# Cascade Network with Deformable Composite Backbone for Formula Detection in Scanned Document Images
## 2 Related Work  
Research progress in the field of document image analysis directly relates to advances in the computer vision research community. The task of formula detection in documents is a well-studied problem [28]. Noticeable progress has been achieved in this domain by implementing custom-heuristics to deep learning-based approaches. Earlier, rule-based approaches developed character-based heuristics to identify formulas in documents [29; 30; 31; 32]. These techniques look for special characters (e.g., \"\(>\)\", \"\(\times\)\", \"=\") that mainly exist in mathematical formulas.  
[PERSON] et al. [12] introduced a model based on fuzzy logic to detect mathematical symbols. The approach predicts the formula region by exploiting the features of mathematical symbols. [PERSON] et al. [2] first employed a conventional OCR method to extract characters. The method treated all the remaining characters as mathematical symbols that OCR was unable to parse.  
Specific OCR systems have been presented that recognize mathematical symbols based on their positions and sizes [2]. [PERSON] et al. [13] segregated the lines containing formulas to the regular textual lines in order to detect isolated formulas in PDF documents.  
Decision trees have been equipped to detect isolated formulas by classifying formula lines with the plain text lines [33]. [PERSON] et al. [15] proposed a similar method based on the projection of the features that only works for isolated formulas in documents.  
Later, machine learning-based algorithms were proposed to alleviate the performance of formula detection systems in documents [14; 34]. [PERSON] et al. [16] leveraged the combination of Conditional Random Field (CRF) and Support Vector Machine (SVM) to classify sparse lines in documents. Subsequently, the method distinguished formulas from other graphical page objects such as figures and tables by applying custom heuristics.  
Suceedingly, researchers have investigated the capabilities of Deep Neural Networks (DNNs) for the problem of formula identification in document images [27; 35]. To the best of our knowledge, [PERSON] et al. [36] exploited Convolutional Neural Networks (CNNs) with spatial context to detect mathematical symbols in document images. Later, [PERSON] et al. [37] presented a deep learning-based formula detection system in PDF documents.  
NLPR-PAL [27] produced the best results in the competition of POD at ICDAR-2017. They proposed a blend of connected components, SVM, and Faster R-CNN [21] to detect figures, formulas, and tables in document images.  
[PERSON] et al. [38] published another CNN-based approach that detects graphical page objects such as tables, figures, and formulas in document images. The authors employed the dynamic programming technique instead of Non-Maximum Suppression (NMS) to refine the final candidate proposals. Semantic segmentation-based architecture such as U-Net [39] has also been utilized to detect mathematical expressions in scientific document images [17].  
Recently, [PERSON] et al. [18] published a method equipped with YOLO [40] to detect mathematical formulas in document images. In another approach [19], SSD [23] was exploited to detect mathematical expressions in PDF documents.  
Another graphical page object detection system was published by [PERSON] et al. [41]. The authors combined deep structure prediction with a traditional approach to detecting page objects, including formulas in document images. [PERSON] et al. [20] introduced a system called _Fi-Fo_ that detects figures and formulas in document images. The authors empirically established that deformable convolutions [42] with Feature Pyramid Networks (FPN) [24] are a better fit as compared to other object detection algorithms. The proposed approach heavily relied on the image transformation pre-processing techniques to produce state-of-the-art results.