Automatic extraction of printed mathematical formulas using fuzzy logic and propagation of context

Abstract.

This paper describes a new method to segment printed mathematical documents precisely and extract formulas automatically from their images. Unlike classical methods, it is more directed towards segmentation rather than recognition, isolating mathematical formulas outside and inside text-lines. Our ultimate goal is to delimit parts of text that could disturb OCR applications, not yet trained for formula recognition and restructuring. The method is based on a global and a local segmentation. The global segmentation separates isolated formulas from the text lines using a primary labeling. The local segmentation propagates the context around the mathematical operators met to discard embedded formulas from plain text. The primary labeling identifies some mathematical symbols by models created at a learning step using fuzzy logic. The secondary labeling reinforces the results of the primary labeling and locates the subscripts and the superscripts inside the text. A heuristic has been defined that guides this automatic process. In this paper, the different modules making up the automated segmentation of mathematical document system are presented with examples of results. Experiments carried out on some commonly seen mathematical documents show that our proposed method can achieve quite satisfactory rates, making mathematical formula extraction more feasible for real-world applications. The average rate of primary labeling of mathematical operators is about 95.3% and their secondary labeling can improve the rate by about 4%. The formula extraction rate, evaluated with 300 formulas and 100 mathematical documents having variable complexity, is close to 93%