What do we mean when we say the images are 3D encoded?
It is a bit misleading and confusing. What we probably should be saying is the images are actually height-fields that also happen to have a pictorial quality to them. So what in the world do we mean by that?
Imagine a papier-mâché model of a moon crater sitting before you on a table. Now imagine that you want to express everything about the shape of crater as a series of numbers. We can express the shape of any terrain as a long series of three numbers. The numbers are the measurement from left to right, the measurement from front to back, and the height of the crater at that point. In other words, pick any spot on the crater: measure how far that is from the left, how far it is from the front, and how high that spot is. We call these three value x, y and z, respectively.
Computer scientists devised any easy way to represent these value. On a flat surface, measure from the left, measure from the bottom and then put a single dot at that spot. Make the dot white for the highest spots on the crater and black for the lowest spots. For heights in between, use varying shades of gray. This is called a height-field. Height fields are used extensively for mapping terrains of everything from planets and moons to imaginary scenes in video games. The image that looks like a smoke ring is a height-field for the crater shown above.
With computer graphics software it is a fairly simple thing to plot the image into a three-dimensional terrain representation (as seen in the top picture). What are the results of plotting a height-field?
Similarly the images on the Shroud of Turin can be plotted into a three-dimensional terrain representation. But, and this is important to understand, paintings and photographs of the human form including the face, cannot be so plotted. There is probably no more important test of any attempt to recreate the images on the Shroud, either to test a hypothesis or to attempt to show how a forger might have created the image, then to see if the image is a height-field. If it won't plot correctly, it is not at all like the image on the Shroud.