Digital ink compression via functional approximation

Abstract

Representing digital ink traces as points in a function space has proven useful for online recognition. Ink trace coordinates or their integral invariants are written as parametric functions and approximated by truncated orthogonal series. This representation captures the shape of the ink traces with a small number of coefficients in a form quite compact and independent of device resolution, and various geometric techniques may be employed for recognition. The simplicity and high performance of this method lead us to ask whether the same idea can be applied to another important aspect in online handwriting -the compression of digital ink strokes. We have investigated Chebyshev, Legendre and Legendre-Sobolev orthogonal polynomial bases as well as Fourier series and have found that Chebyshev representation is the most suitable apparatus for compressing digital curves. We obtain compression rates of 30× to 50× and have the added benefit that the LegendreSobolev form, used for recognition, may be obtained by a single linear transformation.

Compression of Digital-Ink with Pen Slip Using Optimal <i>L</i>₁ Smoothing Splines

“…The basic idea for data compression is similar to Mazalov and Watt's work in [2], but differs in the following two points: (i) Use of the normalized uniform B-spline function for digital-ink compression, and (ii) Pen-slip rejection using optimal L 1 smoothing splines. The idea of L 1 smoothing in (ii) is similar to Nagahara and Martin's work [6], but they have employed the control theoretic approach [7] and not B-spline approach [8] as in this study.…”

“…For example, Mazalov and Watt in [2] have developed a compression method for digital-ink using approximation by orthogonal polynomial functions. Therein, they showed that the digital ink is successfully compressed as a small number of the functional coefficients in a compact form.…”

“…Due to the properties of the basis functions B k (t), the curve x(t) in (2) describes a piecewise polynomials of degree k with the knot points t i and is k − 1 times Proceedings of the 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Okinawa, Nov. [1][2]2013 continuously differentiable. In particular, depending on the choice of the control point τ i , a class of polynomial splines x(t) of degree k can be generated on the interval [t 0 , t m ] for t. Then, the problem of digital-ink compression can be reduced to the one of finding a sequence of control points…”

Linear Compression of Digital Ink via Point Selection

“…We also implement an enhanced version of the compression method [1], based on functional approximation, by representing coefficients in a more compact form. We measure the compression rate and time required to process the experimental datasets and compare with the performance of the linear method.…”

“…An efficient lossy method was developed in [1]. This was based on piecewise functional approximation of curves by truncated orthogonal polynomial series and representation of the pieces by the approximating series coefficients.…”