A First Look at Chebyshev-Sobolev Series for Digital Ink

TL;DR

This paper explores the use of Chebyshev-Sobolev series to represent digital ink as plane curves, aiming to improve symbol recognition tasks by leveraging the properties of this basis.

Contribution

It introduces the application of Chebyshev-Sobolev series for digital ink representation, comparing its potential advantages over Legendre-Sobolev basis in symbol recognition.

Findings

Chebyshev-Sobolev series may outperform Legendre-Sobolev basis in some recognition tasks.

Representation of digital ink as Chebyshev-Sobolev series shows promising properties.

Initial results suggest potential benefits for symbol clustering and classification.

Abstract

Considering digital ink as plane curves provides a valuable framework for various applications, including signature verification, note-taking, and mathematical handwriting recognition. These plane curves can be obtained as parameterized pairs of approximating truncated series (x(s), y(s)) determined by sampled points. Earlier work has found that representing these truncated series (polynomials) in a Legendre or Legendre-Sobolev basis has a number of desirable properties. These include compact data representation, meaningful clustering of like symbols in the vector space of polynomial coefficients, linear separability of classes in this space, and highly efficient calculation of variation between curves. In this work, we take a first step at examining the use of Chebyshev-Sobolev series for symbol recognition. The early indication is that this representation may be superior to Legendre-Sobolev representation for some purposes.