Symbolic and Visual Retrieval of Mathematical Notation using Formula Graph Symbol Pair Matching and Structural Alignment

Large data collections containing millions of math formulae in different formats are available on-line. Retrieving math expressions from these collections is challenging. We propose a framework for retrieval of mathematical notation using symbol pairs extracted from visual and semantic representations of mathematical expressions on the symbolic domain for retrieval of text documents. We further adapt our model for retrieval of mathematical notation on images and lecture videos. Graph-based representations are used on each modality to describe math formulas. For symbolic formula retrieval, where the structure is known, we use symbol layout trees and operator trees. For image-based formula retrieval, since the structure is unknown we use a more general Line of Sight graph representation. Paths of these graphs define symbol pairs tuples that are used as the entries for our inverted index of mathematical notation. Our retrieval framework uses a three-stage approach with a fast selection of candidates as the first layer, a more detailed matching algorithm with similarity metric computation in the second stage, and finally when relevance assessments are available, we use an optional third layer with linear regression for estimation of relevance using multiple similarity scores for final re-ranking. Our model has been evaluated using large collections of documents, and preliminary results are presented for videos and cross-modal search. The proposed framework can be adapted for other domains like chemistry or technical diagrams where two visually similar elements from a collection are usually related to each other

Unconstrained Scene Text and Video Text Recognition for Arabic Script

Building robust recognizers for Arabic has always been challenging. We demonstrate the effectiveness of an end-to-end trainable CNN-RNN hybrid architecture in recognizing Arabic text in videos and natural scenes. We outperform previous state-of-the-art on two publicly available video text datasets - ALIF and ACTIV. For the scene text recognition task, we introduce a new Arabic scene text dataset and establish baseline results. For scripts like Arabic, a major challenge in developing robust recognizers is the lack of large quantity of annotated data. We overcome this by synthesising millions of Arabic text images from a large vocabulary of Arabic words and phrases. Our implementation is built on top of the model introduced here [37] which is proven quite effective for English scene text recognition. The model follows a segmentation-free, sequence to sequence transcription approach. The network transcribes a sequence of convolutional features from the input image to a sequence of target labels. This does away with the need for segmenting input image into constituent characters/glyphs, which is often difficult for Arabic script. Further, the ability of RNNs to model contextual dependencies yields superior recognition results.Comment: 5 page

A Transformer Architecture for Online Gesture Recognition of Mathematical Expressions

The Transformer architecture is shown to provide a powerful framework as an end-to-end model for building expression trees from online handwritten gestures corresponding to glyph strokes. In particular, the attention mechanism was successfully used to encode, learn and enforce the underlying syntax of expressions creating latent representations that are correctly decoded to the exact mathematical expression tree, providing robustness to ablated inputs and unseen glyphs. For the first time, the encoder is fed with spatio-temporal data tokens potentially forming an infinitely large vocabulary, which finds applications beyond that of online gesture recognition. A new supervised dataset of online handwriting gestures is provided for training models on generic handwriting recognition tasks and a new metric is proposed for the evaluation of the syntactic correctness of the output expression trees. A small Transformer model suitable for edge inference was successfully trained to an average normalised Levenshtein accuracy of 94%, resulting in valid postfix RPN tree representation for 94% of predictions.Comment: 12 pages, 3 Figures, 4 Table

Content Recognition and Context Modeling for Document Analysis and Retrieval

The nature and scope of available documents are changing significantly in many areas of document analysis and retrieval as complex, heterogeneous collections become accessible to virtually everyone via the web. The increasing level of diversity presents a great challenge for document image content categorization, indexing, and retrieval. Meanwhile, the processing of documents with unconstrained layouts and complex formatting often requires effective leveraging of broad contextual knowledge. In this dissertation, we first present a novel approach for document image content categorization, using a lexicon of shape features. Each lexical word corresponds to a scale and rotation invariant local shape feature that is generic enough to be detected repeatably and is segmentation free. A concise, structurally indexed shape lexicon is learned by clustering and partitioning feature types through graph cuts. Our idea finds successful application in several challenging tasks, including content recognition of diverse web images and language identification on documents composed of mixed machine printed text and handwriting. Second, we address two fundamental problems in signature-based document image retrieval. Facing continually increasing volumes of documents, detecting and recognizing unique, evidentiary visual entities (\eg, signatures and logos) provides a practical and reliable supplement to the OCR recognition of printed text. We propose a novel multi-scale framework to detect and segment signatures jointly from document images, based on the structural saliency under a signature production model. We formulate the problem of signature retrieval in the unconstrained setting of geometry-invariant deformable shape matching and demonstrate state-of-the-art performance in signature matching and verification. Third, we present a model-based approach for extracting relevant named entities from unstructured documents. In a wide range of applications that require structured information from diverse, unstructured document images, processing OCR text does not give satisfactory results due to the absence of linguistic context. Our approach enables learning of inference rules collectively based on contextual information from both page layout and text features. Finally, we demonstrate the importance of mining general web user behavior data for improving document ranking and other web search experience. The context of web user activities reveals their preferences and intents, and we emphasize the analysis of individual user sessions for creating aggregate models. We introduce a novel algorithm for estimating web page and web site importance, and discuss its theoretical foundation based on an intentional surfer model. We demonstrate that our approach significantly improves large-scale document retrieval performance

Math Search for the Masses: Multimodal Search Interfaces and Appearance-Based Retrieval

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.Comment: Paper for Invited Talk at 2015 Conference on Intelligent Computer Mathematics (July, Washington DC