Handwriting Feature Extraction via Legendre-Sobolev Matrix Representation

The two-dimensional nature of mathematical formulas and the large set of mathematical characters with different variations in style and size form the main challenges in mathematical handwriting recognition. To address these difficulties, the way handwritten data is represented and the methods to compute certain features from the chosen representation are important questions. To this aim, we treat handwritten characters as approximated parametrized coordinate curves in Legendre-Sobolev bases. This representation empowers us to study the geometrical features of handwritten characters as a whole. These geometrical features are used to find to baselines, bounding boxes, loops, and cusps appearing in handwritten characters. Computing these features relies on mathematical operations such as derivatives, roots, and gcds of polynomials. This paper studies the problem of computing these operations without the conversion to the monomial basis, seeking improvement in speed and accuracy.