We propose a new framework for the recognition of online handwritten graphics. Three main features of the framework are its ability to treat symbol and structural level information in an integrated way, its flexibility with respect to different families of graphics, and means to control the tradeoff between recognition effectiveness and computational cost. We model a graphic as a labeled graph generated from a graph grammar. Non-terminal vertices represent subcomponents, terminal vertices represent symbols, and edges represent relations between subcomponents or symbols. We then model the recognition problem as a graph parsing problem: given an input stroke set, we search for a parse tree that represents the best interpretation of the input. Our graph parsing algorithm generates multiple interpretations (consistent with the grammar) and then we extract an optimal interpretation according to a cost function that takes into consideration the likelihood scores of symbols and structures. The parsing algorithm consists in recursively partitioning the stroke set according to structures defined in the grammar and it does not impose constraints present in some previous works (e.g. stroke ordering). By avoiding such constraints and thanks to the powerful representativeness of graphs, our approach can be adapted to the recognition of different graphic notations. We show applications to the recognition of mathematical expressions and flowcharts. Experimentation shows that our method obtains state-of-the-art accuracy in both applications.
We present a new approach for parsing two-dimensional input using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics. The approach reports all identifiable parses of the input. The parses are represented as a fuzzy set, in which the membership grade of a parse measures the similarity between it and the handwritten input. To identify and report parses efficiently, we adapt and apply existing techniques such as rectangular partitions and shared parse forests, and introduce new ideas such as relational classes and interchangeability. We also present a correction mechanism that allows users to navigate parse results and choose the correct interpretation in case of recognition errors or ambiguity. Such corrections are incorporated into subsequent incremental recognition results. Finally, we include two empirical evaluations of our recognizer. One uses a novel user-oriented correction count metric, while the other replicates the CROHME 2011 math recognition contest. Both evaluations demonstrate the effectiveness of our proposed approach.