Color image analysis of quaternion discrete radial Krawtchouk moments
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Color image analysis of quaternion discrete radial Krawtchouk moments Hicham Amakdouf 1 & Amal Zouhri 1 & Mostafa EL Mallahi 1,2 & Hassan Qjidaa 1 Received: 15 February 2019 / Revised: 11 November 2019 / Accepted: 27 May 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
In this work, we suggest a new set of quaternion discrete radial Krawtchouk moments (QDRKMs) for color image reconstruction and classification. These new discrete moments are represented over a disk by using discrete orthogonal radial Krawtchouk moments. The use of Quaternion discrete moments for color image eliminates the discretization errors produced when the Quaternion continuous moments are used. Furthermore, this approach is suggested for highly accurate calculation of QDRKMs in polar coordinates where the kernel is exactly calculated by over circular color pixels. The translation, scaling, and rotation (TSR) invariances for QDRKMs are proved. Theoretical analysis and numerical experiments investigation were shown in terms of the performance description of TSR invariances, classification and robustness to different noises of the QDRKMs compared with continuous quaternion Legendre–Fourier moments using COIL 100 database. Keywords Color image analysis; quaternion . Discrete radial Krawtchouk moments . Classification and recognition of color image
* Hicham Amakdouf [email protected] Amal Zouhri [email protected] Mostafa EL Mallahi [email protected] Hassan Qjidaa [email protected]
1
Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar el Mahraz, Fez, Morocco
2
Sidi Mohamed Ben Abdellah University, Laboratory of Computer Science and Interdisciplinary Physics, ENS, Fez, Morocco
Multimedia Tools and Applications
1 Introduction In recent years, and with the fast progress of mathematics, computer science, and technological development of digital cameras, almost of the images are chromatic. Indeed, to transmit or stock more information, the digital color images have more potential than a gray level or binary image. Moreover, the values associated of three colors such as green, blue, and red for each level of the pixel or and as well its hue, brightness, and saturation, can be successful when used in many images processing tasks such as reconstruction, object classification, recognition, registration, and segmentation. The traditional approach to treatment with digital color images has each level separate while processing, employing a gray level method, and to combining the individual output results. As a consequently, this method misses the inherent correlation between the entities of three colors level. The main problem is therefore to handle three values of each pixel level in entirety. To solve this problem, recently, algebra quaternion color image analysis to represent digital color images by encoding three levels into the imaginary parts by B. J. Chen et al. [4]. The performance of this quaternion algebra is widely seen when a digital color image is treated as
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