1. Point-Cloud
3D Modeling

2. 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

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

4. 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

5. Laser Scanners
Scanning System
Processing : workflow

6. 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.

7. Large Scale Scanning
Car-mounted
Laser scanner
Scanned Data

8. Large Scale Datasets

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

10. 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

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

12. 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

13. 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

14. Surface Reconstruction: Cocone Algorithmp+
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

15. Sample Reconstructed Surfaces