A Heuristic Algorithm for Mathematical Markup Encoding Based on the Relative Positions of Characters

Mathematical expressions (MEs) are the most crucial technical content in scientific documents, yet their presentations are not easy to describe. However, LaTeX, one of the primary markup languages in mathematics, enables MEs to be easily understood by computer software. This paper presents a heuristic algorithm based on character relative positioning for converting any MEs in a PDF document into LaTeX markup strings. Unlike OCR-based approaches, our method takes a different approach, as it does not require processing the page images of the document. Instead, it utilizes embedded information within the PDF as input. By using precompiled PDF parsers that provide bounding boxes for each character and analyzing the relative positions of characters, we can effectively decode the mathematical encoding of MEs in LaTeX. To evaluate the performance of our proposed method compared to other related works, we utilized the publicly available dataset IM2LATEX-100K, which includes LaTeX mathematical formulas from high-energy physics and theoretical domains. The dataset was chosen due to its diverse mathematical structures and symbols and its sufficient size for validating the algorithm's performance and robustness. Experimental results demonstrate that our algorithm exhibits strong recognition capabilities, outperforming the state-of-the-art methods with a 4% improvement in image edit distance. The performance of our algorithm significantly surpasses existing methods, affirming the effectiveness of our proposed approach.