About a year ago I participated in a seminar about computer graphics. From now on you can download my results, check the links below. I worked on the topic described in
Parameterization-free Projection for Geometry Reconstruction
Yaron Lipman, Daniel Cohen-Or, David Levin, Hillel Tal-Ezer
ACM Trans. Graph., Vol. 26, No. 3, Article 22, July 2007
It’s about an operator that can be used in context of the 3D scanning problem. When scanning shapes, the 3D-scanner often just produces a set of points (a point cloud). Multiple scans from different positions are required to reach all surface points of the scanned shape. They lead to multiple sets that have to be combined into the final point cloud. Such a combination could increase noise and other errors.
The operator can rework such a point cloud to improve it’s quality. As input this operator only requires the coordinates of the points, no further properties like normal vectors or other local orientation data. It is a projection operator since it projects a given point set X onto another point set P. A slightly exaggerated example of such a projection is shown in the following figure.
The projected set approximates the surface defined by the points in P quite well. Furthermore the projected points are nicely distributed. An example for such a distribution improvement is given in the next figure, where the Stanford Bunny from the Stanford 3D Scanning Repository is shown.
One possible application for such an operator is down-sampling, where |X| is small compared to |P|. Similarly up-sampling can be performed by choosing |X| larger than |P|. Another application was already noted above: Preprocessing of a given point set to make it more suitable for some other method or application.
More information, including a detailed elaboration of the original paper’s proof, are in my term paper linked below. However it is only available in German for now. The other download link leads to my program MNGeoRecon which implements the presented method. The program is written in English and requires Windows, Java, Java3D.
Download-Link: MNGeoRecon 1.2
Download-Link: MNGeoRecon - Term paper (German)
Update: Check the FAQ for details on Java and Java3D installations.