Computer modeling of a Michelangelo sculpture may shed new light on the work's mysterious past.
The statue known as the Florentine Pietà stands in the Museum of the Opera del Duomo in Florence, perhaps a 15-minute walk from where the artist, Michelangelo, is now buried. The work depicts four figures, larger than life, carved from a single block of marble. Mary Magdalen holds up the broken body of Christ, aided by Nicodemus above her, and the Virgin Mary to the right. Only the figures of Christ and Magdalen are finished. Various parts of the statue were broken and repaired, including the arms of Christ, and his left leg is missing. The Virgin's face is only roughly blocked out. Nicodemus bears the unfinished features of the artist himself.
The statue, one of three Pietà sculptures Michelangelo created, may have been intended to be mounted on an altar above his grave. As the story is told, the artist took a hammer to his unfinished work in 1555 and tried to destroy it. It was then partly repaired and finished by Tiberio Calcagni, an otherwise undistinguished contemporary. This unplanned collaboration has made the Florentine Pietà one of the most intriguing of Michelangelo's works.
Now researchers from IBM's Thomas J. Watson Research Center, led by Gabriel Taubin, in collaboration with Temple University art historian Jack Wasserman, have spent the last year creating a three-dimensional virtual representation of Michelangelo's statue, down to the finest details of cracks, chisel marks and texture. The IBM reconstruction will enable Wasserman and art historians throughout the world to study the statue at resolutions ranging from meters to a fraction of a millimeter, while viewing it from any vantage point, including those that would be impossible in real life.
The model, says Wasserman, should make possible an unprecedented technical and stylistic analysis of the Pietà, which might answer questions about how Michelangelo worked, his sense of proportion, whether he meant the statue to be his tomb monument (as historians suggest), and why he mutilated the work. Already, IBM has been able to provide images of what the statue would have looked like had Calcagni not been enlisted to repair what Michelangelo had destroyed. What's more, the methods developed by IBM to digitally capture the Florentine Pietà should be applicable to a wide range of imaging technologies. The techniques could be used to digitize other real-world objects and works of art or to graphically represent three-dimensional objects on the Internet, allowing online catalogs to include three-dimensional, 360-degree displays of products.
ART AS DATA
The project began two years ago, when IBM was approached by Wasserman, who believed that a digital representation of the Pietà could help unravel some of the mystery that has surrounded the work for more than four centuries. With funding from the IBM Foundation, researchers from Taubin's visual and geometric computing group embarked on what may become one of the most intensive studies of a single work of art ever done. They have made three trips to Florence, taking thousands of digital photographs of the statue, representing billions of bytes of data.
The technological challenge was twofold, explains Josh Mittleman, a
member of the visual and geometric computing group: first, capturing the larger-than-life statue in minute detail and then dealing with the mountain of data that would result. "A two-and-a-quarter-meter-tall statue rendered to a resolution below a millimeter, with geometry, textures, reflectance and so forth, is a whole lot of data," he says. "Enabling a user to get at that data quickly and easily is a very difficult research problem."
The IBM researchers took on the first challenge using a digital camera developed by a small Pittsburgh company called Visual Interface Inc. The camera, known as the Virtuoso Shape Camera, was originally designed to help plastic surgeons plan operations by taking three-dimensional photographs of a patient's face. The camera projects stripes of light onto the subject and then takes six overlapping images using six different lenses. For the Pietà project, the camera was modified so that in addition to taking six black-andwhite images simultaneously, it would take six color images from the same position, each with a different set of lighting conditions. The researchers also projected a grid of laser points on the statue to aid in aligning the images.
After 12 days of scanning the Pietà in Florence, the researchers had captured 600 images, each covering about 100 square inches (650 square centimeters) of surface. Once all the parts were aligned, the team ran an algorithm to merge them into a single triangle mesh. "The number of scans and measured points we were dealing with, combined with the accuracy we wanted to achieve, made these tasks interesting research problems," says Fausto Bernardini, an expert in computational geometry who developed most of the algorithms used to reconstruct the virtual statue. "We had to come up with new algorithms to process the data and produce the final model."
Taubin and his IBM colleagues also added their own "photometric" algorithm, developed from computer vision technology, to allow them to capture the statue's color and texture. "With the photometric approach, we can factor out specifics of the lighting," explains IBM's Holly Rushmeier, a research staff member and expert on the role of lighting in graphics. "We do that by taking the six color images with different light sources. Turn on light one, take the picture. Turn on light two, and so on. We then use our own algorithm to get the level of detail we need."
BRINGING A STATUE TO LIFE
The result is a virtual statue constructed from a mosaic of some 10 million triangles and 1 billion to 2 billion bytes of data refining the geometry and adding detailed color and texture information. To accommodate this mountain of data on a PC, the IBM researchers designed a special viewer. Users first see a simplified model of the statue that can be viewed from any angle. They can then mark a portion of the statue to view in greater detail, whereupon the server will add data to the image.
Using the close-up view, says Mittleman, "users can study fine surface detail. Large portions of the statue are unfinished, not polished. You can see the sculptor's tool marks, which differ on different parts of statue. It is a very rich area of research for the historian."
Early results were presented in December at a press conference at the Pierpont Morgan Library in New York City. Although the model is still being assembled, Wasserman reported that he has already been able to draw some conclusions about Michelangelo's work. By viewing the statue from above, for instance, it becomes clear that Christ's arm is not embracing Mary Magdalen, as scholars have suggested. When the statue is viewed from below -- as it would have been if it had been mounted on Michelangelo's tomb -- figures that appear distorted at eye level become more realistic. "The proportions," says Wasserman, "seem based more on reality than on some kind of hypothesis -- on, say, some kind of antinature philosophy." Even the relationships between the figures seem to change, says Wasserman: for instance, the form of Mary Magdalen, which normally seems detached from the others, becomes more a part of the entire composition when viewed from below.
"This is beginning to confirm hypotheses I had," says Wasserman, "as well as to reveal things I hadn't even considered. That's the beauty of this technology."
Current plans call for compiling the finished model, together with the viewer, on a CD-ROM to be included in a book of analytical and theoretical essays on the sculpture that will be edited by Wasserman and published by Princeton University Press. But IBM intends to make the work still more widely available. The December press conference unveiled a kiosk with an interactive multimedia touch screen that provides not just the model itself, but background on the project, the history of the sculpture, explanations by Wasserman and discussion of the technology involved. The kiosk could be the first of many, according to Paula Baker, director of corporate support plans and programs at IBM. "We hope to make the Pietà software available in kiosks to
institutions around the world," she says, "and to the public, students and scholars internationally."
Gary Taubes is a freelance writer who lives in Venice, California.
