A comparative study of OCR systems for mathematical expression recognition: architecture, performance, and practical applications

Optical Character Recognition (OCR) of mathematical expressions presents different challenges beyond conventional text recognition, requiring accurate modeling of two-dimensional spatial arrangements, hierarchical symbol structure, and specialized notation. This study conducts a systematic evaluation of twelve OCR systems—seven general-purpose and five math-specific—on a curated dataset of 1,200 expressions spanning elementary algebra, calculus, linear algebra, and advanced symbolic notation, captured in handwritten, printed, and photographed form. We propose an evaluation framework that jointly quantifies character-level accuracy, structural fidelity, LaTeX generation quality, and semantic correctness, addressing well-known limitations of purely string-based metrics such as Character Error Rate (CER) and BiLingual Evaluation Understudy (BLEU). Our numerical experiments show that specialized mathematical OCR systems attain 89–92% expression-level accuracy, substantially outperforming general-purpose OCR baselines (36–45%) on structurally complex formulas. We further introduce the Mathematical Expression Recognition Score (MERS), a composite index integrating structural accuracy, symbol recognition, and layout preservation, and use decision tree analysis to derive optimal model selection criteria as a function of expression complexity, notation category, and input modality. In contrast to existing tree- or image-based metrics for formula evaluation, MERS is designed to be model- and representation-agnostic, enabling consistent comparison across heterogeneous OCR architectures and LaTeX rendering variants.