Point-Cloud 3D Modeling

3D Model Representation This approach aims to represent 3D models as an unstructured set of points. Each has A position, A Color, A normal, etc. This representation is simple, a model is a set of sample points. However, this representation is not compact not easy to process or render

Acquisition This representation is often the output of various scanning devices Stereo Illumination Structured Lighting 3D laser Scanners

Structured Light for 3D Scanning A structured light scanning system containing a pair of digital cameras and a single projector, Two images of an object illuminated by different bit planes of a Gray code structured light sequence A reconstructed 3D point cloud. Courtesy: G. Taubin & D. Lanman

Laser Scanners Scanning System Processing : workflow

Laser 3D Scanner 3D Laser Scanning is a cost effective way to gather high accuracy 3D data real models.  A 3D Laser Scanning systems will quickly capture millions of points to be used to create Polygon Models, IGES / NURBS Surfaces, or for 3D Inspection against an existing CAD model.

Large Scale Scanning Car-mounted Laser scanner Scanned Data

Large Scale Datasets

Surface Reconstruction Space Subdivision Schemes Uniform grid Octree Kd-Tree Voronoi Diagram

Voronoi Cell of x Voronoi Diagrams Voronoi edge Voronoi vertex Voronoi Cell of x The set of points that are closer to x than to any other sample point

Medial Axis Medial Axis: Find all circles that tangentially touch the curve in at least 2 points Medial axis = centers of all those circles

Surface Reconstruction Preliminaries: ε-sampling f(x) ≡ feature size at point x = distance to the medial axis at point x Sampling criterion: each sample point x is at most εf(x) from the next closest sample (0 < ε < 1, typically). Important note: When ε is small, the curve locally looks flat f(x) x

Surface Reconstruction: Curve Reconstruction Algorithm: Find the closest point, p, to x and connect them Find the closest point, q, to x such that the angle pxq is at least 90°. Guaranteed to work when ε ≤ ⅓ p x q

Surface Reconstruction: Cocone Algorithm p+ p+ ≡ pole of p = point in the Voronoi cell farthest from p ε < 0.1 → the vector from p to p+ is within π/8 of the true surface normal The surface is nearly flat within the cell p Voronoi cell of p

Sample Reconstructed Surfaces