CDM: A Reliable Metric for Fair and Accurate Formula Recognition
  Evaluation
Authors: name: Bin Wang, name: Fan Wu, name: Linke Ouyang, name: Zhuangcheng Gu, name: Rui Zhang, name: Renqiu Xia, name: Bo Zhang, name: Conghui He

Formula recognition presents significant challenges due to the complicated
structure and varied notation of mathematical expressions. Despite continuous
advancements in formula recognition models, the evaluation metrics employed by
these models, such as BLEU and Edit Distance, still exhibit notable
limitations. They overlook the fact that the same formula has diverse
representations and is highly sensitive to the distribution of training data,
thereby causing the unfairness in formula recognition evaluation. To this end,
we propose a Character Detection Matching (CDM) metric, ensuring the evaluation
objectivity by designing a image-level rather than LaTex-level metric score.
Specifically, CDM renders both the model-predicted LaTeX and the ground-truth
LaTeX formulas into image-formatted formulas, then employs visual feature
extraction and localization techniques for precise character-level matching,
incorporating spatial position information. Such a spatially-aware and
character-matching method offers a more accurate and equitable evaluation
compared with previous BLEU and Edit Distance metrics that rely solely on
text-based character matching. Experimentally, we evaluated various formula
recognition models using CDM, BLEU, and ExpRate metrics. Their results
demonstrate that the CDM aligns more closely with human evaluation standards
and provides a fairer comparison across different models by eliminating
discrepancies caused by diverse formula representations.