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[Submitted on 25 Jul 2026] Title:A Heisenberg Lift Descriptor for Order Sensitive Online Handwriting Recognition View a PDF of the paper titled A Heisenberg Lift Descriptor for Order Sensitive Online Handwriting Recognition, by Hassan Ugail and 1 other authors View PDF HTML (experimental) Abstract:Online handwriting recognition systems typically represent pen trajectories through fixed-length Euclidean shape descriptors that capture the spatial outline of each stroke, but are insensitive to the order in which that outline is produced. Two strokes that trace the same region of the plane in opposite directions are indistinguishable to any such order-blind representation, yet their traversal directions may carry decisive class information in characters where loop orientation and stroke sequencing matter. This paper introduces a Heisenberg-lift framework that addresses this gap through a compact, interpretable, order-sensitive augmentation for online pen-trajectory features. The simplest instance is the terminal signed area, a single parameter-free scalar appended to an existing Euclidean descriptor at negligible computational cost. Evaluated on two standard online handwriting benchmarks, this one-scalar addition, consistently raises classifier accuracy over the Euclidean baseline. On the hardest character pair in our study, the letters o and y, the signed area alone achieves perfect separation while the Euclidean baseline falls short. The advantage grows further under additive coordinate noise, a practically relevant degradation in pen-trajectory data. A richer fifteen-dimensional extension, derived from a noncommutative Heisenberg-group subdivision scheme, provides additional gains in noisy and loop-structured conditions. Dimension-matched statistical controls confirm that all improvements reflect geometric information rather than feature-count inflation. The resulting descriptor is lightweight, closed-form, and directly interpretable, making it a practical augmentation for online handwriting and related document-trajectory classification pipelines in which the direction of stroke execution carries discriminative information. Subjects: Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2609.17565 [cs.CV] (or arXiv:2609.17565v1 [cs.CV] for this version) https://doi.org/10.48550/arXiv.2609.17565 arXiv-issued DOI via DataCite Submission history From: Hassan Ugail [view email] [v1] Sat, 25 Jul 2026 19:29:10 UTC (837 KB) Full-text links: Access Paper: View a PDF of the paper titled A Heisenberg Lift Descriptor for Order Sensitive Online Handwriting Recognition, by Hassan Ugail and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.CV new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators 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. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)