Quaternion Fourier transform-based alpha-rooting color image enhancement in 2 algebras: commutative and non-commutative

Artyom M. Grigoryan; Alexis A. Gomez Sr.

doi:10.1117/12.3017692

7 June 2024 Quaternion Fourier transform-based alpha-rooting color image enhancement in 2 algebras: commutative and non-commutative

Artyom M. Grigoryan, Alexis A. Gomez Sr.

Author Affiliations +

Proceedings Volume 13033, Multimodal Image Exploitation and Learning 2024; 1303304 (2024) https://doi.org/10.1117/12.3017692
Event: SPIE Defense + Commercial Sensing, 2024, National Harbor, Maryland, United States

Abstract

In this paper, we describe new methods of color image enhancement alpha-rooting by the 2D quaternion discrete Fourier transform (QDFT) in the commutative algebra, or the (2,2)-model. In this model, the concept of the convolution is unique, which is very important when transforming tasks with color images into the frequency domain. Also, there are only two types of the exponential function and therefore only two QDFTs. Both these transforms can be used to reduce the convolution to operation of multiplication. Illustrative examples on color image enhancement are given. Measures of the image enhancement and selection of the best parameters of alpha-rooting are described. A comparison with the traditional non-commutative quaternion algebra is discussed and shown that the (2,2)-model is more effective in image enhancement.

Conference Presentation

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Artyom M. Grigoryan and Alexis A. Gomez Sr. "Quaternion Fourier transform-based alpha-rooting color image enhancement in 2 algebras: commutative and non-commutative", Proc. SPIE 13033, Multimodal Image Exploitation and Learning 2024, 1303304 (7 June 2024); https://doi.org/10.1117/12.3017692

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available