Spline-Guided Segmentation of Handwritten Physico-Mathematical Documents for Improved OCR Accuracy

Handwritten physics and mathematics documents pose a significant challenge to optical character recognition due to oscillatory baselines, dense expressions, and mixed symbolic–graphical layouts. These features cause fragmentation in standard segmentation pipelines. This article presents a new segmentation method using shape-preserving coconvex splines of degree ≤ 2, incorporating curvature for the first time. During preprocessing, manually annotated baselines are approximated by splines that preserve local convexity and concavity while avoiding oscillatory artefacts. The fitted curves define curvature-adaptive cutting masks that replace rigid rectangular slicing. Resulting fragments are normalised and processed by a YOLOv8-S detector trained with spline-guided geometric aug- mentation, increasing dataset diversity without requiring new labels. A graph-based module then reconstructs the full page structure. On a test set of handwritten STEM exams, the method achieves high precision (0.925), recall (0.859), and mAP scores, while reducing layout error. These findings show that mathematically grounded curvature modelling improves robustness and enables scalable reconstruction of handwritten documents.