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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...
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...
In this paper we consider the initial
boundary value problem of a parabolic-elliptic system for image
inpainting, and establish the existence and uniqueness of weak
solutions to the system in dimension two.
We demonstrate searching of mathematical expressions in technical digital libraries on a MREC collection of 439,423 real scientific documents with more than 158 million mathematical formulae. Our solution—the WebMIaS system—allows the retrieval of mathematical expressions written in TeX or MathML. TeX queries are converted on-the-fly into tree representations of Presentation MathML, which is used for indexing. WebMIaS allows complex queries composed of plain text and mathematical formulae, using...
In this work-in-progress report we propose a workflow for metadata extraction from articles in a digital form. We decompose the problem into clearly defined sub-tasks and outline possible implementations of the sub-tasks. We report the progress of implementation and tests, and state future work.
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