Scanning the fragments of the Forma Urbis Romae

Photographs and text by Marc Levoy
May 29, 1999

After scanning the statues of Michelangelo, the last project we undertook during our year in Italy was to scan the 1,163 fragments of the Forma Urbis Romae, a giant map of ancient Rome carved onto marble slabs in the 3rd century A.D. Piecing this map together has been one of the great unsolved problems of archaeology. The prospect of tackling a 3D jigsaw puzzle of such historical importance is exciting. However, before we can try solving the puzzle, we had to scan the fragments. Here's how we proceeded.

Our story begins at the Museum of Roman Civilization (Museo della Civiltà Romana), a vast edifice located in the Roman suburb of EUR (Exposizione Universale di Roma). The museum, and the suburb that surrounds it, were built by Benito Mussolini in the 1930's and 40's. Unfortunately, fascist town planning tends to be both grand and sterile, and the buildings of EUR have not aged gracefully,

The Museum of Roman Civilization tells the story of ancient Rome, from its beginnings in the 5th century B.C. until its fall a thousand years later. Each room is devoted to a particular era or emperor, and the story is told with maps, text, and exquisitely detailed models and casts. Sadly, the museum is a long way from the city center, and copies of artworks are shunned by today's sophisticated tourists, so the museum is usually deserted.

The centerpiece of the museum is "Il Plastico", a huge scale model of the ancient city in the time of Constantine (about 300 A.D.). The model, which measures 60 feet on a side, includes everything within the ancient city walls, whose brick ramparts still surround the city today. In the foreground is the Circus Maximus, Rome's racetrack, built to accommodate 150,000 spectators. Behind it are the imperial palaces on the Palatine Hill, and to their right is the Colosseum.

Although the model is usually viewed from a balcony, we were permitted to make a closer examination. The craftsmanship is remarkable. Pictured here is the aqueduct that fed water to the imperial palaces. Although it no longer carries water, this aqueduct can still be seen today, spanning the modern Via di San Gregorio.

So how do archaeologists know what the ancient city looked like?

Aside from its largest monuments, and those that have been excavated, most of ancient Rome lies buried beneath the modern city. If so, then how can Il Plastico purport to show neighborhoods, streets, even individual houses that no longer exist? Ancient descriptions of the city, for example by Pliny, tell us about the appearance and general placement of important buildings, but these narratives contain no drawings, so their usefulness is limited.

The single most important document on ancient Roman topography is a map created in ancient times - the Forma Urbis Romae. Measuring 60 feet across, 45 feet high, and carved onto marble slabs several inches thick, it once graced the back wall of a room (shown here by a yellow arrow) in the Templum Pacis. There is evidence that the Menorah, looted from the Temple in Jerusalem in 70 A.D, was also displayed in the Templum Pacis. The map, carved between A.D. 203 and 211, during the reign of Septimius Severus, shows every street, building, room, and staircase on the ground floor of the city - a feat of mapmaking that has never been matched. Incidentally, Il Plastico is at the same scale as the Forma Urbis, 240:1.

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. Here is a photograph of the wall. Clearly visible are rows of holes where the map was attached using bronze clamps. The windows are modern.

The blossoming of the Italian Renaissance fostered a new interest in classical antiquity, and in 1562 an attempt was made, under the direction of Cardinal Alessandro Farnese, to collect the then-known fragments of the map and document them. In the 400 years since, hundreds more fragments have been found, and the map has become an object of intense scholarship. We were lucky enough to find in an antiquarian bookshop a copy of this rare 1960 book, The Marble Map of Ancient Rome (La Pianta Marmorea di Roma Antica), by Carettoni, Colini, Cozza, and Gatti. The most authoritative study of the map in this century, it also includes glass-plate photographic reproductions of every incised fragment. Shown here is a fragment from the map, set alongside its photograph and the book itself.

How are we planning to "solve" the problem of the Forma Urbis?

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 solve the map was our own idea, but it was naive.

First of all, we'll never "solve" the entire map; only 15% of its fragments remain. However, experts believe that due to the unique way the map fell from the wall and was buried by other rubble, this 15% is clustered in a few areas of the city. As a result, they believe that many of the fragments are likely to fit together. Fortunately, these areas are important ones, including portions of the imperial forums, the Colosseum, and the Palatine Hill. What does remain of the map is about 200 identified fragments, many of which have also been fit together, 500 unidentified fragments, some partially fit together and some not, and 400 fragments that have no incisions. 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.

Our first idea was to search among digital photographs of the fragments for matches between the borders or incised designs on their top surfaces. Unfortunately, the top surfaces of the fragments are often eroded, reducing the effectiveness of such an approach. Moreover, scholars have been searching for 500 years 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 digital signatures for the geometry of these border surfaces and to search among the signatures for matches.

(Photograph courtesy of Prof. Rodriguez-Almeida.) For example, here is a photograph of four fragments fit together in the early 1980's by Emilio Rodriguez-Almeida, the greatest living expert on the map. As this photograph shows, the matches between fragments are not obvious from an examination of their top surfaces. These particular pieces do fit, however, as can be verified by examining the surfaces, largely hidden in this photograph, where they mate.

Our proposed approach is a classic N^2 search problem. Since features on the scale of 1mm 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 must first build 3D geometric and photographic models of every fragment of the map, and the resolution of these models should be 1mm or finer. (The photographic reproductions in the book by Carettoni et al. are good, but they are too contrasty. Also, the original glass plates have been lost, and in any case they didn't include photographs of the unincised fragments.) To build these models, we need 3D scans of the fragments.

So in March of 1999, we returned to the Archeological Superintendency with a proposal to digitize all 1,163 fragments of the map at a spatial resolution of 0.25mm for geometry and 0.125mm for color. Although the superintendent, Eugenio La Rocca, was supportive, there was understandable hesitation from the curators - the map is a priceless artifact, the fragments are large, heavy, and fragile, and there are so many of them. The project seemed impossible. After a few back-of-the-envelope calculations, we convinced them that with enough people and scanners, we could set up an "assembly line" that would do the job in 2 weeks. (This estimate proved to be wrong - see the bottom of this page.) We also convinced them that we could do the job safely. (Fortunately, in this matter we were right.) Eventually they acquiesced, and two of them, Anna Mura Somella and Laura Ferrea, became our enthusiastic collaborators. In the space of a few weeks in April, 1999, we obtained the necessary permissions, found funding (some of which was provided by the City of Rome), assembled a team (which included Laura Ferrea), rented an apartment in Rome, and moved ourselves and several tons of computers and scanners from Florence to the Eternal City.

Where exactly did we move to?

Scanning the fragments

Until recently, the fragments of the Forma Urbis were housed in the museum of the city of Rome (Museo di Roma), in Palazzo Braschi, a few steps from Piazza Navona. When that museum was closed recently for restoration, the fragments, ranging in size from a few inches to 4 feet across, were packed into crates and moved to, of all places, the basement of the Museum of Roman Civilization, location of Il Plastico, in the Roman suburb of EUR. The main gallery of this basement is shown at left.

On April 13, we visited the museum in order to plan our scan of the map. The museum director, with officials from the archaeological office in attendance, brought us to the basement and directed our attention to the space beneath the spotlights on the left side. This is what we saw. We were quiet for a long time. I thought about the last scene from Indiana Jones and the Lost Ark. Sensing our confusion and terror, our guide from the archaeological office explained with some amusement that these crates represented the entire contents of the Antiquarium Comunale; the Forma Urbis occupied only 20 of them. Whew.

This same basement gallery, though cold, damp, and extremely dusty, was otherwise a good place to set up a temporary computer graphics laboratory. In the foreground is a crate of small fragments, some of which are sitting on the table behind, unwrapped and ready for scanning. From right to left in the background is our Cyberware laser scanner, a photographic camera stand, and a cluster of Silicon Graphics workstations. Hidden behind the workstations is a Cyberware Model 15 scanner, which we had shipped from the United States so that we could scan two fragments at the same time, doubling our throughput.

Although most fragments of the Forma Urbis are small, some are large and weigh several hundred pounds, so our team in Rome includes two handsome gentlemen like Valerio, pictured here gently lowering a fragment onto a motorized rotary table for scanning.

Here we see one of the smaller, unidentified, fragments in the process of being scanned. As with the statues of Michelangelo, we are attempting to digitize every accessible surface. This is an easy task on a fragment like this, but a much harder job on fragments consisting of several pieces attached by iron pins, like number 37 (pictured above).

Sitting at our Silicon Graphics Octane, PhD student David Koller examines the computer model of a newly scanned fragment. Although we have attempted to automate the scanning process as much as possible, fragments must be moved by hand several times during scanning, forcing us to perform interactive alignment of the resulting meshes. Moreover, every fragment has a different geometry, so the aligned meshes for each fragment must be examined interactively on a workstation screen to look for holes. It is a tedious job.

At left is a rendering of the raw 3D data for a fragment. The fragment is 5 inches across, small enough to be scanned using our Cyberware Model 15. In order to see the entire surface, linear scans were taken from 18 different directions. Even so, at least one hole is evident (blue circle). It is less than a millimeter across, so we'll fill it later using an automatic hole-filling algorithm. The 18 scans have been aligned with each other using a modified iterated-closest-points (ICP) algorithm followed by a global relaxation procedure designed to minimize alignment errors across the entire fragment. The residual error, about 0.25mm, is visible as interpenetrating surfaces (yellow circle). Our volumetric range image merging software (vrip) will replace these interpenetrating surfaces with a single surface at an average location. Below the rendering is a profile plot of the 4 scans that saw one particular incision (at the red line on the rendering). The incision is 3mm wide x 0.75mm deep, large by Forma Urbis standards. A photograph of the fragment is shown for comparison.

To reduce the time required to scan each fragment, we are not using the color camera built into our Cyberware scanner. Instead, we have assembled this separate color digitization station, which can operate in parallel with the Cyberware scanner. Its images are also of slightly higher quality than the color camera installed in our scanner. The spotlights surrounding the table have been arranged to cast a raking light across the fragments, a lighting configuration frequently employed when photographing incised stone artifacts.

Here are two photographs of a fragment, taken at two different magnifications. The fragment, numbered 010g, 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 (for example just below the center of the lower image) are staircases, and the rectangles composed of round pits (for example at the top center of the lower image) are porticos supported by columns. Note the marble veining, which is an additional clue for solving the puzzle. We have digitized these fragments finely enough to create a 1:1 photographic reproduction of the entire map at 100 dpi, a portion of which might be mounted on the wall above Il Plastico in the museum. That is, after we have mosaiced together the thousands of high-magnification photographs which, like the lower image here, cover only a portion of a fragment.
Click here for a 1669 x 1045 pixel (296KB) or 3337 x 2090 pixel (775 KB) image of the complete mosaiced fragment (added June 26, 2000).

A collage, assembled from our data after we returned to the United States, containing thumbnail photographs of every known fragment of the map.
(Collage courtesy of James Davis.)
Click here for a 1750 x 1188 pixel (598 KB) or 3500 x 2376 pixel (2.2 MB) version. (The original is 7000 x 4752 pixels.)

As with our scan of Michelangelo's David, months of planning and back-of-the-envelope calculations failed to prepare us adequately for the difficulty of this project. By the time we had finished scanning in the Galleria dell'Accademia and the Medici Chapel, it was May 10. Attrition had pared our scanning team from 22 people down to only 6, and our budget (and our spirits) were nearly exhausted. Moreover, we had only four weeks left before the customs carnets expired on our scanners and computers, at which time we would be forced to ship them back to the United States. To scan the entire Forma Urbis in such a short time, we instituted round-the-clock scanning, 24 hours a day 7 days a week, using 2 laser scanners and our photographic camera stand. We kept up this pace for 25 days, sleeping in shifts, sometimes sharing beds in shifts. But we managed to finish. The dataset contains 8 billion polygons and 6 thousand color images, occupying 40 gigabytes. Processing this data and trying to solve the puzzle will take months, possibly years. For more information about this project, click here, and click here for an online sample database containing models and photographs of 28 fragments of the map

The heroes of the Forma Urbis scan were:

Sean Anderson < seander@cs.stanford.edu >
David Koller < dk@graphics.stanford.edu >
Marc Levoy < levoy@cs.stanford.edu >
Lucas Pereira < lucasp@graphics.stanford.edu >
Kari Pulli < kapu@graphics.stanford.edu >
Szymon Rusinkiewicz < smr@graphics.stanford.edu >

We also had help from:

Barbara Caputo < b.caputo@caspur.it >
Maisie Tsui < tsui@leland.stanford.edu >

Our collaborators in Rome were:

Prof. Eugenio La Rocca, Sovraintendenza ai musei, gallerie, monumenti, e scavi, Comune di Roma
Dott.ssa Susanna Le Pera, Sovraintendenza ai musei, gallerie, monumenti, e scavi, Comune di Roma
Dott.ssa Anna Mura Somella, Musei Capitolini
Dott.ssa Laura Ferrea, Musei Capitolini

levoy@cs.stanford.edu

	Our story begins at the Museum of Roman Civilization (Museo della Civiltà Romana), a vast edifice located in the Roman suburb of EUR (Exposizione Universale di Roma). The museum, and the suburb that surrounds it, were built by Benito Mussolini in the 1930's and 40's. Unfortunately, fascist town planning tends to be both grand and sterile, and the buildings of EUR have not aged gracefully,
	The Museum of Roman Civilization tells the story of ancient Rome, from its beginnings in the 5th century B.C. until its fall a thousand years later. Each room is devoted to a particular era or emperor, and the story is told with maps, text, and exquisitely detailed models and casts. Sadly, the museum is a long way from the city center, and copies of artworks are shunned by today's sophisticated tourists, so the museum is usually deserted.
	The centerpiece of the museum is "Il Plastico", a huge scale model of the ancient city in the time of Constantine (about 300 A.D.). The model, which measures 60 feet on a side, includes everything within the ancient city walls, whose brick ramparts still surround the city today. In the foreground is the Circus Maximus, Rome's racetrack, built to accommodate 150,000 spectators. Behind it are the imperial palaces on the Palatine Hill, and to their right is the Colosseum.
	Although the model is usually viewed from a balcony, we were permitted to make a closer examination. The craftsmanship is remarkable. Pictured here is the aqueduct that fed water to the imperial palaces. Although it no longer carries water, this aqueduct can still be seen today, spanning the modern Via di San Gregorio.

	Until recently, the fragments of the Forma Urbis were housed in the museum of the city of Rome (Museo di Roma), in Palazzo Braschi, a few steps from Piazza Navona. When that museum was closed recently for restoration, the fragments, ranging in size from a few inches to 4 feet across, were packed into crates and moved to, of all places, the basement of the Museum of Roman Civilization, location of Il Plastico, in the Roman suburb of EUR. The main gallery of this basement is shown at left.
	On April 13, we visited the museum in order to plan our scan of the map. The museum director, with officials from the archaeological office in attendance, brought us to the basement and directed our attention to the space beneath the spotlights on the left side. This is what we saw. We were quiet for a long time. I thought about the last scene from Indiana Jones and the Lost Ark. Sensing our confusion and terror, our guide from the archaeological office explained with some amusement that these crates represented the entire contents of the Antiquarium Comunale; the Forma Urbis occupied only 20 of them. Whew.
	This same basement gallery, though cold, damp, and extremely dusty, was otherwise a good place to set up a temporary computer graphics laboratory. In the foreground is a crate of small fragments, some of which are sitting on the table behind, unwrapped and ready for scanning. From right to left in the background is our Cyberware laser scanner, a photographic camera stand, and a cluster of Silicon Graphics workstations. Hidden behind the workstations is a Cyberware Model 15 scanner, which we had shipped from the United States so that we could scan two fragments at the same time, doubling our throughput.
	Although most fragments of the Forma Urbis are small, some are large and weigh several hundred pounds, so our team in Rome includes two handsome gentlemen like Valerio, pictured here gently lowering a fragment onto a motorized rotary table for scanning.
	Here we see one of the smaller, unidentified, fragments in the process of being scanned. As with the statues of Michelangelo, we are attempting to digitize every accessible surface. This is an easy task on a fragment like this, but a much harder job on fragments consisting of several pieces attached by iron pins, like number 37 (pictured above).
	Sitting at our Silicon Graphics Octane, PhD student David Koller examines the computer model of a newly scanned fragment. Although we have attempted to automate the scanning process as much as possible, fragments must be moved by hand several times during scanning, forcing us to perform interactive alignment of the resulting meshes. Moreover, every fragment has a different geometry, so the aligned meshes for each fragment must be examined interactively on a workstation screen to look for holes. It is a tedious job.
	At left is a rendering of the raw 3D data for a fragment. The fragment is 5 inches across, small enough to be scanned using our Cyberware Model 15. In order to see the entire surface, linear scans were taken from 18 different directions. Even so, at least one hole is evident (blue circle). It is less than a millimeter across, so we'll fill it later using an automatic hole-filling algorithm. The 18 scans have been aligned with each other using a modified iterated-closest-points (ICP) algorithm followed by a global relaxation procedure designed to minimize alignment errors across the entire fragment. The residual error, about 0.25mm, is visible as interpenetrating surfaces (yellow circle). Our volumetric range image merging software (vrip) will replace these interpenetrating surfaces with a single surface at an average location. Below the rendering is a profile plot of the 4 scans that saw one particular incision (at the red line on the rendering). The incision is 3mm wide x 0.75mm deep, large by Forma Urbis standards. A photograph of the fragment is shown for comparison.
	To reduce the time required to scan each fragment, we are not using the color camera built into our Cyberware scanner. Instead, we have assembled this separate color digitization station, which can operate in parallel with the Cyberware scanner. Its images are also of slightly higher quality than the color camera installed in our scanner. The spotlights surrounding the table have been arranged to cast a raking light across the fragments, a lighting configuration frequently employed when photographing incised stone artifacts.
	Here are two photographs of a fragment, taken at two different magnifications. The fragment, numbered 010g, 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 (for example just below the center of the lower image) are staircases, and the rectangles composed of round pits (for example at the top center of the lower image) are porticos supported by columns. Note the marble veining, which is an additional clue for solving the puzzle. We have digitized these fragments finely enough to create a 1:1 photographic reproduction of the entire map at 100 dpi, a portion of which might be mounted on the wall above Il Plastico in the museum. That is, after we have mosaiced together the thousands of high-magnification photographs which, like the lower image here, cover only a portion of a fragment. Click here for a 1669 x 1045 pixel (296KB) or 3337 x 2090 pixel (775 KB) image of the complete mosaiced fragment (added June 26, 2000).
	A collage, assembled from our data after we returned to the United States, containing thumbnail photographs of every known fragment of the map. (Collage courtesy of James Davis.) Click here for a 1750 x 1188 pixel (598 KB) or 3500 x 2376 pixel (2.2 MB) version. (The original is 7000 x 4752 pixels.)