对比不同多项式基底，提升数学手写识别的精度与效率
Well-Conditioned Polynomial Representations for Mathematical Handwriting Recognition
- 采用勒让德、切比雪夫等基底表示手写轨迹
- 控制条件数降低计算成本，符号间差异度可量化
- 适合需要高效手写识别的系统开发者
以往研究使用参数化平面曲线的多项式表示法处理数学手写内容，多项式基于勒让德或勒让德-索博列夫分级基底，实现数字墨迹的紧凑几何表达。初步结果也展示了切比雪夫和切比雪夫-索博列夫基底的表现。本文探讨了基底选择与多项式阶数之间的权衡，以实现高精度建模且计算成本低。为此，考虑这些基底下多项式求值的条件数，并通过各类内积界定符号间变化的范数。
原文摘要 · Abstract (English)
Previous work has made use of a parameterized plane curve polynomial representation for mathematical handwriting, with the polynomials represented in a Legendre or Legendre-Sobolev graded basis. This provides a compact geometric representation for the digital ink. Preliminary results have also been shown for Chebyshev and Chebyshev-Sobolev bases. This article explores the trade-offs between basis choice and polynomial degree to achieve accurate modeling with a low computational cost. To do this, we consider the condition number for polynomial evaluation in these bases and bound how the various inner products give norms for the variations between symbols.
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