This paper presents the detection and classification part of an industrial machine for automated assembly of decorative tessellae over patterned tiles that have significant reliefs. The machine consists of two vision systems for detecting the tiles and the tessellae, and a robotic manipulator to make the assembly. One of the vision systems detects the tessellae and the other one detects and classifies the tiles, finding the positions and orientations on the tiles where tessellae have to be mounted. Lateral illumination is used to enhance shadows and characterize the relief pattern. The shadow pattern is used as the main feature for classifying a tile to a model. The method works with a variety of models, is quite robust, and achieves very good classification results, as required for an industrial application.