Open Competition 3 - Information Technology (September 2002)

Geometric Surface Classification and Identification by Conformal Structure

Sponsor: Geometric Informatics Inc.

• Project duration: 5/1/2004 - 4/30/2007
• Total project (est.): $2,515,976.00
• Requested ATP funds: $1,915,976.00

Although people do it fairly well, teaching a computer to recognize a complex, three-dimensional object (such as a human face) from a variety of angles and views under a variety of lighting conditions has proven notoriously difficult. Automated facial recognition systems and their failures have attracted a lot of attention, but they are just one aspect of a much larger domain - the general problem of classifying and identifying complex, 3-D geometric surfaces by computer. Typical applications include 3-D surface matching for facial ID recognition, analyzing brain scan images for certain diseases, efficient rendering of 3D images for movies and computer games, and even powering a web search engine for 3D "virtual reality" web pages (VRML). Geometric Informatics proposes a radically new approach to these tasks based on recent developments in Riemannian geometry in mathematics and computational conformal geometry in computer science. GI's approach utilizes the Riemann surface structure of surfaces which describes the intrinsic geometric properties of surfaces. GI has invented practical algorithms that completely compute out the Riemann surface structure for general surfaces for the first time in history. All surfaces can be naturally classified by their Riemann surface structure (or conformal structure), the equivalent classes form a finite dimensional space, and each class can be identified by a small set of parameters - conformal invariants. This allows a large-scale 3-D image database to be indexed and searched efficiently. GI's approach relies only on the geometry of the surface to determine correspondence. In principle it is unaffected by variation in aspect angles, lighting, image resolution, or even the posture of the object. Occlusion - a major stumbling block of other techniques - is less of an issue because only portions of the target are needed to obtain an accurate match. The fundamental research challenges are to take an academic result and reduce it to a set of efficient, practical algorithms that are both fast and reliable enough for real-world applications. Rapid searching of huge databases of geometric data is another key issue, requiring a refined indexing method to locate matches as rapidly as possible. If successful, GI researchers expect to achieve a system of algorithms which can process geometric surfaces in three dimensions and match them with a success rate of better than 99 percent; current state of the art is closer to 47 percent using 3-D image-processing techniques. In addition to obvious applications in biometrics and face-recognition security systems, GI's technology is expected to have broad applications in 3D database management for industry, in searching and indexing VRML web sites, and in medical image analysis. The algorithms also could reduce drastically the computation requirements for 3D rendering, enabling a major impact on the movie industry, video games, and mobile communication devices. A particularly novel potential application is "3D ink", a technique for rendering three-dimensional information in a two-dimensional image so that, for example, a finely detailed 3D image of a new car could be printed inexpensively in coded form in the pages of a car magazine where readers could scan it into their computers and with a simple application reconstruct the surface. A small start-up company with limited resources, Geometric Informatics does not have the resources to pursue this work without ATP support. Venture capital firms have shied away from the perceived high risk of the development work.

For project information:

Dr. Hugh Rutledge, (617) 623-2033
hugh@intlpress.com

ATP Project Manager

Jack Boudreaux, (301) 975-3560
jack.boudreaux@nist.gov