We propose an algorithm to segment 3D medical images that combines deformable anatomical models and deep learning. The aim is to develop a method that is flexible enough to be applied to different anatomies and image modalities. To this end, we replace heuristic boundary detection in model-based segmentation with convolutional neural networks (CNNs). The method samples 1D profiles along the surface of statistical shape models (SSMs) and identifies potential boundary locations via CNNs. The SSM is then iteratively deformed towards the predicted boundaries, ultimately producing the desired 3D surface model. We evaluate the method on three datasets corresponding to liver computed tomography (CT) scan, knee femoral bone magnetic resonance imaging (MRI) and pelvic bone CT. For the liver dataset, our method produces an average symmetric surface distance (AD) of 1.06 mm, for the knee FB, and AD of 0.85 mm and for the pelvic bone, an AD of 1.24 mm. The results are comparable to those of state of the art, model-based heuristic intensity model methods, with the advantage of not depending on manually defined heuristics.