The content of this repository is related to the project that helps eliminate numerical instability and high-order orthogonal moment calculation error while preserving it's orthogonality, which is one of the most important properties of these types of functions.
The high-order orthogonal polynomial base causes a numerical instability that makes it difficult to calculate the moments. In this project, we analyze the calculation of the following discrete orthogonal polynomials,
- Tchebycheff polynomials
- Krawtchouk polynomials
- Hahn polynomials
- Meixner polynomials
- Charlier polynomials
The source codes of the project are described in the chapter 3: "Computation of 2D and 3D high-order discrete orthogonal moments" of the book "Recent Progress in Moments and Moment Invariants" GCSR Volume 7 Edited by Dr. George A. Papakostas.
If you find these codes useful as a support tool.
You can access the information about the book through the following link: https://sciencegatepub.com/sgp-books/gcsr/gcsr_vol7/
or you can directly download the chapter using the following link: https://sciencegatepub.com/?smd_process_download=1&download_id=3179
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José S. Rivera-Lopez, César Camacho-Bello, and Lucia Gutiérrez-Lazcano, Chapter 3. “Computation of 2D and 3D High-order Discrete Orthogonal Moments”. Recent Progress in Image Moments and Moment Invariants, GCSR Volume 7 (2021), 53-74, DOI: 10.15579/gcsr.vol7.ch3.
Bibtex: @article{Rivera2021Recent, title={Recent Progress in Image Moments and Moment Invariants}, author={José S. Rivera-Lopez and César Camacho-Bello and Lucia Gutiérrez-Lazcano}, journal={Science Gate}, volume={7}, pages={53--74}, year={2021}, URL={https://sciencegatepub.com/sgp-books/gcsr/gcsr_vol7/}, ISBN={2241-9063} }
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C. Camacho-Bello and J. S. Rivera-Lopez, “Some computational aspects of tchebichef moments for higher orders,”Pattern Recognition Letters, vol. 112, pp. 332–339, 2018.
Bibtex: @article{camacho2018some, title={Some computational aspects of Tchebichef moments for higher orders}, author={Camacho-Bello, C{\'e}sar and Rivera-Lopez, Jos{\'e} S}, journal={Pattern Recognition Letters}, volume={112}, pages={332--339}, year={2018}, publisher={Elsevier} }
- Download this repository.
- To obtain discrete ortogonal moments of image test run the file "Discrete_orthogonal_moments.m" using Matlab.
- By default the value assigned for the order of calculation of the moment is the maximum possible. Change the value of "n" in line 66 from "Discrete_orthogonal_moments.m", to obtain different orders of discrete orthogonal moments form image test.
- By default set discrete orthogonal polynomials is Tchebichef polynomial. For obtain different set polynomial modify line 69 from "Discrete_orthogonal_moments.m" corresponding to the calculation of the polynomial base.