Segmentation and Geometry of 3D Scenes from Unorganized Point Clouds George Kamberov Department of Computer Science Stevens Institute of Technology Hoboken, NJ USA We present a new method for defining orientation and topology (a collection of neighborhoods), and assigning principal curvature frames, and mean and Gauss curvatures to the points of an unorganized 3D point-cloud. The neighborhoods are estimated by measuring implicitly the surface distance between points. The 3D shape recovery is based on conformal geometry, works directly on the cloud, and does not rely on the generation of polygonal or smooth models. The implicit surface distance estimate is used to define a metric for scoring how well an orientation and topology fits a given cloud.