Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments
Abstract
:1. Introduction
2. Classical Chebyshev Orthogonal Polynomials
2.1. Chebyshev Orthogonal Moments
2.2. Fractional Order Orthogonal Chebyshev Moments (FCMs)
Algorithm 1: Orthogonal Fractional Chebyshev Moments [18] | |
Input | |
Step 1 | Generate image coordinates from Equation (15) |
Step 2 | Generate normalized fractional order Chebyshev forandEquation (11) |
Step 3 | Calculatefrom Equation (14) |
Output | Image moment at. |
2.3. Proposed Generalized Fractional Order Orthogonal Chebyshev Polynomials (GFCPs)
2.4. Proposed Generalized Fractional Order Orthogonal Chebyshev Moments (GFCMs)
Algorithm 2: Generalized Fractional order Orthogonal Chebyshev Moments (GFCMs) [19] | |
Input | |
Step 1 | Create image coordinates from Equation (24). |
Step 2 | Compute Equation (20) forand |
Step 3 | from Equation (23) |
Output | Image moment at. |
3. Proposed Generalized Orthogonal Laguerre Polynomials (GLPs)
3.1. Proposed Generalized Laguerre Orthogonal Moments (GLMs)
Algorithm 3: Generalized Laguerre Orthogonal Moments (GLMs) [21] | |
Input | |
Step 1 | Computeforandfrom Equation (29) |
Step 2 | Calculatefrom Equation (31) |
Output | Image moment at. |
3.2. Proposed Generalized Laguerre Fractional Order Orthogonal Polynomials (GLFPs)
3.3. Proposed Generalized Laguerre Fractional Order Orthogonal Moments (GLFMs)
Algorithm 4: Generalized Laguerre Fractional Order Orthogonal Moments (FGLMs) [21] | |
Input | |
Step 1 | Computeforand |
Step 2 | Calculatefrom Equation (37) |
Output | Image moment at. |
4. Discussion and Numerical Results
4.1. Image Representation
4.2. Computational Time
5. Conclusions
Funding
Acknowledgments
Conflicts of Interest
References
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Farouk, R.M. Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments. J. Imaging 2020, 6, 54. https://doi.org/10.3390/jimaging6060054
Farouk RM. Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments. Journal of Imaging. 2020; 6(6):54. https://doi.org/10.3390/jimaging6060054
Chicago/Turabian StyleFarouk, R. M. 2020. "Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments" Journal of Imaging 6, no. 6: 54. https://doi.org/10.3390/jimaging6060054
APA StyleFarouk, R. M. (2020). Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments. Journal of Imaging, 6(6), 54. https://doi.org/10.3390/jimaging6060054