Geometric Techniques for Digital Ink Geometric Techniques for Digital Ink

Handwriting is one of the most natural ways for a human to record knowledge. In recent years this type of human-computer interaction has received increasing attention due to the rapid evolution of digital ink hardware. This thesis contributes to the art of efficient recognition of handwriting and compact storage of digital ink. In the first part of the thesis, we focus on the development of algorithms for transformation-invariant recognition of handwritten mathematical characters. We first implement a rotation-independent classification method based on the theory of integral invariants of parametric curves. We then extend this method to shearinvariant recognition. Presence of affine transformations creates difficulties in parameterization of coordinate functions and size normalization of handwritten samples. We therefore present an affine-invariant size normalization approach and develop a mixed parameterization, which is insensitive to large affine transformations and yields a relatively high recognition rate. In the second part of the thesis, we develop digital ink compression algorithms taking advantage of the theory of approximation of curves with orthogonal polynomial series. We then test the compression rate for Chebyshev, Legendre and LegendreSobolev orthogonal polynomials, as well as for Fourier series. By studying the compression ratio for representing coefficients in Unicode and binary formats, we show that Chebyshev polynomials give the best compression rate and can be successfully used in related applications.