<![CDATA[This study analyses the fundamental trade-offs in optimising contrast enhancement of retinal fundus images by presenting a mathematical formalisation within the framework of nonlinear discrete operator theory. This study tests the hypothesis that the polarisation of performance between local adaptive and global operators is a fundamental mathematical consequence of the operator architecture used. The BBHE and CLAHE operators are used as the primary representations for each architecture. An orthogonal evaluation framework was introduced, using AMBE to quantify global brightness preservation and EME to quantify local contrast dispersion. Quantitative results on Fundus imagery shows a statistically significant performance polarisation (p < 0.001; Cohen’s d > 2.8). BBHE achieves the lowest AMBE value , which indicates high luminance fidelity, whereas CLAHE produces the highest EME value , which shows superiority in strengthening local contrasts. Pareto-boundary-based geometric analysis confirms the existence of a structural trade-off between brightness preservation and contrast enhancement, and demonstrates that the ideal quadrant (low AMBE and high EME simultaneously) is unattainable by any single operator. Theoretically, these findings validate the AMBE–EME conflict as a structural constraint in the design of image enhancement operators. The main contribution of this research is the mathematical formalisation of the trade-off and the theoretical foundation for developing future image enhancement operators via a constrained optimisation approach.]]>
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