What is meant by the statement: the image is superficial?
In the simplest sense, it means that the images are on the surface only. The thread or yarn of the Shroud's fabric consists of a varying number of flax fibers spun together. The number of fibers ranges from about 70 to 120. Because the fibers are spun any particular fiber, which may be as long as two feet in length, will at times along its length be in the middle of the thread and near the outside. The images reside on sections of fibers that are at the surface or within one or two fibers deep from the surface. In other words the images are superficial to a depth of only one to three fibers.
But more than that, the image on the fibers is extraordinarily thin, about the thickness of the outer wall of a soap bubble floating in the air.
This completely rules out the use of any liquid colorant such as paint, dye or stain. Any liquid colorant would soak into the thread. Only a very thick paint would remain on the surface and this would be nearly impossible to apply while maintaining the thin quality of the images. But we really don't need to be concerned with this because there is ample evidence that the images are not painted.