1. Spatial Subdivision Techniques SAMPL Group Presentation By Gerald Dalley

2. 6 Feb 20012Spatial Subdivision Techniques Presentation Overview Motivation Correspondence Searching in Range Image Registration Nearest-Neighbor Searches in Matching What’s Wrong with Brute Force? Spatial Subdivision Techniques Uniform Subdivision-- O(1) to O(N) Octrees -- O(log N) k-D Trees -- O(log N) BSP Trees -- O(log N)

3. 6 Feb 20013Spatial Subdivision Techniques Correspondence Searching in Range Image Registration: Range Image Registration

4. 6 Feb 20014Spatial Subdivision Techniques Correspondence Searching in Range Image Registration: Range Image Registration (cont.)

5. 6 Feb 20015Spatial Subdivision Techniques Correspondence Searching in Range Image Registration: Correspondence Search ? ? ? ? ? ? ? ? ? ? ?

6. 6 Feb 20016Spatial Subdivision Techniques Nearest-Neighbor Searches in Matching Images from http://avalon.viewpoint.com/ Feature X Feature Y

7. 6 Feb 20017Spatial Subdivision Techniques Spatial Subdivision Techniques: Why Bother? O(N) vs. O(log N) Nearest-neighbor searches Range Image Registration DAGSI and Billion-Point Data High-dimensional feature-based object/image matching Ray-object intersections Range Image Registration Ray tracing Volumetric object representations

8. 6 Feb 20018Spatial Subdivision Techniques Spatial Subdivision Techniques: Uniform Subdivision

9. 6 Feb 20019Spatial Subdivision Techniques Spatial Subdivision Techniques: Octrees (shown as a Quadtree)

10. 6 Feb 200110Spatial Subdivision Techniques Spatial Subdivision Techniques: k-D Trees

11. 6 Feb 200111Spatial Subdivision Techniques Spatial Subdivision Techniques: Binary Space Partitioning (BSP) Trees 1 2l 2r 3rl 3lr 3rr 3ll

12. 6 Feb 200112Spatial Subdivision Techniques For Further Information… Foley, van Dam, Feiner, Hughes. Computer Graphics: Principles and Practice. Addison-Wesley. 2 nd Ed. 1992. (newer edition available too) Uniform Subdivision Octrees BSP Trees Intersection tests Jerome H. Friedman, Jon Louis Bentley, and Raphael Ari Finkel. “An Algorithm for Finding Best Matches in Logarithmic Expected Time.” ACM Transaction on Mathematical Software, 3(3):209–226, September 1977. k-D Trees Michael Abrash. Michael Abrash’s Graphics Programming Black Book. BSP Trees