April 18, 2003

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Publications in Computational Geometry on Surface Reconstruction:

• Point clouds, Surface Reconstruction, and Differential Geometry: two selected topics, F. Cazals.
• Why is 3D scanning hard? Keynote speaker: Marc Levoy.
• Shock Scaffold Segregation and Surface Recovery, by F. Leymarie & B. Kimia.

BibTeX references.

Surface Reconstruction is the process which consists of turning a 3D point cloud into a surface, either triangulated, defined implicitly, or defined parametrically. Most surface reconstruction methods rely at some point upon estimates of differential quantities, so that several interesting questions lie at the crossroads of surface reconstruction and applied differential geometry. This talk will discuss two of them. In the first part, we will recall the fundamentals of the so-called natural interpolation method, and will discuss its application to surface reconstruction. In the second part, we will present a provably good algorithm to estimate local differential properties of any fixed order over a sampled smooth surface. The method consists of fitting the local representation of the manifold using a jet --- i.e., a truncated Taylor expansion, using either a polynomial interpolation or approximation.

Improvements in optical rangefinding technology have made it easy to acquire dense 3D samples of an object or scene. However, a fully automated procedure for assembling this data to create a geometric model still eludes us. This is especially true for large or complicated objects scanned under non-laboratory conditions. For example, although Stanford's Digital Michelangelo Project produced some nice models, it did not achieve many of its stated objectives.

In this talk, I briefly survey the unsolved problems of 3D scanning. For some of these problems, well defined solutions exist, and steady progress can be made on them. Examples of this type include calibration of scanning platforms, multi-view registration, surface reconstruction, view planning, and the handling of large datasets. For other problems, solutions exist but the problem is usually badly conditioned due to noise. Examples of this type include multi-view registration in the presence of scanner miscalibration, estimation of surface reflectance, and the scanning of optically uncooperative materials. In still other cases, the problem itself is ill-posed, admitting multiple correct answers. Classic examples of this type are surface reconstruction in the presence of missing data (i.e. holes), and estimation of surface shape and reflectance in the presence of interreflections or subsurface scattering. Finally, there are problems for which no good solutions exist, such as scanning geometrically convoluted objects, and insuring safety for the objects being scanned.

I end with a (mostly) upbeat assessement of the long-term prospects for 3D scanning and some predictions concerning its likely impact on industry and popular culture.

• Abstract.
   
• HTML presentation

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Comments, suggestions, etc., mail to: leymarie@lems.brown.edu