Abstract We present a discriminative learning algorithm for the probabilistic estimation of two-dimensional probabilistic context-free grammars (2D-PCFG) for mathematical expressions recognition and retrieval. This algorithm is based on a generalization of the H-criterion as the objective function and the growth transformations as the optimization method. For the development of the discriminative estimation algorithm, the N-best interpretations provided by the 2D-PCFG have been considered. Experimental results are reported on two available datasets: Im2Latex and IBEM. The first experiment compares the proposed discriminative estimation method with the classic Viterbi-based estimation method. The second one studies the performance of the estimated models depending on the length of the mathematical expressions and the number of admissible errors in the metric used.

Searching for information in printed scientific documents is a challenging problem that has recently received special attention from the Pattern Recognition research community. Mathematical expressions are complex elements that appear in scientific documents, and developing techniques for locating and recognizing them requires the preparation of datasets that can be used as benchmarks. Most current techniques for dealing with mathematical expressions are based on Machine Learning techniques which require a large amount of annotated data. These datasets must be prepared with ground-truth information for automatic training and testing. However, preparing large datasets with ground-truth is a very expensive and time-consuming task. This paper introduces the IBEM dataset, consisting of scientific documents that have been prepared for mathematical expression recognition and searching. This dataset consists of 600 documents, more than 8200 page images with more than 160000 mathematical expressions. It has been automatically generated from the version of the documents and can be enlarged easily. The ground-truth includes the position at the page level and the transcript for mathematical expressions both embedded in the text and displayed. This paper also reports a baseline classification experiment with mathematical symbols and a baseline experiment of Mathematical Expression Recognition performed on the IBEM dataset. These experiments aim to provide some benchmarks for comparison purposes so that future users of the IBEM dataset can have a baseline framework.