A Fully Convolutional Network (FCN) based deep architecture called Dual Path U-Net (DPU-Net) is proposed for automatic segmentation of the lumen and media-adventitia in IntraVascular UltraSound (IVUS) frames, which is crucial for diagnosis of many cardiovascular diseases and also for facilitating 3D reconstructions of human arteries. One of the most prevalent problems in medical image analysis is the lack of training data. To overcome this limitation, we propose a twofold solution. First, we introduce a deep architecture that is able to learn using a small number of training images and still achieves a high degree of generalization ability. Second, we strengthen the proposed DPU-Net by having a real-time augmentor control the image augmentation process. Our real-time augmentor contains specially-designed operations that simulate three types of IVUS artifacts and integrate them into the training images. We exhaustively assessed our twofold contribution over Balocco's standard publicly available IVUS 20 MHz and 40 MHz B-mode dataset, which contain 109 training image, 326 test images and 19 training images, 59 test images, respectively. Models are trained from scratch with the training images provided and evaluated with two commonly used metrics in the IVUS segmentation literature, namely Jaccard Measure (JM) and Hausdorff Distance (HD). Experimental results show that DPU-Net achieves 0.87 JM, 0.82 mm HD and 0.86 JM, 1.07 mm HD over 40 MHz dataset for segmenting the lumen and the media, respectively. Also, DPU-Net achieves 0.90 JM, 0.25 mm HD and 0.92 JM, 0.30 mm HD over 20 MHz images for segmenting the lumen and the media, respectively. In addition, DPU-Net outperforms existing methods by 8-15% in terms of HD distance. DPU-Net also shows a strong generalization property for predicting images in the test sets that contain a significant amount of major artifacts such as bifurcations, shadows, and side branches that are not common in the training set. Furthermore, DPU-Net runs within 0.03 s to segment each frame with a single modern GPU (Nvidia GTX 1080). The proposed work leverages modern deep learning-based method for segmentation of lumen and the media vessel walls in both 20 MHz and 40 MHz IVUS B-mode images and achieves state-of-the-art results without any manual intervention. The code is available online at https://github.com/Kulbear/IVUS-Ultrasonic.