Title: Mathematical model of image transformation based on optimisation theory and its application

Authors: Yanbo Zhang

Addresses: School of Tourism Data, Guilin Tourism University, Guilin 541006, Guangxi, China

Abstract: The advantages of mathematical image models include visibility, comparability and mobility, which evolve with different research objects. Mathematical models use images and integral equations to describe phenomena, understand patterns and connect changes. Electronic imaging helps visualise image transformations and supports the construction of mathematical models. However, current models often fail to precisely reflect image changes and are complex to build, so optimal solutions are lacking. This study analysed the significance, steps and methods of constructing an image transformation mathematical model. It applied optimisation theory to improve the model's robustness. Under this theory, the optimal transformation approximation error decreases over time, whilst the contrast correlation function increases. The mean error of the mathematical model was approximately 0.46, whereas the mean value of the contrast correlation function was 0.60. Overall, the optimal transformation error decreases by 0.57, and the contrast function value increased by 0.43. The robustness of the optimised model was 11.31% higher than the original, and its prediction accuracy improved by 9.90%. In conclusion, combining electronic imaging with optimisation theory can achieve more accurate mathematical models of image transformation than simple electronic imaging.

Keywords: image transformation; optimisation theory; electronic imaging; mathematical model.

DOI: 10.1504/IJDSDE.2024.145221

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.5, pp.427 - 440

Received: 25 Oct 2024
Accepted: 24 Dec 2024
Published online: 26 Mar 2025 *

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