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Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing

Olga Drblíková (2007)

Kybernetika

This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...

Using Discourse Context to Interpret Object-Denoting Mathematical Expressions

Wolska, Magdalena, Grigore, Mihai, Kohlhase, Michael (2011)

Towards a Digital Mathematics Library. Bertinoro, Italy, July 20-21st, 2011

We present a method for determining the context-dependent denotation of simple object-denoting mathematical expressions in mathematical documents. Our approach relies on estimating the similarity between the linguistic context within which the given expression occurs and a set of terms from a flat domain taxonomy of mathematical concepts; one of 7 head concepts dominating a set of terms with highest similarity score to the symbol’s context is assigned as the symbol’s interpretation. The taxonomy...

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