Probabilistic mathematical formula recognition using a 2D context-free graph grammar

We present a probabilistic framework for the mathematical expression recognition problem. The developed system is flexible in that its grammar can be extended easily thanks to its graph grammar which eliminates the need for specifying rule precedence. It is also optimal in the sense that all possible interpretations of the expressions are expanded without making early commitments or hard decisions. In this paper, we give an overview of the whole system and describe in detail the graph grammar and the parsing process used in the system, along with some preliminary results on character, structure and expression recognition performances

Efficient Analysis of Complex Diagrams using Constraint-Based Parsing

This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of substantial complexity. The system is probably the first to demonstrate efficient diagram parsing using grammars that easily be retargeted to other domains. The work assumes that the diagrams are available as a flat collection of graphics primitives: lines, polygons, circles, Bezier curves and text. This is appropriate for future electronic documents or for vectorized diagrams converted from scanned images. The classes of diagrams that we have analyzed include x,y data graphs and genetic diagrams drawn from the biological literature, as well as finite state automata diagrams (states and arcs). As an example, parsing a four-part data graph composed of 133 primitives required 35 sec using Macintosh Common Lisp on a Macintosh Quadra 700.Comment: 9 pages, Postscript, no fonts, compressed, uuencoded. Composed in MSWord 5.1a for the Mac. To appear in ICDAR '95. Other versions at ftp://ftp.ccs.neu.edu/pub/people/futrell

Stochastic Attribute-Value Grammars

Probabilistic analogues of regular and context-free grammars are well-known in computational linguistics, and currently the subject of intensive research. To date, however, no satisfactory probabilistic analogue of attribute-value grammars has been proposed: previous attempts have failed to define a correct parameter-estimation algorithm. In the present paper, I define stochastic attribute-value grammars and give a correct algorithm for estimating their parameters. The estimation algorithm is adapted from Della Pietra, Della Pietra, and Lafferty (1995). To estimate model parameters, it is necessary to compute the expectations of certain functions under random fields. In the application discussed by Della Pietra, Della Pietra, and Lafferty (representing English orthographic constraints), Gibbs sampling can be used to estimate the needed expectations. The fact that attribute-value grammars generate constrained languages makes Gibbs sampling inapplicable, but I show how a variant of Gibbs sampling, the Metropolis-Hastings algorithm, can be used instead.Comment: 23 pages, 21 Postscript figures, uses rotate.st