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2000 International Geoscience and Remote Sensing Symposium,

Institute Electrical and Electronics Engineers, Honolulu, July 24-28, 2000.

 

Multispectral Analysis of Ancient Maya Pigments:

Implications for the Naj Tunich Corpus

 

 

Gene A. Ware, Douglas M. Chabries, and Richard W. Christiansen Brigham Young University

College of Engineering and Technology, 270 CB, Brigham Young University, Provo, Utah 84602

Phone (801) 378-43261 FAX  (802) 378-5705 / Email dougc@byu.edu

 

James E. Brady California State University at Los Angeles

 Department of Anthropology, California State University, Los Angeles, California 90032

Phone (323) 343-24401 FAX (323) 343-2446 / Email jbrady@calstatela.edu 

 

Curtis E. Martin United States Air Force Academy

Department of Mathematics, 2354 Fairchild Drive, Suite 6D2A, USAF Academy, Colorado 80840-6252

Phone (719) 333-65381F AX (719) 333-2114 / Email Curtis.Martin@usafa.af.mil

 

INTRODUCTION

 

                Naj Tunich, in southeastern Peten, Guatemala, is one of only five caves currently known to contain Maya hieroglyphic writing [I]. It is universally recognized as the preeminent Maya cave site because its corpus of inscriptions exceeds those of the other four caves combined. In June of 1998, over half of these inscriptions were documented at visible and near-infrared wavelengths using multi-spectral imaging techniques.

 

                Spectral differences were noted in the Naj Tunich images especially in the infrared. Spectral signatures were used to identify differences in the Naj Tunich pigments and suggest that at least three different pigments were used. More importantly, the ability to document spectral differences reveals far more complexity in the Naj Tunich corpus than previously appreciated. Several instances of over-painting, repainting or touching up were discovered. The cases of over-painting reveal the temporal complexity of the drawings and suggest that the painting occurred over a longer period of time than had been proposed by previous investigation. The ability to characterize pigment composition using spectral data had also led us to question a number of relational differences and similarities between drawings proposed on the basis of stylistic analysis.

 

NAJ TUNICH MULTISPECTRAL IMAGES

 

Archaeological multispectral imaging has its roots in remote sensing of the earth from space. In an archaeological setting, the remoteness is measured in meters instead of hundreds of kilometers. Multispectral imaging refers to a set of images of the same scene but with each image centered at a different optical wavelength. This data set can then be processed to extract information related to variations between images which is not available when the images are observed separately.

 

                The Naj Tunich multispectral images were acquired using a Kodak Megaplus Camera (Model 4.2i) with a spatial resolution of 2024 by 2044 pixels. Optical interference filters mounted in a filter wheel were used to define the image central wavelength and bandwidth. This set of filters, each 40 nm in bandwidth, were centered at wavelengths of 400 through 1000 nm in increments of 50 nm.

 

                Operation as deep as one kilometer in the cave required the camera and associated computer hardware to be operated from a marine battery. Ring and auxiliary strobe units were used for lighting. Image data were recorded on computer hard drives and on compact disks (CDs).

 

SPECTRAL CLUSTERING

 

                The multispectral images of a particular inscription may be stacked on top of each other forming an image cube. Viewed downward from the top of the cube, pixels with the same spatial location but with different wavelengths will be observed. Such a set of pixels defining the spectral reflectance at a particular spatial location in the observed scene is defined as the vector x ij where the indices identify the spatial location. The image cube may then be considered as a set of spectral reflectance vectors, one for each spatial location.

 

                The objective of this spectral clustering analysis is to group together spectral reflectance vectors with similar spectral shapes independent of the vector magnitudes. To this end, each vector is normalized by its own magnitude before use in the analysis.

 

                The spectral clustering analysis was accomplished using an unsupervised vector quantization (VQ) algorithm based on the scheme proposed by Linde, Buzo, and Gray known as the LBG algorithm [2]. This algorithm, chosen because it is conceptually straightforward, is easily implemented and does not require the analyst to know accurate data statistics.

 

                Our previous experience with the LBG algorithm in a hyperspectral clustering application suggested that successful results could be obtained with the Naj Tunich data set. Unlike the traditional VQ clustering approach where the vectors are derived from spatially adjacent locations in the image, spectral clustering partitions the normalized spectral reflectance vectors, ij , into groups based on spectral shape independent of spatial location. After spectral clustering, vectors in a particular cluster are more alike in spectral shape than those in any other cluster.

 

                In order to separate the spectral vectors based on the spectral shape, the distortion measure of the LBG algorithm was changed from a Euclidean metric to an angle-based distance measure, d (, ŷ), where:

 

                                                                          d (, ŷ) = l – x · y ,                                                                   (1)

*is a normalized spectral reflectance vector, ŷ is a normalized adaptive cluster center vector, and the vector inner product is represented by the dot. This angle-based measure is equal to (1-cos θ), where θ is the angle between two vectors in the space of the spectral reflectance vectors. At completion of the cluster processing, the adaptive cluster center is the arithmetic mean of all vectors in the cluster.

 

                The LBG algorithm with an angle-based distance measure was used to process selected cave inscriptions. Using this algorithm with two clusters separated pigmented from non-pigmented vectors in nearly every case. When two pigments appeared to be present, the four cluster analysis typically assigned two clusters to the pigment vectors and distributed the remaining two clusters between two background vectors.

 

RESULTS

 

                Because of the large number of drawings in the Naj Tunich corpus and the extensive data set generated by taking multiple images of each drawing segment, it has not yet been possible to process all of the material that was collected. Nevertheless, a number of surprises were noted in the field and these were given a high priority in processing.

Text Box:  
Fig. 1 Drawing 62 at three wavelengths.
Drawing 62, a profile human face, appears to have a uniform dark paint in the visible (represented by the 550 nm image of Fig. 1) and hence appears dark to the eye and to conventional photography. However, portions of the face around the nose, a portion of the eye, the lip, and the fang show significant fading in the near infrared perhaps due to the use of a mineral-based pigment. The forehead, most of the eye and the rear portion of the jaw remain dark at 950 nm indicating the use of a carbon based pigment. The presence of two different pigments in Drawing 62 suggests that the profile was over-painted at the time of creation or, more likely, touched up at a later date.

 

Text Box:  

Fig. 2  Drawing 62 in RGB color and four cluster color.
                Using spectral classification, the situation becomes even more clear (Fig. 2). The forehead and the majority of the eye are clearly distinguished from the nose, lip, fang and the rest of the eye. What was not obvious in the infrared image was that remnants of both pigments are present along the rear of the jaw. Small remnants of the carbon based pigment (colored blue) are also noted along the nose, lip and fang which may indicate that it was the earlier of the two pigments to be applied.

 

                In the glyph text designated Drawing 34 (Fig. 3a), differences are apparent with the last two glyphs in the right column badly faded. The faded glyphs become more clearly defined in Figure 3b which spectrally distinguishes between pigment and wall.

 

                When the spectral classification of the pigmented regions in Drawing 34 is viewed, an unexpected picture emerges (Fig. 4). The visually darker pigment on the left is present throughout most of the inscription (Fig. 4a). There are even vestigial amounts of the darker pigment in the very faded glyph at the bottom of the right Text Box:  

Fig. 3 and 4  Drawing 34 in RGB color (left) and four cluster color (right).
column. Thus, while the faded glyphs at the bottom right represent a possible example of a second painting episode with a lighter pigment (Fig. 4b), it is now clear that the entire text was overpainted at a later time. If the mineral based pigment is the later of the two, then it is also evident that much of the inscription flaked off the wall prior to repainting.

The evidence of overpainting is relevant to fundamental problems in interpretation of the Naj Tunich corpus. A critical one is dating. Although there are Maya calendar dates in the .Naj Tunich inscriptions, they use the Calendar Round or Short Count as opposed to the Long Count. The Long Count is simply a count of days from a known starting point (3114 B.C.) which can be correlated with our calendar. Calendar Round dates, on the other hand, specify a particular day from the 360 day solar calendar and a particular day from the 260 day ritual calendar forming a cycle or round that takes 52 years to complete. The problem is in knowing to which round a date belongs.

 

The situation was somewhat simplified at Naj Tunich, by the presence of two distance numbers among the original inscriptions. Distance numbers instruct a reader to count forward or backward from a specified date which is usually an ending of an important period in the long count system and therefore is a date known to archaeologists. Both of the Naj Tunich distance numbers refer to a period ending in A.D. 741 and an assumption was made that all other Naj Tunich Calendar Round dates fell into the same round [3]. The weakness of this assumption was demonstrated in 1988 when a newly discovered branch of the cave was found to contain a text with a distance number dating to the preceding round. At the very least, all of the dates should have been computed for both rounds, but even this would not address the possibility that some of the dates may belong to an even earlier round.

 

Stone's interpretation of the dating makes the painting at Naj Tunich a phenomenon that occurred over a very short period at the end of a millennium long use of the cave [3]. This possibly suggests that the painting reflects a fundamental change in the in use and meaning of the cave itself in which this important pilgrimage spot is becoming less sacred. The evidence for over-painting and touch-up provided by multispectral imaging suggests a greater temporal complexity to the inscriptions.  Given the preservation in the cave that allowed the paintings to survive at least 1200 years, one must suspect that the initial painting must have been on the wall for some time to require repair. It was also clearly important that, once painted, these messages remain readable today.

 

CONCLUSIONS

 

The application of digital multispectral imaging to the Naj Tunich inscriptions has opened a new dimension for the analysis of the corpus. Spectral classification using the LBG algorithm with an angle-based measure is effective in revealing pigment compositional differences leading to identification of over-painting as well as basic inscriptional interrelationships. This, in turn, has led to an increased understanding of both the temporal and artistic complexity of the inscriptions and their setting. It is expected, as additional processing techniques are applied to the images, that new techniques will emerge for the analytical study of ancient Maya cave inceptions.

 

REFERENCES

 

 [1] James E. Brady, Gene A. Ware, Barbara Luke, Allan Cobb, John Fogarty, and Beverly Shade, "Preclassic Cave Utilization Near Cobanerita, San Benito, Peten." Mexicon, vol. 19, no. 5, 1997, pp. 91-96.

[2] Yoseph Linde, Andrés Buzon, and Robert M. Gray. "An Algorithm for Vector Quantizer Design." IEEE Transactions on Communications, vol. COM-28, no. 1, Jan. 1980, pp. 84-95.

[3] Andrea J. Stone, Images from the Underworld, Austin: University of Texas Press, 1995.

 

Research supported by the Center for Advanced Study In the Visual Arts of the National Gallery of Art,

and the Foundation for the Advancement of Mesoamerican Studies, Inc.

All images are used by permission of the College of Engineering and Technology, Brigham Young University.

 

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