Transitioning from manual to automated composite manufacturing has the potential to optimize both cost and efficiency for many industries, yet quality control is a key challenge. This paper introduces a method for the task of quality inspection in low-contrast, hard-to-model, contours of glass fiber plies in industrial composite layups. Our approach is based on per-pixel classification using a deep neural network and we introduce a novel regularization formulation based on a geometrical prior to encourage smooth and continuous contours. Training and evaluation is performed on a dataset collected from layups in a prototype glass fiber mould, showing its capabilities in an industrial scenario.