Given the large variety and complexity of tables, table structure extraction is a challenging task in automated document analysis systems. We present a pair of novel deep learning models (Split and Merge models) that given an input image, 1) predicts the basic table grid pattern and 2) predicts which grid elements should be merged to recover cells that span multiple rows or columns. We propose projection pooling as a novel component of the Split model and grid pooling as a novel part of the Merge model. While most Fully Convolutional Networks rely on local evidence, these unique pooling regions allow our models to take advantage of the global table structure. We achieve state-of-the-art performance on the public ICDAR 2013 Table Competition dataset of PDF documents. On a much larger private dataset which we used to train the models, we significantly outperform both a state-ofthe-art deep model and a major commercial software system.