Next Article in Journal
Detection of HER2 from Haematoxylin-Eosin Slides Through a Cascade of Deep Learning Classifiers via Multi-Instance Learning
Next Article in Special Issue
Individualised Halo-Free Gradient-Domain Colour Image Daltonisation
Previous Article in Journal
Full 3D Microwave Breast Imaging Using a Deep-Learning Technique
Previous Article in Special Issue
Origins of Hyperbolicity in Color Perception
Article

On Computational Aspects of Krawtchouk Polynomials for High Orders

1
Department of Computer Engineering, University of Baghdad, Baghdad 10071, Iraq
2
Department of Computer Science, Liverpool John Moores University, Liverpool L3 3AF, UK
*
Author to whom correspondence should be addressed.
Current address: Department of Computer Engineering, University of Baghdad, Baghdad 10071, Iraq.
These authors contributed equally to this work.
Received: 2 July 2020 / Revised: 8 August 2020 / Accepted: 11 August 2020 / Published: 13 August 2020
Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods. View Full-Text
Keywords: Krawtchouk polynomials; Krawtchouk moments; high order polynomials; propagation error; image reconstruction analysis Krawtchouk polynomials; Krawtchouk moments; high order polynomials; propagation error; image reconstruction analysis
Show Figures

Figure 1

MDPI and ACS Style

Mahmmod, B.M.; Abdul-Hadi, A.M.; Abdulhussain, S.H.; Hussien, A. On Computational Aspects of Krawtchouk Polynomials for High Orders. J. Imaging 2020, 6, 81. https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging6080081

AMA Style

Mahmmod BM, Abdul-Hadi AM, Abdulhussain SH, Hussien A. On Computational Aspects of Krawtchouk Polynomials for High Orders. Journal of Imaging. 2020; 6(8):81. https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging6080081

Chicago/Turabian Style

Mahmmod, Basheera M.; Abdul-Hadi, Alaa M.; Abdulhussain, Sadiq H.; Hussien, Aseel. 2020. "On Computational Aspects of Krawtchouk Polynomials for High Orders" J. Imaging 6, no. 8: 81. https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging6080081

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop