Neural-spline optimization framework for robust document image binarization

This paper presents Neural-Spline Optimization (NSO), a structured learning framework for document image binarization in which a compact tensor-product B-spline surface replaces a fixed analytic fusion function within an explicit thresholding rule. Instead of learning a dense pixel-to-label mapping from scratch, NSO learns a low-dimensional decision surface over page-level intensity descriptors while preserving the analytical structure of the underlying binarization operator. The paper is focused on the computational and methodological aspects of learning this surface, and on the manner in which controlled adaptivity should be introduced around it. Three closely related variants are considered within a common formulation: direct global spline optimization, spline-guided pixel-domain refinement, and bounded residual learning in control-point space. The main new contribution is the residual control-point variant, which introduces data-driven updates directly in the spline parameter space while preserving a single global and exportable decision surface. The mathematical formulation includes spline construction, differentiable relaxation of the hard decision rule, structural objective design, and deployment-oriented regularization. The experimental analysis is concentrated on optimization behaviour, interpretability, and structural changes under a fixed public protocol. The resulting framework provides an interpretable and computationally compact alternative to purely pixel-based deep binarization models, with a balanced trade-off between accuracy, robustness, and deployment simplicity rather than uniform maximization of all evaluation measures.