Chronic wounds affect 6.5 million Americans. Wound assessment via algorithmic analysis of smartphone images has emerged as a viable option for remote assessment. Methods: We comprehensively score wounds based on the clinically-validated Photographic Wound Assessment Tool (PWAT), which comprehensively assesses clinically important ranges of eight wound attributes: Size, Depth, Necrotic Tissue Type, Necrotic Tissue Amount, Granulation Tissue type, Granulation Tissue Amount, Edges, Periulcer Skin Viability. We proposed a DenseNet Convolutional Neural Network (CNN) framework with patch-based context-preserving attention to assess the 8 PWAT attributes of four wound types: diabetic ulcers, pressure ulcers, vascular ulcers and surgical wounds. Results: In an evaluation on our dataset of 1639 wound images, our model estimated all 8 PWAT sub-scores with classification accuracies and F1 scores of over 80%. Conclusions: Our work is the first intelligent system that autonomously grades wounds comprehensively based on criteria in the PWAT rubric, alleviating the significant burden that manual wound grading imposes on wound care nurses.