The Pieta' Project

Pietà Project - Overview

We have been engaged in a project to create a detailed three dimensional model of Michelangelo's Florentine Pietà (shown in the photograph). This project was defined and driven by the research interests of Dr. Jack Wasserman, professor emeritus of art history at Temple University. Dr. Wasserman had been studying Michelangelo's Florentine Pietà for several years, intending primarily to fully document all aspects of the statue and its history for future researchers; and secondarily to investigate his own theories on Michelangelo's composition. He had used high-quality photography, x-ray and ultra-violet light studies, as well as researching the complex history and symbolism of the statue and its analysis by past art historians. Dr. Wasserman believed that this work presented certain puzzles that could not be solved by these methods alone, and conceived the idea of creating a digital model as an additional analytic tool. He felt that the Pietà was especially well-suited to study through this new technology.

Accounts from Michelangelo's contemporaries tell us that the artist intended the Florentine Pietà as his own tomb monument. Beginning late in his life, in the 1550s, he executed a massive work, 2.25 meters tall, four larger-than-life figures carved from a single block of marble. The Christ figure in the center rests across the lap of the Virgin Mary, supported on the left by Mary Magdalen. Behind and above, supporting the Christ is a figure believed to represent Nicodemus and to bear the face of Michelangelo himself. At some point, Michelangelo decided for unknown reasons to break off parts of the statue. He then abandoned it, and shortly before his death permitted one of his students, Tiberio Calcagni, to repair the statue. Calcagni re-attached several pieces to the statue and partially finished the figure of the Magdalen [Giorgio Vasari, Life of Michelangelo, 1568]. Thus, what we see today is, in a sense, a composite of Michelangelo's work and his student's; his original design, damaged, repaired, and overlain by later work. Identifying and separating each phase of the statue's life is of paramount interest to the art historian, and crucial to divining Michelangelo's original intent and his purpose in breaking his work.

Various considerations limit the historian's ability to study the statue by traditional means. The value of the work precludes certain methods: The statue cannot be moved, altered, or damaged. Access to it is restricted, so even those researchers able to travel to Florence may not have the time or freedom they need to study it. The statue's complex geometry limits other techniques: A camera cannot capture certain views of the statue because it occludes itself or because the room in which it stands is too small to place the camera properly. A sufficiently-detailed 3D model would transcend all these problems, allowing a researcher to examine the statue at his leisure from any viewpoint, to add or remove parts, and to analyze it using computational techniques impossible in reality. All these considerations combined to convince Dr. Wasserman that a digital model would be a valuable tool for his research.

To Dr. Wasserman's goals, we added one of our own: To develop technology that could be used in future projects and form the basis for a practical scanning system accessible to a wide range of users. To that end, we decided to restrict ourselves to inexpensive cameras and computers for both the scanning and analysis of our data.

Scanning and Model Generation

We specifically chose to develop a scanning method based on inexpensive hardware. The base scanner was purchased from Visual Interface Inc. It consists of six black-and-white cameras that capture images of a striped pattern projected on an object by the scanner. Accompanying software computes a triangle mesh from the captured images using principles of stereo computer vision. The scanner also has a color camera mounted on the top, to capture a color image registered with the triangle mesh.

We added a photometric system to the base scanner, consisting of a system of five lights. We capture five additional color images for each mesh, one taken with each of these lights. By comparing the appearance of a surface point under these varying lighting conditions, we can compute surface normals at a higher resolution than the meshes, and extract flat color reflectances that do not include the effects of any single light source. The scanner captures an area approximately 20 cm by 20 cm. Covering the entire surface of the statue therefore required hundreds of meshes. To facilitate the alignment of these small patches, an array of laser dots was projected on the statue to provide fixed landmarks.

Converting the small meshes into a single, coherent model requires a considerable amount of processing. To summarize briefly: We perform a series of operations to align the individual small meshes. We begin by aligning the laser dots, and then refine that result with an automatic technique that essentially matches geometric features on the meshes themselves. A conformance step accounts for measurement errors within each mesh by comparing overlapping meshes. Next, we use our new Ball Pivoting Algorithm to merge the points from all the small meshes into a single triangle mesh. We then use another series of operations to combine all of the photometric normals and colors into a consistent set of texture maps on the surface of the triangle mesh.

Using the Model

Our goal has been to use our model to provide Dr. Wasserman with insights about the statue that he could not obtain by looking at the statue directly or by using traditional photography. Our digital model offers four classes of new capabilities. First, we can provide precisely controlled and impossible views. One goal is to understand how Michelangelo proportioned the statue to suit the view he intended the observer to have. We allow the art historian to examine the proportions from various precisely-defined views, and also from physically impossible views, such as directly above the statue. Second, we can provide precise measurements between points on the statue. The statue itself can not be marked, and a straight line between two points on the statue is often obstructed by other pieces of the statue. On the digital model, specific points can be marked and distances calculated accurately. Third, we can generate images of the statue as it would appear in environments other than the museum in which it is exhibited today. For example, we can produce an image of how it may have looked when it was displayed out-of-doors. Finally, we can alter the statue itself. We can disassemble it, taking away the parts of the statue that were restored by Calcagni. The art historian can then view the statue as it was after Michelangelo removed those limbs. We can change the color of the statue, perhaps to give it a virtual cleaning. All of these capabilities can be provided by a technician working with the art historian.

Our ultimate goal, however, is to let the art historian interact with the model directly. The complete model, with 14 million triangles and more than 1 gigabyte of additional surface details, cannot be displayed interactively on any system currently available and is far beyond the capabilities of a laptop computer. We are developing a viewer that avoids these limitations. The left window displays a geometrically-simplified version of the statue, which the user can navigate interactively. The user can frame an area to examine in more detail; the detail is computed by a server from the full-resolution model and appears in the right window. In this second view, the user can drag the mouse to interactively change the direction of the incident light in order to examine small bumps and ridges.

The final results of our project appear in Dr. Wasserman's book, published by Princeton University Press.