Intensity-curvature functional based digital high pass filter of the bivariate cubic B-spline model polynomial
Carlo Ciulla1, Grace Agyapong2
1Faculty of Information Systems, Visualization, Multimedia, and Animation, University of Information Science and Technology, St. Paul the Apostle, Partizanska B.B., Ohrid, 6000, Republic of North Macedonia. cxc2728@njit.edu.
Visual Computing for Industry, Biomedicine, and Art
|April 3, 2020
Summary
This study introduces an intensity-curvature functional (ICF) based high-pass filter (HPF) designed using bivariate cubic B-splines. ICF-based HPF shows promise, though traditional HPFs yield sharper images.
Area of Science:
- Digital Image Processing
- Computational Imaging
- Applied Mathematics
Background:
- High-pass filters (HPFs) are crucial for image enhancement.
- Existing HPF designs often lack theoretical grounding in curvature concepts.
- The intensity-curvature concept offers a novel approach to signal processing.
Purpose of the Study:
- To design and mathematically describe an intensity-curvature functional (ICF) based digital high-pass filter (HPF).
- To validate the hypothesis that ICF acts as an HPF signal.
- To compare the performance of the ICF-based HPF against traditional and PSO-based HPFs.
Main Methods:
- Calculation of ICF using a bivariate cubic B-spline model.
- Development of the intensity-curvature concept for 2D image analysis.
- Empirical comparison of ICF-based HPF with ten other HPFs, including traditional and particle swarm optimization (PSO) based methods, in image and k-space.
Main Results:
- The theoretical basis for ICF as an HPF signal was established.
- Empirical validation confirmed ICF's HPF capability.
- Both traditional HPF and ICF-based HPF outperformed PSO-based filtering.
- Traditional HPF resulted in sharper images compared to ICF-based HPF.
Conclusions:
- A mathematical framework for designing 2D HPFs from bivariate polynomial functions using the ICF concept was confirmed.
- The ICF-based HPF is a viable alternative, though traditional HPFs offer superior sharpness.
- Further research can explore optimizing ICF-based filters for enhanced image sharpness.
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