Colin Berry writes:
I will not be intimidated by “Fourier transforms” and similar injections of computer mumbo-jumbo, which in this instance has contributed precisely nothing.
In reality, we are talking about applied mathematics not mumbo-jumbo. Fourier transforms are critical in the medical field for MRI processing, in chemistry for various types of spectroscopy including AMS for carbon dating and in physics to help solve differential equations. Fourier transforms make digital low pass filtering possible in modern digital communications.
The computer science department at the University of New Mexico has prepared some excellent introductory information on the use of Fourier transforms in image processing. One example they provide has to do with removing banding patterns such as that caused by electro-magnetic interference of non-digital television signals.
It is evident to many people (except Colin) that there is a significant banding pattern – sometimes called variegation or a plaid pattern – in the cloth of the Shroud of Turin. What is it? What are the consequences? What might it tell us about the history of the cloth? What clues might it offer into how the images were formed?
But Colin writes:
A few moments of thought about the imprinting of a certain transverse crease should be sufficient to demolish any notion that vertical banding was the cause of the gaunt-looking features. There is another explanation for the cut-off peripheries of the face, and it’s nothing to do with colour variations in the yarn, and everything to do with the mechanism of image imprinting.
Oh, really? Are we to believe Colin or are we to believe our own eyes (spectacular images below) and Ray Rogers who has actually examined and probed the cloth as a scientists and was able to write:
Bands of slightly different color can be seen in Shroud photographs. They are most visible in ultraviolet-fluorescence photographs (see Hands UV). Both warp and weft yarns show this property. Some areas show darker warp yarns and some show darker weft yarns. In some places bands of darker color cross. In other places bands of lighter color cross. The effect is somewhat like a plaid.
All of the bleaching processes used through history remove lignin and most associated flax impurities (e.g., flax wax and hemicelluloses). The more quantitative the bleaching process the whiter the product. The bands of different color on the Shroud are the end result of different amounts of impurities left from the bleaching process.
Anna Maria Donadoni, a curator at the Museum of Egyptology in Turin, pointed out locations where batches of yarn ended in the weave and new yarn had been inserted in order to continue weaving. The yarn ends were laid side by side, and the weave was compressed with the comb. The ends are often visible, and the overlaps correspond to zones of different color in the weave. The different batches of yarn show different colors.
Where darker bands of yarn intersect image areas, the image is darker. Where lighter bands intersect an image area, the image appears lighter. This proves that the image color is not a result of reactions in the cellulose of the linen. Some impurities on the surface of the different batches of yarn produced the image color. This observation is extremely important when tests are being made on image-formation hypotheses. If image color is not simply a result of color formation in the cellulose of the linen fibers, image formation must be a much more complex process than we originally thought.
In an email in February of 2005, Rogers pointed out that the color from the shroud’s image could be removed with adhesive tape whereas the color from banding could not be removed. It was inherently part of the fabric’s color. He concluded the email with . . .
The end product of this line of reasoning tells us that the image-forming process was a result of what was on the cloth when the image formed. Something dehydrated the impurity layer without damaging the flax fibers.
Barrie Schwortz did some of the earliest technical work to show one optical illusion effect of the banding. He did so on one side of the face. The left image shows vertical banding on the outside portion of each cheek that extends upward and downward well above and below the face, particularly so on the right side. The middle image shows the area Barrie chose to add +20 points (Photoshop calibration) of RGB luminance. The effect is immediately obvious in the right picture.
One day I received an email from Robert Doumax, an imaging expert in Bordeaux, France. He had created a Fourier transform filter to isolate both vertical and horizontal banding in the fabric of the shroud. With his filter I was able to examine the effects of it. I chose the following face image to work with.
Warning: If you continue to read this posting ( Read More) you will encounter some spectacular images you may have never seen before.
Step 1: I created a negative/mirror image of the image. No other adjustments were made.
Step 2: I converted the image to grayscale. The filter, as written, only works with grayscale images.
The following image is a contrast enhanced version of the grayscale image above. It is for reference purposes only. It was not used with the filter.
Step 3: I applied filtering to remove horizontal and vertical bands. This gave the picture a very different look. Notice the broader face and the shape of the nose.
The following image is a contrast enhanced version of the above grayscale image It is for reference purposes only.
Step 4: I computed the difference between the source image and the filtered image to get an isolated view of the banding.
There is some residual face image and some loss of the herringbone pattern in the difference picture. This is probably due to the fact that the banding lines were not perfectly parallel to each other resulting in some imprecise frequency of noise calculations.