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Published on: August 30, 2013
Differentiation of discrete multidimensional signals
Hany Farid1, Eero P Simoncelli
1Computer Science Department, Dartmouth College, Hanover, NH 03755, USA. farid@cs.dartmouth.edu
Summary
We developed new finite-size kernels for accurately differentiating multidimensional signals. These optimized filters improve gradient calculations in image and signal processing applications.
Area of Science:
- Signal Processing
- Image Analysis
- Numerical Methods
Background:
- Accurate differentiation of discrete multidimensional signals is crucial for various image and signal processing tasks.
- Existing methods often lack rotation-invariance and sufficient accuracy for complex signal analysis.
Purpose of the Study:
- To design finite-size, linear-phase, separable kernels for accurate multidimensional signal differentiation.
- To develop a robust optimization framework ensuring rotation-invariance of the gradient operator.
Main Methods:
- Formulated the problem as optimizing gradient operator rotation-invariance.
- Derived simultaneous constraints for 1D low-pass prefilter and differentiator filters.
- Developed a numerical procedure for constraint optimization and filter construction.
- Extended the formulation to higher dimensions and higher-order directional derivatives.
Main Results:
- Successfully constructed a set of example finite-size, linear-phase, separable differentiation kernels.
- Demonstrated significantly improved accuracy compared to commonly used filters in the literature.
- Validated the effectiveness of the rotation-invariance optimization approach.
Conclusions:
- The proposed method yields highly accurate differentiation kernels for multidimensional signals.
- This approach offers a superior alternative for gradient estimation in image and signal processing.
- The developed framework is extendable to more complex differentiation tasks.
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