海森堡提升描述符用于顺序敏感的在线手写识别

中文摘要 AI 辅助

在线手写识别系统通常通过固定长度的欧几里得形状描述符来表示笔迹轨迹，这些描述符捕捉每个笔画的轮廓空间，但对轮廓生成顺序不敏感。以相反方向绘制平面同一区域的两个笔画，对于任何此类顺序无关的表示都是不可区分的，然而在循环方向和笔画顺序至关重要的字符中，其绘制方向可能携带决定性的类别信息。本文引入了一种海森堡提升框架，通过一种紧凑、可解释、顺序敏感的增强方式来解决这一不足，用于在线笔迹轨迹特征。最简单的实例是终端有向面积，这是一个无参数的标量，以可忽略的计算成本附加到现有欧几里得描述符上。在两个标准在线手写基准上的评估表明，这一标量添加持续提高了分类器相对于欧几里得基线的准确性。在我们研究中最难的字符对（字母o和y）上，仅凭有向面积就实现了完美分离，而欧几里得基线则未能达到。在加性坐标噪声（笔迹轨迹数据中一种实际相关的退化）下，这一优势进一步扩大。一个更丰富的十五维扩展，源自非交换海森堡群细分方案，在噪声和循环结构条件下提供了额外增益。维度匹配的统计对照证实，所有改进均反映几何信息而非特征数量膨胀。所得描述符轻量、闭式且直接可解释，使其成为在线手写及相关文档轨迹分类流程中实用的增强，在这些流程中，笔画执行方向携带判别性信息。

英文摘要

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.

发表机构

• University of Bradford（布拉德福德大学）
• Rochester Institute of Technology（罗切斯特理工学院）

机构由 AI 辅助整理，请以论文原文为准。