Richard Zanibbi

Ayush Kumar Shah, Bryan Manrique Amador, Abhisek Dey et al.

Most molecular diagram parsers recover chemical structure from raster images (e.g., PNGs). However, many PDFs include commands giving explicit locations and shapes for characters, lines, and polygons. We present a new parser that uses these born-digital PDF primitives as input. The parsing model is fast and accurate, and does not require GPUs, Optical Character Recognition (OCR), or vectorization. We use the parser to annotate raster images and then train a new multi-task neural network for recognizing molecules in raster images. We evaluate our parsers using SMILES and standard benchmarks, along with a novel evaluation protocol comparing molecular graphs directly that supports automatic error compilation and reveals errors missed by SMILES-based evaluation. On the synthetic USPTO benchmark, our born-digital parser obtains a recognition rate of 98.4% (1% higher than previous models) and our relatively simple neural parser for raster images obtains a rate of 85% using less training data than existing neural approaches (thousands vs. millions of molecules).

Yejing Xie, Richard Zanibbi, Harold Mouchère

In this paper, we present a novel approach to Handwritten Mathematical Expression Recognition (HMER) by leveraging graph-based modeling techniques. We introduce an End-to-end model with an Edge-weighted Graph Attention Mechanism (EGAT), designed to perform simultaneous node and edge classification. This model effectively integrates node and edge features, facilitating the prediction of symbol classes and their relationships within mathematical expressions. Additionally, we propose a stroke-level Graph Modeling method for both local (LGM) and global (GGM) information, which applies an end-to-end model to Online HMER tasks, transforming the recognition problem into node and edge classification tasks in graph structure. By capturing both local and global graph features, our method ensures comprehensive understanding of the expression structure. Through the combination of these components, our system demonstrates superior performance in symbol detection, relation classification, and expression-level recognition.

Behrooz Mansouri, Douglas W. Oard, Anurag Agarwal et al.

There are now several test collections for the formula retrieval task, in which a system's goal is to identify useful mathematical formulae to show in response to a query posed as a formula. These test collections differ in query format, query complexity, number of queries, content source, and relevance definition. Comparisons among six formula retrieval test collections illustrate that defining relevance based on query and/or document context can be consequential, that system results vary markedly with formula complexity, and that judging relevance after clustering formulas with identical symbol layouts (i.e., Symbol Layout Trees) can affect system preference ordering.

Parag Mali, Puneeth Kukkadapu, Mahshad Mahdavi et al.

We introduce the Scanning Single Shot Detector (ScanSSD) for locating math formulas offset from text and embedded in textlines. ScanSSD uses only visual features for detection: no formatting or typesetting information such as layout, font, or character labels are employed. Given a 600 dpi document page image, a Single Shot Detector (SSD) locates formulas at multiple scales using sliding windows, after which candidate detections are pooled to obtain page-level results. For our experiments we use the TFD-ICDAR2019v2 dataset, a modification of the GTDB scanned math article collection. ScanSSD detects characters in formulas with high accuracy, obtaining a 0.926 f-score, and detects formulas with high recall overall. Detection errors are largely minor, such as splitting formulas at large whitespace gaps (e.g., for variable constraints) and merging formulas on adjacent textlines. Formula detection f-scores of 0.796 (IOU $\geq0.5$) and 0.733 (IOU $\ge 0.75$) are obtained. Our data, evaluation tools, and code are publicly available.

Shaurya Rohatgi, Wei Zhong, Richard Zanibbi et al.

Query Auto Completion (QAC) is among the most appealing features of a web search engine. It helps users formulate queries quickly with less effort. Although there has been much effort in this area for text, to the best of our knowledge there is few work on mathematical formula auto completion. In this paper, we implement 5 existing QAC methods on mathematical formula and evaluate them on the NTCIR-12 MathIR task dataset. We report the efficiency of retrieved results using Mean Reciprocal Rank (MRR) and Mean Average Precision(MAP). Our study indicates that the Finite State Transducer outperforms other QAC models with a MRR score of $0.642$.

Richard Zanibbi, Kenny Davila, Andrew Kane et al.

With the ever-increasing quantity and variety of data worldwide, the Web has become a rich repository of mathematical formulae. This necessitates the creation of robust and scalable systems for Mathematical Information Retrieval, where users search for mathematical information using individual formulae (query-by-expression) or a combination of keywords and formulae. Often, the pages that best satisfy users' information needs contain expressions that only approximately match the query formulae. For users trying to locate or re-find a specific expression, browse for similar formulae, or who are mathematical non-experts, the similarity of formulae depends more on the relative positions of symbols than on deep mathematical semantics. We propose the Maximum Subtree Similarity (MSS) metric for query-by-expression that produces intuitive rankings of formulae based on their appearance, as represented by the types and relative positions of symbols. Because it is too expensive to apply the metric against all formulae in large collections, we first retrieve expressions using an inverted index over tuples that encode relationships between pairs of symbols, ranking hits using the Dice coefficient. The top-k formulae are then re-ranked using MSS. Our approach obtains state-of-the-art performance on the NTCIR-11 Wikipedia formula retrieval benchmark and is efficient in terms of both index space and overall retrieval time. Retrieval systems for other graphical forms, including chemical diagrams, flowcharts, figures, and tables, may also benefit from adopting our approach.

Richard Zanibbi, Awelemdy Orakwue

We summarize math search engines and search interfaces produced by the Document and Pattern Recognition Lab in recent years, and in particular the min math search interface and the Tangent search engine. Source code for both systems are publicly available. "The Masses" refers to our emphasis on creating systems for mathematical non-experts, who may be looking to define unfamiliar notation, or browse documents based on the visual appearance of formulae rather than their mathematical semantics.

Christoph Riedl, Richard Zanibbi, Marti A. Hearst et al.

We report the findings of a month-long online competition in which participants developed algorithms for augmenting the digital version of patent documents published by the United States Patent and Trademark Office (USPTO). The goal was to detect figures and part labels in U.S. patent drawing pages. The challenge drew 232 teams of two, of which 70 teams (30%) submitted solutions. Collectively, teams submitted 1,797 solutions that were compiled on the competition servers. Participants reported spending an average of 63 hours developing their solutions, resulting in a total of 5,591 hours of development time. A manually labeled dataset of 306 patents was used for training, online system tests, and evaluation. The design and performance of the top-5 systems are presented, along with a system developed after the competition which illustrates that winning teams produced near state-of-the-art results under strict time and computation constraints. For the 1st place system, the harmonic mean of recall and precision (f-measure) was 88.57% for figure region detection, 78.81% for figure regions with correctly recognized figure titles, and 70.98% for part label detection and character recognition. Data and software from the competition are available through the online UCI Machine Learning repository to inspire follow-on work by the image processing community.