
Main Results:
- The procedure successfully extends 1-D gradient estimators to 2-D.
- The method's design simplicity, rooted in 1-D principles, is highlighted.
- The procedure's applicability to constructing higher-order derivative estimators is demonstrated.
Conclusions:
- The presented computational procedure offers a simplified and effective way to implement 2-D gradient estimation.
- This approach facilitates the development of more advanced derivative estimators in image processing.
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