This paper introduces a new approach to automatically quantify the severity of knee OA using X-ray images. Automatically quantifying knee OA severity involves two steps: first, automatically localizing the knee joints; next, classifying the localized knee joint images. We introduce a new approach to automatically detect the knee joints using a fully convolutional neural network (FCN). We train convolutional neural networks (CNN) from scratch to automatically quantify the knee OA severity optimizing a weighted ratio of two loss functions: categorical cross-entropy and mean-squared loss. This joint training further improves the overall quantification of knee OA severity, with the added benefit of naturally producing simultaneous multi-class classification and regression outputs. Two public datasets are used to evaluate our approach, the Osteoarthritis Initiative (OAI) and the Multicenter Osteoarthritis Study (MOST), with extremely promising results that outperform existing approaches.