height-field
The Height Map
As with any 3D computer graphic, XYZ values can be stored as a long list of three numbers. But for terrains, computer programmers found an interesting and practical way to store this information in a pseudo-image called a height-map or height-field. In a height-map the X and Y values are as you expect them to be, the coordinates on the surface such as a piece of paper. The Z values, however at stored by miniscule dots or pixels of varying degrees of gray from black to white. A black dot represents the minimum height such as the floor of the crater and a white dot represents the maximum height somewhere on the rim. Various shades of gray represent different heights. You can create a height-map on a piece of paper but it would take you a year to do it if you want to be accurate. For every point on you crater you must put a dot that is somewhere between white and black until you get something that looks like the fuzzy smoke ring pictured in this book. But radar and laser devices connected to computers can do the job faster than the blink of an eye.
If our height-field is on paper, as ours of our imagination is, then we need to get it into our computer. The easiest way to do that is with a scanner. We then need some software to examine every XY point on the paper and examine the dot at that point to determine the shade of gray. We are now ready to plot. But because we are interested in producing a 3D representation on a 2D surface—our computer screen, we need to tell the software what our viewing angle should be and where virtual light is to be introduced to give the shape a visual sense of three-dimensionality.
It turns out, and this is quite astonishing and completely unprecedented in the world of art or photography, the images on the shroud are height-maps. To be totally precise about it the images are not images at all. They are height-maps that happen to look like images. What is encoded in what we see, that looks like the image of a man, is the data for plotting the shape and form of a man’s head and body as a terrain.
Body to Cloth Distance
It could very well be that the image somehow and in some way represented the distance between the cloth and a body. That is a plausible explanation. In fact, that is the only explanation that anyone could come up with at the time. But the data does not prove that. It only demonstrates that the image acts like a height-field.
We have to say that it acts like a height-field and not that it is a height-field in the same way that we need to say that the image acts like a photographic negative, which it most decidedly is not or else it would not act like a height-field.
Caused by a Lengthy Exposure in the Sun?
Picknett and Prince should have stopped while they were ahead. Even lighting, “caused by a lengthy exposure in the sun” has nothing to do with creating the sort of data contained in a height-field, data that represents distance. As the sun journeys across the sky, its rays strike the body being photographed from different angles. It softens harsh shadows. Every professional photographer knows the problem of harsh shadows caused by the sun. If you have ever witnessed an advertising photo shoot, you have certainly seem the large white reflectors, sometimes held aloft by assistants, used to spread out the sun’s light and make it strike models from different angles. But even lighting does not make for spatial information any more so than does uneven lighting.
If the sun perhaps rose in east and travelled about in a pinwheel fashion casting at different times of days light from every part of the sky, we might get a enough softening to elicit a simulation of 3D for the gross shape of the head and body but not for discrete features. But a sun travelling from East to West, even with an arc, will not do what Picknett and Prince imply. To suggest, that the 3-D information to a degree does not exist and that yet it supports rather than undermines their hypothesis that the image on the shroud is medieval photograph by Leonardo is curious double speak. An experiment, a simple experiment would have shown how wrong they were.
Why Picknett and Prince Are Wrong
The simple fact of the matter is that to encode distance information with light in a photograph, the light coming from a more distant point such as the recesses of the eyes must be less than the light coming from a closer point such as the tip if the nose. Now, in fact, that really happens, but not in a way that is sufficient to create the height-field image that exists on the shroud.
Assuming a 16 foot distance between a body and a piece of cloth—about as short a distance as you can use to make a life-size photograph—a one inch difference between the tip of the nose and side of the nose where it meets the cheek would produce a 1% difference in the amount of light striking the cloth. The difference would be imperceptible. On the shroud the difference between these two points on the face is about 60%. Variations in color and reflectivity of the body’s surfaces caused by natural angles would dramatically affect the amount of light that would strike the cloth. The shadows and the variations would overwhelm the slight difference in light caused by distance. We need only recall the metaphor of Russell’s desk to realize this. A photograph made with light is simply and unequivocally, without the need for further qualification, a representation of a 3D shape in 2D space. It is not, it cannot be, a height-field. Hence, the image on the shroud is not in any way a photograph.
Cyberspace Speculation
Cyberspace is filled with conjecture about the height-field observation. Proponents of the shroud’s authenticity use this information to say that it proves that a body lay under the cloth, that the image was created when the body of Christ dematerialized during the resurrection releasing energy that somehow did the imaging. It shows no such thing. The only thing it shows is that the image acts like a height-field.
Picknett and Prince have a point when they say that the scale was unknown, but it is a pointless point. When NASA uses radar and lasers to measure the relative height of features on the moon and the earth, when meteorologists similarly measure the height of the swirls in a hurricane, they know the scale. But they know the scale because they have benchmark values that they have estimated in the past. Hence the computer programs know how high a crater is, approximately. It knows how high the bands of hurricane are, approximately. Thus when NASA or meteorologists build a three-dimension representation in two-dimensional space, they create approximately accurate pictures.
Adjusting Scale
With any height-field, you can adjust the scale to just about anything you want. You can make crest of a crater’s edge or the nose on the shroud face seem as high as Mount Everest or so low that only an ant could notice the perturbations on the surface. Not knowing the scale is not a problem if you have a basis for estimating it. For instance, if you are reasonably sure that the image is of a man, adjusting the scale to what seems reasonable for a man is appropriate.
Picknett and Prince were right when they wrote, “we . . . believed that the Shroud exhibits amazing, inexplicable, and unique 3-D information. . . . we could not see how [Leonardo da Vinci] had managed to produce that particular effect and felt that attempting to replicate it would be a real stumbling block in our experimental work. Had they tried they would have certainly found that it was a real stumbling block.
Thanks to Nicholas Allan
Fortunately, Nicholas Allan did build a gigantic camera and created a life-size image on cloth of a life-size statue, he created an amazing photograph. It looked quite realistic. But when attempts are made to see if it is anything like a height-field it fails. Allan’s photograph is a 3D representation in a 2D field. The shroud images are height-fields from which a 3D representation in a 2D field can be derived.
In the case of the shroud we don’t get a perfect three-dimensional rendering for many reasons: If, as scientists suspect, what is encoded on the shroud is the distance between any point on the man’s body and the cloth loosely draped about him, then the distance will be distorted by the drape of the cloth. We can assume it is not perfectly flat. We don’t know how fading of the images and the aging of the cloth might have altered the accuracy of height-field data. There are bloodstains and dirt that cause distortions.
The negativity and the so-called 3D encoding hardly cover the mystery of the images’ properties.