Interpretable Structural Modeling of MR Images Using Q-Bezier Curves: A Geometry-Aware Paradigm Beyond Deep Learning

Abstract

Magnetic resonance (MR) imaging plays a critical role in diagnostic workflows, yet its reliability is frequently compromised by scanner-dependent bias, contrast variability, and intensity drift. Although deep learning methods achieve high performance, they generally require extensive supervision and demonstrate limited robustness across diverse clinical settings. To address these challenges, we propose a transparent, geometry-aware framework for annotation-free MR enhancement based on q-B & eacute;zier curves. This model incorporates an adaptive deformation parameter q(x) that modulates local curvature, facilitating flexible adaptation to complex anatomical boundaries. The framework comprises three principal mechanisms: (i) adaptive q(x) for local responsiveness, (ii) monotone q-Bezier tone curves for intensity standardization, and (iii) Tikhonov-regularized optimization for smooth mapping. As a result, the operator remains interpretable, operates in linear time, and provides explicit control over smoothness. The proposed approach was validated across five public cohorts (BraTS, ACDC, PROMISE12, fastMRI, IXI), demonstrating significant improvements in image fidelity (SSIM, CNR, NIQE) and downstream segmentation accuracy (Dice, HD95) relative to variational filters and state-of-theart foundation models. Additionally, cross-vendor experiments confirm its robustness without the need for retraining. Collectively, these findings establish q-Bezier modeling as a principled, lightweight, and clinically interpretable alternative that complements deep learning by providing a geometry-aware pathway to robust MR representation.