Marc Levoy
Computer Science Department
Stanford University
April 14, 2000
Presented at the Siggraph "Digital Campfire"
on Computers and Archeology
Snowbird, Utah
Recent improvements in laser rangefinder technology, together with algorithms for combining multiple range and color images, allow us to reliably and accurately digitize the external shape and surface characteristics of many physical objects. Examples include machine parts, design models, toys, and artistic and cultural artifacts. As an application of this technology, I and a team of 30 faculty, staff, and students from Stanford University and the University of Washington spent the 1998-99 academic year in Italy scanning the sculptures and architecture of Michelangelo. During our year abroad, we also became involved in several side projects. One of these was the digitization of the Forma Urbis Romae.
The Forma Urbis Romae, also called the Severan Marble Plan, is one of the key source documents of ancient Roman topography [Carettoni60]. Measuring 60 feet across, 45 feet high, and 2-4 inches thick, it once graced the back wall of the Roman census bureau, in the Templum Pacis. Carved onto rectangular slabs between A.D. 203 and 211, during the reign of Septimius Severus, its surface incisions show every street, building, room, and staircase in the city - a feat of mapmaking that has never been matched (figure 1).
With the disintegration of the Roman Empire in the 5th century A.D., the Forma Urbis suffered the same fate as the rest of the city. For several hundred years marble slabs were systematically stripped from the map and either used to construct new buildings or simply burnt in kilns to make lime for cement. At some point there was a general collapse of the map and the building containing it, which fortunately buried the remaining fragments deeply enough to evade the marble scavengers. Also to our great fortune, the wall on which the map was mounted was incorporated into a church, SS. Cosma e Damiano, and thereby escaped destruction (figure 2).
At present there are 1,163 extant fragments of the map. Of these, 200 have been identified and in some cases fit together, 500 are unidentified, and 400 have no surface incisions [Almeida81]. These blank fragments might correspond to the centers of plazas or the Tiber River, or they might represent the borders of the map - nobody knows. It is estimated that these thousand-plus fragments represent about 15% of the original map surface. However, due to the unique way the map fell from the wall and was buried by other rubble, experts believe that this 15% is clustered in only a few areas of the city. As a result, they believe that many of the fragments are likely to fit together. Fortunately, these areas of the city are important ones, including portions of the imperial forums, the Colosseum, and the Palatine Hill.
The idea of using laser scanners and computer graphics to visualize the fragments of the Forma Urbis was first suggested to us in January of 1997 by Susanna Le Pera of the Archeological Superintendency of Rome. The idea of using computer algorithms to also piece the map together the map was our own idea, but it was naive.
We initially thought that it would be a simple matter to search among digital photographs of the fragments for matches between their border shapes or the incised designs on their top surfaces. Unfortunately, these top surfaces are often eroded, reducing the effectiveness of such an approach. Moreover, scholars have spent 500 years searching for matches among these incised designs; it seems unlikely that we will find many more. On the other hand, the fragments are several inches thick, and fragments that do fit together usually mate intimately across at least a portion of the interface surface between them Our idea, not yet tested, is to develop compact signatures for these border surfaces and to search among the signatures for matches.
Our proposed approach is a classic N^2 search problem. Since features on the scale of 1 mm can make or break a potential match, and since there are over a thousand fragments, the search space is large. However, there are several features of the fragments that we can use to speed it up. For example, the slabs comprising the map vary in thickness over a range of several inches, so we can sort the fragments by thickness, then begin our search for matches by looking at close neighbors in the sorted list. Other useful features include marble veining, which is usually highly directional and therefore constrains the space of possible matches, the presence of straight borders and clamp holes, which denote fragments lying at the edges of slabs, and of course the continuity between fragments of the incisions themselves.
In order to test these ideas, we first needed to build 3D geometric and photographic models of every fragment of the map. This was no easy task; the map fragments varied in size from a few inches to several feet across, some of them weighed several hundred pounds, and there were a lot of them. We used two Cyberware laser-stripe triangulation scanners. One was a custom design originally intended for scanning the statues of Michelangelo, which we adapted for use in this project. The other was a Model 15, a relatively inexpensive desktop scanner. Both devices had an X-Y sample spacing of 0.25 mm and a Z-resolution of 50 microns. We also acquired color data. For this we used a Sony DKC-ST5 programmable 3-CCD digital still camera. It had a nominal resolution of 2500 x 2000 pixels, which we set up to provide a resolution of 0.25 mm (300 dpi) on the fragment surfaces.
A laser-stripe scanner digitizes an object by sweeping it with a plane of laser light, imaging the resulting stripe as it moves across the object surface, and analyzing the shape of the stripe 30 times per second. This sweeping motion is typically accomplished either by translating the laser, translating the object, rotating the laser around a point, or rotating the object on a turntable. Between our two scanners we had all four capabilities, which we used in various combinations depending on the size and shape of each fragment. Regardless of the fragment shape, many scans were required to completely cover its surface. To permit these scans to be aligned, we overlapped them substantially, sometimes scanning each surface point several times. This redundancy also allowed us to downweight oblique views, which yield poor data in all laser triangulation systems and particularly poor data when scanning marble, due to subsurface scattering.
Our post-processing pipeline consisted of aligning these multiple scans, combining them together using a volumetric algorithm, and filling holes using space carving [Curless96]. Since the fragments were rotated partially by a motorized turntable and partially by hand, alignment was bootstrapped by aligning each scan to its neighbor interactively. This was followed by automatic pairwise alignment of scans using a modified iterated-closest-points (ICP) algorithm and finally by a global relaxation procedure designed to minimize alignment errors across the entire fragment [Pulli99]. Eventually, we will also map our color data onto these models. A sample 3D model and color photograph is shown in figures 3 and 4, respectively. For a more detailed description of our pipeline, see [Levoy00].
Although our digitization of the Forma Urbis Romae was successful (see figure 5), we faced many logistical problems that future digitizing projects may encounter, so it is worthwhile briefly enumerating them.
First, this project was at the edge of what we consider currently feasible using field-deployable scanning and computer technology. Our target spatial resolution was high - 1/4 mm, our scanning process was long and tedious - the average fragment took an hour to scan, and the resulting archive was large - 8 billion polygons and 6 thousand color images, occupying 40 gigabytes. The whole job took 6 people 25 days, working around the clock on 3 scanning stations simultaneously. Archeologists who embark on similar digitization projects should be well-funded, well-staffed, and technologically competent.
Second, getting permission to scan the Forma Urbis was a long, delicate, and occasionally painful process. Part of the pain was developing meaningful, equitable, and enforceable intellectual property agreements with the cultural institutions whose archeological patrimony we were digitizing. Since the goals of our project were scientific, our arrangement was simple and flexible: we are allowed to use and distribute our models and computer renderings for scientific use only. In the event we, or they, desire to use the models commercially, there will be further negotiations and probably the payment of royalties. In the case of the Forma Urbis, delineating appropriate use is not a significant concern; for Michelangelo's David, it is paramount.
Lastly, we underestimated the difficulty of digitizing under field (non-laboratory) conditions. We performed our scan of the Forma Urbis in the cold, damp, dusty basement of the Museum of Roman Civilization, 7000 miles from our home laboratory, repair shop, and calibration equipment. Shipping 4 tons of equipment to a foreign country, trucking it through narrow streets, and carrying it into historic buildings, was nerve-wracking and expensive. As soon as we moved our equipment into a museum, we became a liability to them - physically, logistically, and legally. During our 5 months of scanning in Italy, we spent $50,000 hiring museum guards to watch over us and the artifacts we scanned, including the Forma Urbis. Scanning during museum hours, which we did for the statues of Michelangelo, posed additional problems: bumped scanners, color images ruined by tourist flashbulbs, and a constant stream of questions (which we always answered).
In this brief paper I have described the beginnings of a multi-year project to digitize and analyze the 1,163 marble fragments of the Forma Urbis Romae, an important source document in Roman topography. In the months (and maybe years) ahead we will process the data we have collected, and we will try to assemble the map. Whether or not we succeed, one of the tangible results of this project will be a set of 3D geometric models and high-resolution color photographs, one per map fragment. Our plan is to make this unique digital archive freely available to the archeological (and computer graphics) research communities.
An important secondary goal of this project was to explore the scientific utility of detailed three-dimensional computer models. We believe they have many uses. For the working art historian or archeologist, 3D models provide a tool for answering specific geometric questions about artifacts. Trying to solving the jigsaw puzzle posed by the Forma Urbis is one obvious example. Questions we have been asked about Michelangelo's statues include computing the number of teeth in the chisels employed in carving the Unfinished Slaves, and determining whether the giant statue of David is well balanced over his ankles, which have developed hairline cracks. For the restorer, a model can, in principle, be used as the official record of diagnostics and restorations performed on an artifact. For educators, while models displayed on a computer screen are not likely to replace the experience of seeing the artifact in person, they can nevertheless enhance the experience by allowing students to examine the object at length, close up, and under user-controllable (virtual) illumination. For museum curators, models serve as an indestructible archive of an artifact, although insuring the longevity of digital archives is an unsolved problem.
The heroes of the Forma Urbis scan were Sean Anderson, Dave Koller, Lucas Pereira, Kari Pulli, and Szymon Rusinkiewicz. We also had help from Barbara Caputo, Domi Pitturo, and Maisie Tsui. Our collaborators in Rome were Eugenio La Rocca, Susanna Le Pera, Anna Mura Somella, and Laura Ferrea. Our sponsors were Stanford University, Interval Research Corporation, and the Paul Allen Foundation for the Arts.
[Almeida81] Almeida, R., Forma urbis marmorea: Aggiornamento generale, Rome, 1981.
[Carettoni60] Carettoni, G., Colini, A., Cozza, L., Gatti, G., La Pianta Marmorea di Roma Antica (The Marble Map of Ancient Rome), Commune di Rome, 1960.
[Curless96] Curless, B., Levoy, M., A Volumetric Method for Building Complex Models from Range Images, Proc. SIGGRAPH '96.
[Levoy00] Levoy, M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller, D., Pereira, L., Ginzton, M., Anderson, S., Davis, J., Ginsberg, J., Shade, J., Fulk, D., The Digital Michelangelo Project: 3D scanning of large statues, To appear in Proc. SIGGRAPH 2000.
[Pulli99] Pulli, K., Multiview registration for large data sets, Proc. Second International Conference on 3-D Digital Imaging and Modeling, IEEE Computer Society Press, 1999.
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| Figure 1: A photograph of fragment 010g of the Forma Urbis Romae (Severan Marble Plan). This fragment is roughly 3 feet across, which is 640 feet on the ground, and it weighs about 150 pounds. Each incised line is a wall; thus, parallelograms with gaps in their borders are rooms with doors. The small V's in narrow rooms are staircases, and sequences of round pits are porticos supported by columns. Note the marble veining, which is an additional clue for solving the puzzle. | Figure 2: The wall of the Templum Sacrae Urbis on which the Severan Marble Plan was hung. Clearly visible are the rows of holes where the map was attached using bronze clamps. The windows are modern. |
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| Figure 3: A computer rendering of the 3D model of fragment 642. This fragment is 5 inches across. The incisions on the fragment surface are approximately 3mm wide x 0.75mm deep. This model was assembled from 18 scans. | Figure 4: A photograph of the fragment, for comparison. This fragment evidently shows a narrow street with rooms - probably shops - opening onto it. The map only shows the first floor of buildings; other than the presence of staircases, there is no information about their height. |
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| Figure 5: A collage, assembled from our digital archive, containing thumbnail photographs of every extant fragment of the Forma Urbis Romae. |
For more information on the Digital Michelangelo Project, see
http://graphics.stanford.edu/projects/mich/.
For more information on the digitizing of the Forma Urbis Romae, see
http://graphics.stanford.edu/projects/forma-urbis/.