PA-CDM: Position-Aware Character Detection Matching for Evaluating Handwritten Mathematical Expression Recognition

Abstract:Handwritten mathematical expression recognition (HMER) is conventionally scored by exact-match rates and string-similarity metrics that are blind to where an error occurs: two predictions with identical token-error counts receive identical scores whether they misplace a subscript or swap the operands of a fraction. Render-based character detection matching (CDM) aligns glyphs robustly but remains position-blind---on controlled fraction-operand swaps it scores 0.8595 where position-aware scoring yields 0.6253. Tree-edit metrics exhibit a complementary blind spot: rewrites outside the parser's normalization coverage are penalized as structural errors (0.8552 where render-based metrics score 1.0). We propose PA-CDM, a position-aware metric that couples character detection matching with position-forest encoding and divergence-level weighting; StructPerturb v2.0, a frozen benchmark of 1,340 controlled perturbation pairs across 15 type--intensity cells; and a cross-metric consistency protocol combining a sensitivity matrix, a human study, and LLM-judge calibration. In a six-annotator study, PA-CDM attains the highest correlation with human judgments among seven automatic metrics (Spearman rho=0.9535, n=990). A frontier LLM judge correlates slightly higher (rho=0.9613) but is costly, nondeterministic, and API-dependent; PA-CDM approaches it at zero marginal cost with deterministic, diagnosable behavior.

Computer Vision and Pattern Recognition (cs.CV); Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2609.12917 [cs.CV]

(or arXiv:2609.12917v1 [cs.CV] for this version)

https://doi.org/10.48550/arXiv.2609.12917 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.