baseline - Baseline Structure Analysis of Handwritten...

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Baseline Structure Analysis of Handwritten Mathematics Notation Richard Zanibbi Dorothea Blostein James R. Cordy Department Computing & Information Science, Queen's University, Kingston, Ontario, Canada { zanibbi, blostein, cordy } @cs.queensu.ca Abstract The structure of mathematics notation is particularly dificult to recognize in handwritten notation because irregular symbol placements are common. We present an eficient and robust method of parsing handwritten and typeset mathematics notation without backtracking. The system is designed to be easily adaptable to various dialects of mathematics notation. The following strategies are used: (I) separate the analysis layout, syntax, and semantics. (2) recursively apply search functions and image partitioning to recognize dominant and nested baselines, and (3) use tree transformations to express computations in a compact, eficiently executable form. 1. Introduction Mathematics notation conveys information using a two- dimensional arrangement of symbols. Recognition software must analyze this spatial structure, in order to convert from a document image to a structural representation such as LaTeX or a semantic representation such as an operator tree or Maple. However, it is difficult to define robust, general and efficient methods for analyzing the spatial structure of mathematics notation. This problem is particularly difficult in handwritten mathematics notation (obtained from scanned document images, or from data tablet input), where irregular placement of symbols is common. 1.1 Summary of Existing Work Research into automatic recognition of mathematical expressions has been ongoing for over thirty years [3,5]. Methods developed for recognizing the two-dimensional layout of symbols in a math expression can be roughly categorized into syntactic (grammar-based) and algorithmic approaches. Syntactic methods have been used extensively, including coordinate grammars [ 1,251, attributed string grammars [2,12,13,14,34], stochastic grammars [ 10,261, structure specification schemes [6], and graph transformation [ 17,22,23,28]. Algorithmic approaches have included recursively locating vertically stacked groups of symbols using procedural [24] and blackboard-style methods [ 15,301, recursive baseline location [20], and minimization of penalty functions on symbol relations [ 161. Another algorithmic approach, projection profile cutting with subsequent adjustments, has been used to 0-7695-1263-1/01/\$10.00 0 2001 IEEE 768 obtain expression structure directly from pixel maps [ 18,27,29]. Ambiguities of symbol layout and identity have been handled by constructing multiple interpretations and then eliminating unsyntactic [3 I] or unlikely [26] interpretations. We obtain two insights from this literature. First, almost all authors use trees to describe the spatial structure of mathematics notation. In many cases the tree is an explicit data structure; in other cases an implicit parse tree is created. Second, mathematical expressions have a preferred direction of interpretarion, as used by human readers; this directionality can be exploited by a recognition system (1,14,25].

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baseline - Baseline Structure Analysis of Handwritten...

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