Intima-media thickness (IMT) of the common carotid artery is routinely measured in ultrasound images and its increase is a marker of pathology. Manual measurement being subject to substantial inter- and intra-observer variability, automated methods have been proposed to find the contours of the intima-media complex (IMC) and to deduce the IMT thereof. Most of them assume that these contours are smooth curves passing through points with strong intensity gradients expected between artery lumen and intima, and between media and adventitia layers. These assumptions may not hold depending on image quality and arterial wall morphology. We therefore relaxed them and developed a region-based segmentation method that learns the appearance of the IMC from data annotated by human experts. This deep-learning method uses the dilated U-net architecture and proceeds as follows. First, the shape and location of the arterial wall are identified in full-image-height patches using the original image resolution. Then, the actual segmentation of the IMC is performed at a finer spatial resolution, in patches distributed around the location thus identified. Eventually, the predictions from these patches are combined by majority voting and the contours of the segmented region are extracted. On a public database of 2676 images the accuracy and robustness of the proposed method outperformed state-of-the-art algorithms. The first step was successful in 98.7 % of images, and the overall mean absolute error of the estimated IMT was of 100±89μ m.