The present work is motivated by the problem of mathematical handwriting recognition where symbols are represented as parametric plane curves in a Legendre-Sobolev basis. An early work showed that approximating the coordinate functions as truncated series in a Legendre-Sobolev basis yields fast and effective recognition rates. Furthermore, this representation allows one to study the geometrical features of handwritten characters as a whole. These geometrical features are equivalent to baselines, bounding boxes, loops, and cusps appearing in handwritten characters. The study of these features becomes a crucial task when dealing with two-dimensional math formulas and the large set of math characters with different variations in style and size.
In an early paper, we proposed methods for computing the derivatives, roots, and gcds of polynomials in Legendre-Sobolev bases to find such features without needing to convert the approximations to the monomial basis. Furthermore, in this paper, we propose a new formulation for the conversion matrix for constructing Legendre-Sobolev representation of the coordinate functions from their moment integrals.
Our findings in employing parametrized Legendre-Sobolev approximations for representing handwritten characters and studying the geometrical features of such representation has led us to develop two Maple packages called LegendreSobolev and HandwritingRecognitionTesting. The methods in these packages rely on Maple’s linear algebra routines.