Table structure recognition is necessary for a comprehensive understanding of documents. Tables in unstructured business documents are tough to parse due to the high diversity of layouts, varying alignments of contents, and the presence of empty cells. The problem is particularly difficult because of challenges in identifying individual cells using visual or linguistic contexts or both. Accurate detection of table cells (including empty cells) simplifies structure extraction and hence, it becomes the prime focus of our work. We propose a novel object-detection-based deep model that captures the inherent alignments of cells within tables and is fine-tuned for fast optimization. Despite accurate detection of cells, recognizing structures for dense tables may still be challenging because of difficulties in capturing long-range row/column dependencies in presence of multi-row/column spanning cells. Therefore, we also aim to improve structure recognition by deducing a novel rectilinear graph-based formulation. From a semantics perspective, we highlight the significance of empty cells in a table. To take these cells into account, we suggest an enhancement to a popular evaluation criterion. Finally, we introduce a modestly sized evaluation dataset with an annotation style inspired by human cognition to encourage new approaches to the problem. Our framework improves the previous state-of-the-art performance by a 2.7% average F1-score on benchmark datasets.