Abstract-We describe a robust and efficient system for recognizing typeset and handwritten mathematical notation. From a list of symbols with bounding boxes the system analyzes an expression in three successive passes. The Layout Pass constructs a Baseline Structure Tree (BST) describing the two-dimensional arrangement of input symbols. Reading order and operator dominance are used to allow efficient recognition of symbol layout even when symbols deviate greatly from their ideal positions. Next, the Lexical Pass produces a Lexed BST from the initial BST by grouping tokens comprised of multiple input symbols; these include decimal numbers, function names, and symbols comprised of nonoverlapping primitives such as "=". The Lexical Pass also labels vertical structures such as fractions and accents. The Lexed BST is translated into L A T E X. Additional processing, necessary for producing output for symbolic algebra systems, is carried out in the Expression Analysis Pass. The Lexed BST is translated into an Operator Tree, which describes the order and scope of operations in the input expression. The tree manipulations used in each pass are represented compactly using tree transformations. The compiler-like architecture of the system allows robust handling of unexpected input, increases the scalability of the system, and provides the groundwork for handling dialects of mathematical notation.

Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with wide-spread availability of Optical Character Recognition (OCR) and text-based search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.

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Categorization of biomedical articles is a central task for supporting various curation efforts. It can also form the basis for effective biomedical text mining. Automatic text classification in the biomedical domain is thus an active research area. Contests organized by the KDD Cup (2002) and the TREC Genomics track (since 2003) defined several annotation tasks that involved document classification, and provided training and test data sets. So far, these efforts focused on analyzing only the text content of documents. However, as was noted in the KDD'02 text mining contest-where figure-captions proved to be an invaluable feature for identifying documents of interest-images often provide curators with critical information. We examine the possibility of using information derived directly from image data, and of integrating it with text-based classification, for biomedical document categorization. We present a method for obtaining features from images and for using them-both alone and in combination with text-to perform the triage task introduced in the TREC Genomics track 2004. The task was to determine which documents are relevant to a given annotation task performed by the Mouse Genome Database curators. We show preliminary results, demonstrating that the method has a strong potential to enhance and complement traditional text-based categorization methods.