Efficient search strategy in structural analysis for handwritten mathematical expression recognition

Abstract

Problems with local ambiguities in handwritten mathematical expressions (MEs) are often resolved at global level. Therefore, keeping local ambiguities is desirable for high accuracy, with a hope that they may be resolved by later global analyses. We propose a layered search framework for handwritten ME recognition. From given handwritten input strokes, ME structures are expanded by adding symbol hypotheses one by one, representing ambiguities of symbol identities and spatial relationships as numbers of branches in the expansion. We also propose a novel heuristic predicting how likely the set of remaining input strokes forms valid spatial relationships with the current partially interpreted structure. Further complexity reduction is achieved by delaying the symbol identity decision. The elegance of our approach is that the search result would be unchanged even if we prune out unpromising branches of the search. Therefore, we can examine a much larger number of local hypotheses with a limited amount of computing resource in making global level decisions. The experimental evaluation shows promising results of the efficiency of the proposed approach and the performance of our system, which results from the system's capacity to examine a large number of possibilities.

Recognition and retrieval of mathematical expressions

“…These methods are discussed further in Section 4.6. Some more recent parsing methods that model uncertainty include fuzzy-logic based parsing [44,53], and A*-penalty-based search [122].…”

“…For example, Kim et al [73] modify the penalty metric used in an A* search for constructing symbol layout trees for handwritten expressions [122]. The penalty metric considers mea-sures of consistency of symbol size, style, and repetition, along with symbol n-grams and repeated subscripting.…”

Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models

“…The primary unit representation in mathematical expression recognition can be mathematical symbols [39] or strokes. When using strokes as primary unit representation, the segmentation into strokes can be explicitly used [42,14,40,37,29] or not [31,22]. The use of explicit segmentation into strokes introduces the problem of grouping them to compose symbols, and it makes the search difficult.…”

“…The second approach is usually computational less expensive but it is prone to segmentation errors. The first approach is computational more expensive and efficient A search strategies must be defined [29].…”

A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets

“…This formulation is similar in some ways to the scoring rules developed by Rhee and Kim [32] to represent all parse trees with identical structure, but differing symbol identities by a single tree with indeterminate terminal symbols. Working in a cost-minimization framework, they defined the cost of a spatial relationship between two indeterminate symbols as the minimum relationship cost between determinate symbols, taken over all recognized possibilities for the indeterminate symbols' identities.…”