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"orig": "forming classification, and adding an adaptive pooling layer of size 28*28. ResNet by default downsamples the image resolution by 32 and then the encoded image is provided to both the Structure Decoder , and Cell BBox Decoder .",
"text": "forming classification, and adding an adaptive pooling layer of size 28*28. ResNet by default downsamples the image resolution by 32 and then the encoded image is provided to both the Structure Decoder , and Cell BBox Decoder .",
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"text": "Structure Decoder. The transformer architecture of this component is based on the work proposed in [31]. After extensive experimentation, the Structure Decoder is modeled as a transformer encoder with two encoder layers and a transformer decoder made from a stack of 4 decoder layers that comprise mainly of multi-head attention and feed forward layers. This configuration uses fewer layers and heads in comparison to networks applied to other problems (e.g. \"Scene Understanding\", \"Image Captioning\"), something which we relate to the simplicity of table images.",
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"text": "The transformer encoder receives an encoded image from the CNN Backbone Network and refines it through a multi-head dot-product attention layer, followed by a Feed Forward Network. During training, the transformer decoder receives as input the output feature produced by the transformer encoder, and the tokenized input of the HTML ground-truth tags. Using a stack of multi-head attention layers, different aspects of the tag sequence could be inferred. This is achieved by each attention head on a layer operating in a different subspace, and then combining altogether their attention score.",
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"text": "Cell BBox Decoder. Our architecture allows to simultaneously predict HTML tags and bounding boxes for each table cell without the need of a separate object detector end to end. This approach is inspired by DETR [1] which employs a Transformer Encoder, and Decoder that looks for a specific number of object queries (potential object detections). As our model utilizes a transformer architecture, the hidden state of the < td > ' and ' < ' HTML structure tags become the object query.",
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"orig": "tention encoding is then multiplied to the encoded image to produce a feature for each table cell. Notice that this is different than the typical object detection problem where imbalances between the number of detections and the amount of objects may exist. In our case, we know up front that the produced detections always match with the table cells in number and correspondence.",
"text": "tention encoding is then multiplied to the encoded image to produce a feature for each table cell. Notice that this is different than the typical object detection problem where imbalances between the number of detections and the amount of objects may exist. In our case, we know up front that the produced detections always match with the table cells in number and correspondence.",
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"orig": "The output features for each table cell are then fed into the feed-forward network (FFN). The FFN consists of a Multi-Layer Perceptron (3 layers with ReLU activation function) that predicts the normalized coordinates for the bounding box of each table cell. Finally, the predicted bounding boxes are classified based on whether they are empty or not using a linear layer.",
"text": "The output features for each table cell are then fed into the feed-forward network (FFN). The FFN consists of a Multi-Layer Perceptron (3 layers with ReLU activation function) that predicts the normalized coordinates for the bounding box of each table cell. Finally, the predicted bounding boxes are classified based on whether they are empty or not using a linear layer.",
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"orig": "Loss Functions. We formulate a multi-task loss Eq. 2 to train our network. The Cross-Entropy loss (denoted as l$_{s}$ ) is used to train the Structure Decoder which predicts the structure tokens. As for the Cell BBox Decoder it is trained with a combination of losses denoted as l$_{box}$ . l$_{box}$ consists of the generally used l$_{1}$ loss for object detection and the IoU loss ( l$_{iou}$ ) to be scale invariant as explained in [25]. In comparison to DETR, we do not use the Hungarian algorithm [15] to match the predicted bounding boxes with the ground-truth boxes, as we have already achieved a one-toone match through two steps: 1) Our token input sequence is naturally ordered, therefore the hidden states of the table data cells are also in order when they are provided as input to the Cell BBox Decoder , and 2) Our bounding boxes generation mechanism (see Sec. 3) ensures a one-to-one mapping between the cell content and its bounding box for all post-processed datasets.",
"text": "Loss Functions. We formulate a multi-task loss Eq. 2 to train our network. The Cross-Entropy loss (denoted as l$_{s}$ ) is used to train the Structure Decoder which predicts the structure tokens. As for the Cell BBox Decoder it is trained with a combination of losses denoted as l$_{box}$ . l$_{box}$ consists of the generally used l$_{1}$ loss for object detection and the IoU loss ( l$_{iou}$ ) to be scale invariant as explained in [25]. In comparison to DETR, we do not use the Hungarian algorithm [15] to match the predicted bounding boxes with the ground-truth boxes, as we have already achieved a one-toone match through two steps: 1) Our token input sequence is naturally ordered, therefore the hidden states of the table data cells are also in order when they are provided as input to the Cell BBox Decoder , and 2) Our bounding boxes generation mechanism (see Sec. 3) ensures a one-to-one mapping between the cell content and its bounding box for all post-processed datasets.",
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"orig": "The loss used to train the TableFormer can be defined as following:",
"text": "The loss used to train the TableFormer can be defined as following:",
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"orig": "l$_{box}$ = \u03bb$_{iou}$l$_{iou}$ + \u03bb$_{l}$$_{1}$ l = \u03bbl$_{s}$ + (1 \u2212 \u03bb ) l$_{box}$ (1)",
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"orig": "where \u03bb \u2208 [0, 1], and \u03bb$_{iou}$, \u03bb$_{l}$$_{1}$ \u2208$_{R}$ are hyper-parameters.",
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"orig": "TableFormer uses ResNet-18 as the CNN Backbone Network . The input images are resized to 448*448 pixels and the feature map has a dimension of 28*28. Additionally, we enforce the following input constraints:",
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"orig": "Although input constraints are used also by other methods, such as EDD, ours are less restrictive due to the improved runtime performance and lower memory footprint of TableFormer. This allows to utilize input samples with longer sequences and images with larger dimensions.",
"text": "Although input constraints are used also by other methods, such as EDD, ours are less restrictive due to the improved runtime performance and lower memory footprint of TableFormer. This allows to utilize input samples with longer sequences and images with larger dimensions.",
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"orig": "The Transformer Encoder consists of two \"Transformer Encoder Layers\", with an input feature size of 512, feed forward network of 1024, and 4 attention heads. As for the Transformer Decoder it is composed of four \"Transformer Decoder Layers\" with similar input and output dimensions as the \"Transformer Encoder Layers\". Even though our model uses fewer layers and heads than the default implementation parameters, our extensive experimentation has proved this setup to be more suitable for table images. We attribute this finding to the inherent design of table images, which contain mostly lines and text, unlike the more elaborate content present in other scopes (e.g. the COCO dataset). Moreover, we have added ResNet blocks to the inputs of the Structure Decoder and Cell BBox Decoder. This prevents a decoder having a stronger influence over the learned weights which would damage the other prediction task (structure vs bounding boxes), but learn task specific weights instead. Lastly our dropout layers are set to 0.5.",
"text": "The Transformer Encoder consists of two \"Transformer Encoder Layers\", with an input feature size of 512, feed forward network of 1024, and 4 attention heads. As for the Transformer Decoder it is composed of four \"Transformer Decoder Layers\" with similar input and output dimensions as the \"Transformer Encoder Layers\". Even though our model uses fewer layers and heads than the default implementation parameters, our extensive experimentation has proved this setup to be more suitable for table images. We attribute this finding to the inherent design of table images, which contain mostly lines and text, unlike the more elaborate content present in other scopes (e.g. the COCO dataset). Moreover, we have added ResNet blocks to the inputs of the Structure Decoder and Cell BBox Decoder. This prevents a decoder having a stronger influence over the learned weights which would damage the other prediction task (structure vs bounding boxes), but learn task specific weights instead. Lastly our dropout layers are set to 0.5.",
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"orig": "For training, TableFormer is trained with 3 Adam optimizers, each one for the CNN Backbone Network , Structure Decoder , and Cell BBox Decoder . Taking the PubTabNet as an example for our parameter set up, the initializing learning rate is 0.001 for 12 epochs with a batch size of 24, and \u03bb set to 0.5. Afterwards, we reduce the learning rate to 0.0001, the batch size to 18 and train for 12 more epochs or convergence.",
"text": "For training, TableFormer is trained with 3 Adam optimizers, each one for the CNN Backbone Network , Structure Decoder , and Cell BBox Decoder . Taking the PubTabNet as an example for our parameter set up, the initializing learning rate is 0.001 for 12 epochs with a batch size of 24, and \u03bb set to 0.5. Afterwards, we reduce the learning rate to 0.0001, the batch size to 18 and train for 12 more epochs or convergence.",
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"orig": "TableFormer is implemented with PyTorch and Torchvision libraries [22]. To speed up the inference, the image undergoes a single forward pass through the CNN Backbone Network and transformer encoder. This eliminates the overhead of generating the same features for each decoding step. Similarly, we employ a 'caching' technique to preform faster autoregressive decoding. This is achieved by storing the features of decoded tokens so we can reuse them for each time step. Therefore, we only compute the attention for each new tag.",
"text": "TableFormer is implemented with PyTorch and Torchvision libraries [22]. To speed up the inference, the image undergoes a single forward pass through the CNN Backbone Network and transformer encoder. This eliminates the overhead of generating the same features for each decoding step. Similarly, we employ a 'caching' technique to preform faster autoregressive decoding. This is achieved by storing the features of decoded tokens so we can reuse them for each time step. Therefore, we only compute the attention for each new tag.",
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"orig": "5.2. Generalization",
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"orig": "TableFormer is evaluated on three major publicly available datasets of different nature to prove the generalization and effectiveness of our model. The datasets used for evaluation are the PubTabNet, FinTabNet and TableBank which stem from the scientific, financial and general domains respectively.",
"text": "TableFormer is evaluated on three major publicly available datasets of different nature to prove the generalization and effectiveness of our model. The datasets used for evaluation are the PubTabNet, FinTabNet and TableBank which stem from the scientific, financial and general domains respectively.",
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"orig": "We also share our baseline results on the challenging SynthTabNet dataset. Throughout our experiments, the same parameters stated in Sec. 5.1 are utilized.",
"text": "We also share our baseline results on the challenging SynthTabNet dataset. Throughout our experiments, the same parameters stated in Sec. 5.1 are utilized.",
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"orig": "The Tree-Edit-Distance-Based Similarity (TEDS) metric was introduced in [37]. It represents the prediction, and ground-truth as a tree structure of HTML tags. This similarity is calculated as:",
"text": "The Tree-Edit-Distance-Based Similarity (TEDS) metric was introduced in [37]. It represents the prediction, and ground-truth as a tree structure of HTML tags. This similarity is calculated as:",
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"orig": "TEDS ( T$_{a}$, T$_{b}$ ) = 1 \u2212 EditDist ( T$_{a}$, T$_{b}$ ) max ( | T$_{a}$ | , | T$_{b}$ | ) (3)",
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"orig": "where T$_{a}$ and T$_{b}$ represent tables in tree structure HTML format. EditDist denotes the tree-edit distance, and | T | represents the number of nodes in T .",
"text": "where T$_{a}$ and T$_{b}$ represent tables in tree structure HTML format. EditDist denotes the tree-edit distance, and | T | represents the number of nodes in T .",
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"orig": "Structure. As shown in Tab. 2, TableFormer outperforms all SOTA methods across different datasets by a large margin for predicting the table structure from an image. All the more, our model outperforms pre-trained methods. During the evaluation we do not apply any table filtering. We also provide our baseline results on the SynthTabNet dataset. It has been observed that large tables (e.g. tables that occupy half of the page or more) yield poor predictions. We attribute this issue to the image resizing during the preprocessing step, that produces downsampled images with indistinguishable features. This problem can be addressed by treating such big tables with a separate model which accepts a large input image size.",
"text": "Structure. As shown in Tab. 2, TableFormer outperforms all SOTA methods across different datasets by a large margin for predicting the table structure from an image. All the more, our model outperforms pre-trained methods. During the evaluation we do not apply any table filtering. We also provide our baseline results on the SynthTabNet dataset. It has been observed that large tables (e.g. tables that occupy half of the page or more) yield poor predictions. We attribute this issue to the image resizing during the preprocessing step, that produces downsampled images with indistinguishable features. This problem can be addressed by treating such big tables with a separate model which accepts a large input image size.",
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"orig": "Table 2: Structure results on PubTabNet (PTN), FinTabNet (FTN), TableBank (TB) and SynthTabNet (STN).",
"text": "Table 2: Structure results on PubTabNet (PTN), FinTabNet (FTN), TableBank (TB) and SynthTabNet (STN).",
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"orig": "FT: Model was trained on PubTabNet then finetuned.",
"text": "FT: Model was trained on PubTabNet then finetuned.",
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"orig": "Cell Detection. Like any object detector, our Cell BBox Detector provides bounding boxes that can be improved with post-processing during inference. We make use of the grid-like structure of tables to refine the predictions. A detailed explanation on the post-processing is available in the supplementary material. As shown in Tab. 3, we evaluate our Cell BBox Decoder accuracy for cells with a class label of 'content' only using the PASCAL VOC mAP metric for pre-processing and post-processing. Note that we do not have post-processing results for SynthTabNet as images are only provided. To compare the performance of our proposed approach, we've integrated TableFormer's Cell BBox Decoder into EDD architecture. As mentioned previously, the Structure Decoder provides the Cell BBox Decoder with the features needed to predict the bounding box predictions. Therefore, the accuracy of the Structure Decoder directly influences the accuracy of the Cell BBox Decoder . If the Structure Decoder predicts an extra column, this will result in an extra column of predicted bounding boxes.",
"text": "Cell Detection. Like any object detector, our Cell BBox Detector provides bounding boxes that can be improved with post-processing during inference. We make use of the grid-like structure of tables to refine the predictions. A detailed explanation on the post-processing is available in the supplementary material. As shown in Tab. 3, we evaluate our Cell BBox Decoder accuracy for cells with a class label of 'content' only using the PASCAL VOC mAP metric for pre-processing and post-processing. Note that we do not have post-processing results for SynthTabNet as images are only provided. To compare the performance of our proposed approach, we've integrated TableFormer's Cell BBox Decoder into EDD architecture. As mentioned previously, the Structure Decoder provides the Cell BBox Decoder with the features needed to predict the bounding box predictions. Therefore, the accuracy of the Structure Decoder directly influences the accuracy of the Cell BBox Decoder . If the Structure Decoder predicts an extra column, this will result in an extra column of predicted bounding boxes.",
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"orig": "Table 3: Cell Bounding Box detection results on PubTabNet, and FinTabNet. PP: Post-processing.",
"text": "Table 3: Cell Bounding Box detection results on PubTabNet, and FinTabNet. PP: Post-processing.",
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"orig": "Cell Content. In this section, we evaluate the entire pipeline of recovering a table with content. Here we put our approach to test by capitalizing on extracting content from the PDF cells rather than decoding from images. Tab. 4 shows the TEDs score of HTML code representing the structure of the table along with the content inserted in the data cell and compared with the ground-truth. Our method achieved a 5.3% increase over the state-of-the-art, and commercial solutions. We believe our scores would be higher if the HTML ground-truth matched the extracted PDF cell content. Unfortunately, there are small discrepancies such as spacings around words or special characters with various unicode representations.",
"text": "Cell Content. In this section, we evaluate the entire pipeline of recovering a table with content. Here we put our approach to test by capitalizing on extracting content from the PDF cells rather than decoding from images. Tab. 4 shows the TEDs score of HTML code representing the structure of the table along with the content inserted in the data cell and compared with the ground-truth. Our method achieved a 5.3% increase over the state-of-the-art, and commercial solutions. We believe our scores would be higher if the HTML ground-truth matched the extracted PDF cell content. Unfortunately, there are small discrepancies such as spacings around words or special characters with various unicode representations.",
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"orig": "Table 4: Results of structure with content retrieved using cell detection on PubTabNet. In all cases the input is PDF documents with cropped tables.",
"text": "Table 4: Results of structure with content retrieved using cell detection on PubTabNet. In all cases the input is PDF documents with cropped tables.",
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"orig": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-",
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"orig": "end object detection with transformers. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020 , pages 213-229, Cham, 2020. Springer International Publishing. 5",
"text": "end object detection with transformers. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020 , pages 213-229, Cham, 2020. Springer International Publishing. 5",
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"orig": "[2] Zewen Chi, Heyan Huang, Heng-Da Xu, Houjin Yu, Wanxuan Yin, and Xian-Ling Mao. Complicated table structure recognition. arXiv preprint arXiv:1908.04729 , 2019. 3",
"text": "Zewen Chi, Heyan Huang, Heng-Da Xu, Houjin Yu, Wanxuan Yin, and Xian-Ling Mao. Complicated table structure recognition. arXiv preprint arXiv:1908.04729 , 2019. 3",
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"orig": "[3] Bertrand Couasnon and Aurelie Lemaitre. Recognition of Tables and Forms , pages 647-677. Springer London, London, 2014. 2",
"text": "Bertrand Couasnon and Aurelie Lemaitre. Recognition of Tables and Forms , pages 647-677. Springer London, London, 2014. 2",
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"orig": "[4] Herv\u00b4e D\u00b4ejean, Jean-Luc Meunier, Liangcai Gao, Yilun Huang, Yu Fang, Florian Kleber, and Eva-Maria Lang. ICDAR 2019 Competition on Table Detection and Recognition (cTDaR), Apr. 2019. http://sac.founderit.com/. 2",
"text": "Herv\u00b4e D\u00b4ejean, Jean-Luc Meunier, Liangcai Gao, Yilun Huang, Yu Fang, Florian Kleber, and Eva-Maria Lang. ICDAR 2019 Competition on Table Detection and Recognition (cTDaR), Apr. 2019. http://sac.founderit.com/. 2",
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"orig": "As a first step of our data preparation process, we have calculated statistics over the datasets across the following dimensions: (1) table size measured in the number of rows and columns, (2) complexity of the table, (3) strictness of the provided HTML structure and (4) completeness (i.e. no omitted bounding boxes). A table is considered to be simple if it does not contain row spans or column spans. Additionally, a table has a strict HTML structure if every row has the same number of columns after taking into account any row or column spans. Therefore a strict HTML structure looks always rectangular. However, HTML is a lenient encoding format, i.e. tables with rows of different sizes might still be regarded as correct due to implicit display rules. These implicit rules leave room for ambiguity, which we want to avoid. As such, we prefer to have \"strict\" tables, i.e. tables where every row has exactly the same length.",
"text": "As a first step of our data preparation process, we have calculated statistics over the datasets across the following dimensions: (1) table size measured in the number of rows and columns, (2) complexity of the table, (3) strictness of the provided HTML structure and (4) completeness (i.e. no omitted bounding boxes). A table is considered to be simple if it does not contain row spans or column spans. Additionally, a table has a strict HTML structure if every row has the same number of columns after taking into account any row or column spans. Therefore a strict HTML structure looks always rectangular. However, HTML is a lenient encoding format, i.e. tables with rows of different sizes might still be regarded as correct due to implicit display rules. These implicit rules leave room for ambiguity, which we want to avoid. As such, we prefer to have \"strict\" tables, i.e. tables where every row has exactly the same length.",
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"orig": "We have developed a technique that tries to derive a missing bounding box out of its neighbors. As a first step, we use the annotation data to generate the most fine-grained grid that covers the table structure. In case of strict HTML tables, all grid squares are associated with some table cell and in the presence of table spans a cell extends across multiple grid squares. When enough bounding boxes are known for a rectangular table, it is possible to compute the geometrical border lines between the grid rows and columns. Eventually this information is used to generate the missing bounding boxes. Additionally, the existence of unused grid squares indicates that the table rows have unequal number of columns and the overall structure is non-strict. The generation of missing bounding boxes for non-strict HTML tables is ambiguous and therefore quite challenging. Thus, we have decided to simply discard those tables. In case of PubTabNet we have computed missing bounding boxes for 48% of the simple and 69% of the complex tables. Regarding FinTabNet, 68% of the simple and 98% of the complex tables require the generation of bounding boxes.",
"text": "We have developed a technique that tries to derive a missing bounding box out of its neighbors. As a first step, we use the annotation data to generate the most fine-grained grid that covers the table structure. In case of strict HTML tables, all grid squares are associated with some table cell and in the presence of table spans a cell extends across multiple grid squares. When enough bounding boxes are known for a rectangular table, it is possible to compute the geometrical border lines between the grid rows and columns. Eventually this information is used to generate the missing bounding boxes. Additionally, the existence of unused grid squares indicates that the table rows have unequal number of columns and the overall structure is non-strict. The generation of missing bounding boxes for non-strict HTML tables is ambiguous and therefore quite challenging. Thus, we have decided to simply discard those tables. In case of PubTabNet we have computed missing bounding boxes for 48% of the simple and 69% of the complex tables. Regarding FinTabNet, 68% of the simple and 98% of the complex tables require the generation of bounding boxes.",
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"orig": "Figure 7 illustrates the distribution of the tables across different dimensions per dataset.",
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"orig": "Aiming to train and evaluate our models in a broader spectrum of table data we have synthesized four types of datasets. Each one contains tables with different appear- ances in regard to their size, structure, style and content. Every synthetic dataset contains 150k examples, summing up to 600k synthetic examples. All datasets are divided into Train, Test and Val splits (80%, 10%, 10%).",
"text": "Aiming to train and evaluate our models in a broader spectrum of table data we have synthesized four types of datasets. Each one contains tables with different appear- ances in regard to their size, structure, style and content. Every synthetic dataset contains 150k examples, summing up to 600k synthetic examples. All datasets are divided into Train, Test and Val splits (80%, 10%, 10%).",
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"orig": "The process of generating a synthetic dataset can be decomposed into the following steps:",
"text": "The process of generating a synthetic dataset can be decomposed into the following steps:",
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"text": "Generate table structures: The structure of each synthetic dataset assumes a horizontal table header which potentially spans over multiple rows and a table body that may contain a combination of row spans and column spans. However, spans are not allowed to cross the header - body boundary. The table structure is described by the parameters: Total number of table rows and columns, number of header rows, type of spans (header only spans, row only spans, column only spans, both row and column spans), maximum span size and the ratio of the table area covered by spans.",
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"orig": "5. Render the complete tables: The synthetic table is finally rendered by a web browser engine to generate the bounding boxes for each table cell. A batching technique is utilized to optimize the runtime overhead of the rendering process.",
"text": "Render the complete tables: The synthetic table is finally rendered by a web browser engine to generate the bounding boxes for each table cell. A batching technique is utilized to optimize the runtime overhead of the rendering process.",
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"orig": "Although TableFormer can predict the table structure and the bounding boxes for tables recognized inside PDF documents, this is not enough when a full reconstruction of the original table is required. This happens mainly due the following reasons:",
"text": "Although TableFormer can predict the table structure and the bounding boxes for tables recognized inside PDF documents, this is not enough when a full reconstruction of the original table is required. This happens mainly due the following reasons:",
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"orig": "Figure 7: Distribution of the tables across different dimensions per dataset. Simple vs complex tables per dataset and split, strict vs non strict html structures per dataset and table complexity, missing bboxes per dataset and table complexity.",
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"orig": "2. Generate pair-wise matches between the bounding boxes of the PDF cells and the predicted cells. The Intersection Over Union (IOU) metric is used to evaluate the quality of the matches.",
"text": "Generate pair-wise matches between the bounding boxes of the PDF cells and the predicted cells. The Intersection Over Union (IOU) metric is used to evaluate the quality of the matches.",
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"orig": "3. Use a carefully selected IOU threshold to designate the matches as \"good\" ones and \"bad\" ones.",
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"orig": "3.a. If all IOU scores in a column are below the threshold, discard all predictions (structure and bounding boxes) for that column.",
"text": "3.a. If all IOU scores in a column are below the threshold, discard all predictions (structure and bounding boxes) for that column.",
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"orig": "4. Find the best-fitting content alignment for the predicted cells with good IOU per each column. The alignment of the column can be identified by the following formula:",
"text": "Find the best-fitting content alignment for the predicted cells with good IOU per each column. The alignment of the column can be identified by the following formula:",
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"orig": "alignment = arg min c { D$_{c}$ } D$_{c}$ = max { x$_{c}$ } \u2212 min { x$_{c}$ } (4)",
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"orig": "where c is one of { left, centroid, right } and x$_{c}$ is the xcoordinate for the corresponding point.",
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"orig": "5. Use the alignment computed in step 4, to compute the median x -coordinate for all table columns and the me-",
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"orig": "6. Snap all cells with bad IOU to their corresponding median x -coordinates and cell sizes.",
"text": "Snap all cells with bad IOU to their corresponding median x -coordinates and cell sizes.",
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"orig": "7. Generate a new set of pair-wise matches between the corrected bounding boxes and PDF cells. This time use a modified version of the IOU metric, where the area of the intersection between the predicted and PDF cells is divided by the PDF cell area. In case there are multiple matches for the same PDF cell, the prediction with the higher score is preferred. This covers the cases where the PDF cells are smaller than the area of predicted or corrected prediction cells.",
"text": "Generate a new set of pair-wise matches between the corrected bounding boxes and PDF cells. This time use a modified version of the IOU metric, where the area of the intersection between the predicted and PDF cells is divided by the PDF cell area. In case there are multiple matches for the same PDF cell, the prediction with the higher score is preferred. This covers the cases where the PDF cells are smaller than the area of predicted or corrected prediction cells.",
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"orig": "8. In some rare occasions, we have noticed that TableFormer can confuse a single column as two. When the postprocessing steps are applied, this results with two predicted columns pointing to the same PDF column. In such case we must de-duplicate the columns according to highest total column intersection score.",
"text": "In some rare occasions, we have noticed that TableFormer can confuse a single column as two. When the postprocessing steps are applied, this results with two predicted columns pointing to the same PDF column. In such case we must de-duplicate the columns according to highest total column intersection score.",
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"orig": "9. Pick up the remaining orphan cells. There could be cases, when after applying all the previous post-processing steps, some PDF cells could still remain without any match to predicted cells. However, it is still possible to deduce the correct matching for an orphan PDF cell by mapping its bounding box on the geometry of the grid. This mapping decides if the content of the orphan cell will be appended to an already matched table cell, or a new table cell should be created to match with the orphan.",
"text": "Pick up the remaining orphan cells. There could be cases, when after applying all the previous post-processing steps, some PDF cells could still remain without any match to predicted cells. However, it is still possible to deduce the correct matching for an orphan PDF cell by mapping its bounding box on the geometry of the grid. This mapping decides if the content of the orphan cell will be appended to an already matched table cell, or a new table cell should be created to match with the orphan.",
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"orig": "9a. Compute the top and bottom boundary of the horizontal band for each grid row (min/max y coordinates per row).",
"text": "9a. Compute the top and bottom boundary of the horizontal band for each grid row (min/max y coordinates per row).",
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"orig": "9b. Intersect the orphan's bounding box with the row bands, and map the cell to the closest grid row.",
"text": "9b. Intersect the orphan's bounding box with the row bands, and map the cell to the closest grid row.",
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"orig": "9c. Compute the left and right boundary of the vertical band for each grid column (min/max x coordinates per column).",
"text": "9c. Compute the left and right boundary of the vertical band for each grid column (min/max x coordinates per column).",
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"orig": "9d. Intersect the orphan's bounding box with the column bands, and map the cell to the closest grid column.",
"text": "9d. Intersect the orphan's bounding box with the column bands, and map the cell to the closest grid column.",
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"orig": "9e. If the table cell under the identified row and column is not empty, extend its content with the content of the or-",
"text": "9e. If the table cell under the identified row and column is not empty, extend its content with the content of the or-",
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"orig": "9f. Otherwise create a new structural cell and match it wit the orphan cell.",
"text": "9f. Otherwise create a new structural cell and match it wit the orphan cell.",
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"orig": "Aditional images with examples of TableFormer predictions and post-processing can be found below.",
"text": "Aditional images with examples of TableFormer predictions and post-processing can be found below.",
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"orig": "Figure 8: Example of a table with multi-line header.",
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"orig": "Figure 9: Example of a table with big empty distance between cells.",
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"orig": "Figure 13: Table predictions example on colorful table.",
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"orig": "Figure 16: Example of how post-processing helps to restore mis-aligned bounding boxes prediction artifact.",
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