Ten Years of Lessons from Imaging of the Archimedes Palimpsest

24 Pages·2010·1.38 MB·English

by  Antti Nurminen

Ten Years of Lessons from Imaging of the Archimedes Palimpsest

Roger L. Easton, Jr. 1, William A. Christens-Barry2, Keith T. Knox3

1 Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology,
Rochester NY, USA, [email protected]
2Equipoise Imaging, LLC, Ellicott City MD USA, [email protected]
3Air Force Research Laboratory, Kihei HI, USA, [email protected]

Keywords: Archimedes palimpsest, spectral imaging, image processing, pseudocolor
rendering, statistical image analysis

ABSTRACT

The Archimedes Palimpsest is a circa 10th-century parchment manuscript that was erased
early in the 13th century and overwritten with a Christian prayer book. The source of its name
arises from the fact that the original texts were recognized early in the 20th century to include
partial copies of seven treatises by Archimedes, the oldest extant reproductions of his
writings. The manuscript was sold at auction in 1998 and lent by its new owner to the Walters
Art Museum, which has supervised a ten-year collaboration by conservators, imaging
scientists, and scholars to image, transcribe, and translate the original writings.

Over the course of this project, a variety of imaging and processing techniques were
developed and applied to clarify the original texts. These techniques evolved from spectral
reflective imaging over 30 bands of visible wavelengths to a simpler protocol that produced
pseudocolor rendering from fluorescence and reflective images. The final system added
additional reflective wavelengths produced by light-emitting diodes (LEDs) in the visible and
infrared regions plus low-angle (“raking”) illumination to help visualize the small-scale
topography. Image processing ranged from supervised segmentation via a spectral
pseudoinverse calculation to deterministic renderings in pseudocolor to unsupervised
classification by principal component analysis; all methods developed proved to be useful to
recovering text from some set of leaves. The changes in technology and processing were due
both to the requirements of the project and to the relentless advance in technology over the
time span of the project.

3
HISTORY AND SIGNIFICANCE OF THE CODEX

Almost everything known about the work of Archimedes has been gleaned from three codex
manuscripts, which were rather uninspiringly designated by Johan Ludvig Heiberg as “A”,
“B”, and “C”. The first two vanished from scholarly view by the 16th century, but parts of
seven treatises survive in the last, which is a Byzantine codex from the 10th century. Among
the treatises in codex C are the only extant leaves of On the Method of Mechanical Theorems,
one leaf from the only extant copy of Stomachion (“Stomachache,” likely the oldest known
study of combinatorics), and the oldest known example in the original Greek of Archimedes’
most famous work, On Floating Bodies. The other treatises in the codex are On the
Measurement of the Circle (in which Archimedes derived an excellent estimate of the value of
π), On the Sphere and Cylinder (where he proved that volumes of a sphere and its enclosing
cylinder are in the proportion 2:3), On Spiral Lines (where he derived that the area of a single
revolution of a spiral – his invention – is 1/3 that of the enclosing circle), and On the
Equilibrium of Planes. The manuscript included copies of the diagrams for each treatise,
which have proven to be very significant in the scholarly assessment of the book. Of the seven
works, the Method is arguably the most significant; it is in the form of a letter from
Archimedes to Eratosthenes that outlines methods for proving mathematical conjectures from
mechanical analogies.

The treatises in this codex were copied in the 10th century, probably in Constantinople, in a
book format that is fairly large by modern standards; each parchment leaf measured
approximately 200 mm in width and 300 mm in height. In the 13th century, the codex was
sacrificed to make a copy of an Orthodox Christian liturgical book, the Euchologion: the
parchment pages were disbound, the text erased, and each folio was cut in half along the fold.
The copy of the Euchologion was written over these newly cleaned pages and sheets from
several other codices. Based upon readings of the colophon of the Euchologion obtained
during the imaging project, we now know that Ioannes Myronas was its scribe and that the
book was dedicated on Saturday, 14 April 6737 (corresponding to Easter Saturday, 1229 CE).
Recycling of books in this way was a common practice due to the expense of treating goat or
lamb skin to make new parchment and was feasible because of the durability of the material.
The individual leaves of the new book measure approximately 155 mm wide and 200 mm tall
and the new writings are perpendicular to the erased originals on all but one folio. A few lines
of the original writings on each leaf were hidden in the gutter of the bound prayerbook on all
folios save those in the centers of quires. Iron gall ink was used for the prayerbook text and
most, if not all, of the original texts that were erased. The ink of the later Euchologion is dark
brown in color and the characters are quite readable on most pages, whereas the visibility of
the erased texts ranges from rather obvious to virtually invisible. The remaining ink stains of
the original text are generally more “reddish” in color than the overtext.

The prayer book was used in Christian Orthodox services at the Monastery of St. Sabas in the
Judean desert for hundreds of years. In the 1800s, the book was placed in the library of the
Metochion of the Church of the Holy Sepulchre in Constantinople, where its presence was
noted in 1844 by Constantin von Tischendorf, who was most famous for “borrowing” the
Codex Sinaiticus from St. Catherine’s Monastery. He published observations made during his
visit to Constantinople in the book “Reise in den Orient,” which was published in German in
1846 and in English translation by W.E. Shuckard as “Travels in the East” in 1847. In the
book, Tischendorf noted that the bishop allowed him
4
“to make any use of the manuscripts I found. They were thirty in number, but
they were altogether without any especial interest, with the exception of a
palimpsest upon mathematics.” (Tischendorf, tr. by Shuckard, 1847, p.274)

It is quite likely that this citation refers to the Archimedes palimpsest. Tischendorf apparently
made use of the manuscript in a manner that was no doubt unforeseen by his host, since one
leaf from the codex was found among his papers after Tischendorf’s death and now resides in
the Cambridge University Library as Add. 1879.23. The prayerbook was catalogued as MS
355 in the library of the Metochion in 1899 by Athanasios Papadopoulos-Kerameus. His
reference noted the use of the book at St. Sabas and included a transcription of the Greek
characters of a few lines of the palimpsested text that he could read. The catalogue came to
the attention of the Danish philologist Johan Ludvig Heiberg, who recognized the source of
the palimpsested text and traveled to Constantinople to see the book for himself in 1906.
Heiberg’s only tools to assist his reading were his eyes, natural light, and probably an optical
magnifying lens. The binding of the book prevented him from reading any original text within
the gutter except on folios at the center of a quire, but he was still able to produce an excellent
transcription of the text. During his study, Heiberg had photographs taken of at least 102
pages of the prayerbook of a then-existing total of 354; the 65 photographs of these folios
survive as Ms. Phot 38 in the Royal Library in Copenhagen. Shortly after his viewing of the
palimpsest, Heiberg announced the discovery of new Archimedes text, an item deemed
sufficiently important to merit a front-page story in the New York Times of 16 July 1907.
Heiberg published his results from the Method in the journal Hermes in 1907 and in the
second edition of his three volumes of Archimedis Opera Omnia cum Commentariis Eutocii
published in 1910-1915; the first edition had been published in 1880-1881.

The manuscript disappeared from the Metochion during the upheavals in Europe in the early
20th century and was seen publicly again only after a French family put it up for auction at
Christie’s in New York in 1998. Though virtually nothing definitive is known about the
history of the codex during the intervening nine decades, some facts may be inferred from its
condition at the time of the auction. The most superficial comparison of the manuscript with
Heiberg’s photographs from 1906 show the extent of injury that has been inflicted on the
book during this period. Many pages have been severely damaged by mold that did not exist
in 1906, some pages have disappeared altogether, and four pages have been painted over with
portraits of Christian Evangelists.

Since the auction in 1998, Georgi Parpulov of the Walters Art Museum has unearthed a letter
in French from Salomon Guerson, a vendor of antiquities in Paris, to Professor Harold
Willoughby of the University of Chicago. The letter in the Willoughby Archives in the
Library of the University of Chicago referenced an earlier correspondence between these two
in 1932. The translated letter describes a folio that was

“identified through your mediation by the curator of the Huntington library as
being the manuscript of Archimedes described by J.L. Heiberg in Hermes vol.
42, p. 248. I would like you to know that I wish to sell this manuscript. … I am
asking $6000.”

Though not identified in the letter, the curator at the Huntington Library must have been
Reginald B. Haselden, who pioneered the application of modern technology to the study of
manuscripts and who published the book “Scientific Aids for the Study of Manuscripts” in
5
1935. Parpulov also located the monochrome negative of a photograph of the detached f.57v
of the Euchologion in the same archive; the digitized image of this negative is now included
in the Archimedes Palimpsest database.

As already mentioned, four leaves were erased yet again some time after 1938, overpainted
with forged icons of the four Gospels, and further distressed to appear even more aged. One
hypothesis is that the icons were painted in an attempt to increase the value of these pages, or
perhaps even of the intact codex, in the eyes of less-sophisticated potential purchasers since
books with medieval art were generally considered to be more valuable than plain texts.
Tragically, the original text on two of the overpainted leaves was from the Method.

The outward appearance of the book in 1998 is shown in Figure 1 and one side of one
disbound folio appears in Figure 2. The manuscript was purchased at auction at Christie’s on
28 October 1998 for $2 million US by an anonymous American collector. Its new owner
deposited the manuscript at the Walters Art Museum in Baltimore, MD, USA early in 1999
and funded an intensive program of conservation, imaging, and scholarly study for ten years.
The imaging study was officially completed on the tenth anniversary of the auction with the
posting of all original and many processed images at http://www.archimedespalimpsest.net,
though experimental studies continue. Publication of the scholarly work on the manuscript is
underway, including editions of the Method and Stomachion. A history of the project up
through 2006 is available in (Netz and Noel, 2007).

Figure 1: Appearance of the Archimedes Palimpsest before the auction in 1998 (Walters Art Museum)

The existence of the works by Archimedes beneath the prayerbook text was known at the time
of the auction in 1998, but other original works have been identified in the manuscript during
the course of the imaging project. These include five leaves containing parts of two speeches
6
by the Athenian orator Hypereides that were previously thought lost: four folios of “Against
Diondas” and one of “Against Timandros”. The former speech reveals the political conditions
in Athens after the battle at Chaeronea (Tchernetska, 2005). Seven folios contain a third
recently identified unique manuscript, a commentary on Aristotle’s “Categories” by
Alexander of Aphrodisias. The original text on another set of four folios is a history of St.
Pantoleon, while two folios contain a 10th-century orthodox liturgical text, the Menaion. Two
as-yet unidentified texts appear on six folios. In short, the Archimedes Palimpsest is a
document with writings that are significant to the fields of mathematics, history, and
philosophy. This book is extraordinarily important, even unique, to classical studies. Its
existence raises the question of whether other copies of the Euchologion (or other manuscript)
might still exist that were made from leaves of the original parchments.

Figure 2: Visual appearance of one leaf of the treatise “On Spiral Lines” (Euchologion f. 093v-092r),
oriented with the faint Archimedes text running horizontally and the Euchologion text running
vertically. (Copyright retained by the owner of the Archimedes Palimpsest).

The first, and ultimately most important, objective of the project was the conservation of the
badly damaged manuscript, which was executed by the conservation staff of the Walters Art
Museum under the direction of Abigail Quandt. An important aspect of conservation was the
essential separation of the leaves. To better understand what they were up against, Ms. Quandt
and her colleagues dispatched microscopic core samples of a folio of text to the Canadian
7
Conservation Institute in Ottawa. The analysis reported that the collagen in the parchment is
breaking down, which further intensified the urgency of the conservation. The painstaking
task required removal of both traditional hide glue and modern polyvinyl acetate cement
(PVAC, close kin to wood glue used by modern carpenters) to separate the fragile leaves.
Before imaging, candle wax residue left from hundreds of years of religious services had to be
removed by painstaking scraping with surgical tools under the microscope. It is fair to say that
these efforts by the conservation staff of the museum are largely responsible for the ultimate
success of the project.

THE FORGERIES

During the forensic study of the four leaves with the forged icons in December 1999, John
Lowden of Courtauld Institute in London identified their source as the book “Miniatures des
Plus Anciens Manuscrits Grecs de la Bibliothèque Nationale du VIe au XIVe Siècle”
published by (Henri Omont, 1929). The forged paintings are 1:1 copies that were transferred
via pinpricks, tracings, and preliminary sketches in red. The paintings were artificially aged
by smudging dirt into the paint surface and fraying the edges of the parchment. The pair of
forgeries on the facing leaves f. 57r and 63v of the Method are shown in Figure 3.

Figure 3: Forgeries on facing leaves f. 057r (top) and f. 067v (bottom) showing forged icons painted
over leaves after 1938. The Archiemedes text is largely obscured except in the gutter, where it is seen
to run horizontally. (Copyright retained by the owner of the Archimedes Palimpsest).
8
Dr. Jennifer Giaccai, then on the scientific staff of the Walters Art Museum, studied the
properties of the forged icons, including the paint palette. After using Fourier-transform
infrared spectroscopy to identify the pigments, she determined that one of them,
phthalocyanine green, was not commercially available until 1938. She also concluded that the
same palette was used in a forgery in a manuscript at Duke University whose source had been
identified previously by Lowden.

SPECTRAL IMAGING OF THE MANUSCRIPT

The primary focus of the remainder of this paper is the imaging of the manuscript at so-called
“optical” wavelengths, i.e., the spectral regime from the near-ultraviolet to the near-infrared
regions that may be imaged with a silicon sensor. The imaging team for this task included Dr.
Keith Knox, originally affiliated with the Xerox Research Center in Webster NY and now at
the Air Force Research Laboratory in Kihei HI, Dr. William A. Christens-Barry of Equipoise
Imaging, LLC in Ellicott City, MD, and Dr. Roger L. Easton, Jr. from the Chester F. Carlson
Center for Imaging Science of the Rochester Institute of Technology. Dr. Easton was able to
entice several graduate and undergraduate students and even high school interns to work on
the project. Over the course of the project, one important lesson learned (and subsequently
reinforced in work on other manuscripts) is that every method that has been imagined and
implemented has been useful, if not essential, for some original manuscript in the book. In
other words, the visibility of the original texts in the palimpsest may be affected little, if at all,
by some technique and may be improved significantly by another. It is essential to have a
variety of hardware and software tools in the arsenal and to be flexible in their application.

Over the 10-year duration of the project, the entire manuscript has been imaged using several
techniques and a variety of sensors. The original exploratory imaging sessions, dubbed
“Phase I” took place in the summer of 2000. This work led to adoption of a standard imaging
protocol for Phase II. The team assembled at the Walters Art Museum in Baltimore six times
between 2001 and 2004 for imaging of groups of approximately 15 newly disbound and
conserved folios. An additional session was held in November 2006 to reimage several pages
of the manuscript using experimental techniques and the entire codex was reimaged with a
higher-resolution camera system and illumination from light-emitting diodes in August 2007,
an effort that might appropriately be called “Phase III.” Some pages were imaged yet again in
March 2009 to provide additional image data for new processing algorithms that had been
developed. The techniques included imaging in reflected light at different wavelengths and
different angles, imaging of visible light emitted by the parchment when illuminated by
ultraviolet light (ultraviolet fluorescence imaging). Several different monochromatic and color
digital sensors were used, and the development of the technology over the course of the
project eventually required reimaging with newer systems. Only the spectral imaging
modality will be discussed in this paper; the other methods are treated elsewhere.

In spectral imaging, multiple digital images are collected of the same scene using different
wavebands. The images are subsequently combined by computer to reveal or enhance the
desired features of the scene. The process often is called “multispectral imaging” for a small
number N of relatively broad wavebands (e.g., N ≤ 10 with ∆λ ≥ 25nm) or “hyperspectral
imaging” for a larger number of narrower bands. The subsequent computations may be based
9
on observations of the features or on statistics of the (sometimes quite subtle) variations in the
response of the ink across the different wavebands.

Fluorescence imaging is based on the observation that some materials, particularly those
composed of organic substances, absorb light photons at some energy level and subsequently
emit other photons at lower energies (longer wavelengths) that are characteristic of the
material. These re-emitted photons may be imaged with appropriate sensors. In the ultraviolet
fluorescence imaging used in the project, the ultraviolet photons are absorbed by the
parchment, which then emits visible light that could be imaged with a standard digital camera;
the emitted light is dominated by blue wavelengths just longer than the incident ultraviolet
radiation. As shall be demonstrated, very useful information about the original texts may be
conveyed by the relative intensities of the fluorescent emission over the visible wavelengths.
This information required imaging of the different spectral bands, which could be
implemented with a digital camera with a color sensor or a monochrome camera with external
bandpass filters.

X-ray fluorescence (XRF) imaging is based on the same principle, though both the incident
and emitted photons are highly energetic X rays and thus require special generation and
sensing equipment. These X rays are capable of penetrating obscuring materials, such as dirt
or paint. The spectrum of emitted X rays reveals the relative populations of elements at those
locations, e.g., iron in the ink. XRF imaging proved essential for reading the original text on
leaves with the forged icons and on leaves that were particularly grimy, such as the colophon
of the Euchologion.

The original goal of the imaging was to develop a collection and processing scheme capable
of “stripping off” the prayerbook text to leave the original “undertext” with enhanced contrast
and readability; this objective is perhaps better described as making the overtext “disappear”
into the parchment so that the visibility of the original text is improved. The difference in
color appearance of the inks provided the basis for the original strategy of collecting images
under different illuminations and digitally combining these images to create new images with
enhanced undertext. After considerable experimentation, a method was developed that works
well for the Archimedes texts and for leaves from some of the other manuscripts. We also
learned that the protocol for imaging and processing needed to be modified for use on the
leaves from other original manuscripts. For example, the writings in the Alexander and St.
Pantaleon texts responded rather poorly to the original processing technique, but new imaging
tools have been noted to perform much better in those cases. This is one of the important
lessons learned in the course of this work: that the combination of image collection technique
and image processing varies for different manuscripts within the Archimedes palimpsest.

PHASE-I IMAGING AND IMAGE PROCESSING

The first test images were collected during the summer of 2000, with the goal of “stripping
off” the overtext so that only the original writings remained visible. A scientific digital camera
was used that was state of the art for the time, incorporating a cooled monochromatic charge-
coupled device (CCD) sensor array with 1536 × 1024 picture elements (“pixels”). The cooling
ensured that images had 12 bits of useful dynamic range, which means that the sensor can
distinguish 212 = 4096 different shades of “gray” in the scenes. The five color bands imaged in
the preliminary phase were selected by glass filters that transmitted different bands of light
10
with widths ∆λ ~ 100nm in the ultraviolet, blue, green, red, and infrared regions of the
spectrum. The images were collected under three types of illumination: visible light from
tungsten photofloods, “shortwave” ultraviolet lamps with emission centered about λ ! 254nm,
0
and “longwave” ultraviolet lamps with λ ~ 365 nm. The five filters and three illuminations
0
produced 15 spectral images for subsequent multispectral processing. The individual leaves of
the book, each approximately 150mm × 190mm, were imaged in two sections at a spatial
resolution of about 8 picture elements (pixels) per mm (equivalent to 220 “dots” per inch, or
“dpi”); this is approximately equal to the spatial resolution of the eye at normal reading
distance. The images were processed and digitally stitched via many custom (and time-
consuming) computations to create processed images of the leaves.

Part of the computational intensity was due to the use of glass bandpass filters in the optical
path. Unavoidable small differences in the “tilts” of the filters relative to the sensor had the
effect of translating the recorded images by small distances in varying directions. These
translations had to be removed to “register” the images, i.e., to “line up” the pixels in each
waveband, before performing spectral image processing. As it happened, the registration
process was more difficult than had been envisioned. Even after significant custom image
processing, the resulting images were still imperfect.

The registered images of each leaf may be envisioned as a 3-D array of image data with
coordinates [x,y,λ], i.e., as a “cube” of data. The image datasets were processed using several
spectral segmentation techniques to distinguish among the various classes of object present in
the images, such as “parchment”, “mold”, “overwriting” (from the Euchologion), and
“underwriting” (the desired original text). In general, spectral image processing methods may
be divided into two basic classes: “supervised” and “unsupervised” classification (Duda, et al.,
2000). In this project, the former type of algorithm was used in most of the processing, though
a specific type of unsupervised classification proved essential for leaves of one manuscript.
This type of processing will be described in detail later in this paper.

The mathematical basis for the supervised classification algorithm assumes that a pixel
belonging to a specific class will exhibit a specific “spectral signature,” i.e., a specific set of
gray values over the set of spectral bands. In supervised classification, the user specifies
regions of known object type; the algorithm analyzes these for patterns of pixel brightness vs.
wavelength that are used to “train” the algorithm. The remaining pixels in the scene are
analyzed based on the training data to determine the likelihood of membership in each of the
object classes. For example, a pixel of original text would exhibit a “redder” spectrum than
one for the overtext. If the spectral signature for the specific object class m is represented as
the vector e , then the output values for a pixel belonging to that class should form a vector
m
proportional to e , where the proportionality constant is determined by the “lightness” of that
m
pixel:

e 
a
 
e
 b  ≡e
   m
 
e 
N m
After user-supplied data are analyzed to estimate the vectors for each class, a matrix E of
these spectra signatures is constructed:
11
e  e  e  
 a   a   a  
eb  eb  eb  ≡E
         
      
 
eN1eN2 eNM 

To illustrate the use of this matrix, note that the class membership of a pixel composed purely
of the first object class may be expressed as a vector α of the form:

1 
1
 
0
 2  =α
   1
 
0 
M

where the subscripts on the vector components merely specify the class of object at that pixel.
The matrix E is applied to this vector to produce an output vector that is the spectral signature
for that class:

e  e  e  1  e 
 a   a   a   1   a 
eb  eb  eb  02  = eb 
              
         
 
eN1eN2 eNM 0M eN1

Note that, in general, an individual pixel is heterogeneous, i.e., it is composed of some
mixture of the M object classes, which may be described by a general vector α of the form:

α 
1
 
α
 2  ≡α
  
 
α
 
M

The elements in the vector α clearly must sum to unity if all classes are included.

M
∑α =1

m
m=1

In such a case, the set of measured gray values at a pixel in each of the N bands is determined
by multiplying the spectral signature matrix E by the percentage class vector α to produce a
measured spectral vector r:
12