Spatial Subdivision Techniques SAMPL Group Presentation By Gerald

Spatial Subdivision Techniques SAMPL Group Presentation By Gerald Dalley

Presentation Overview Motivation n Correspondence Searching in Range Image Registration Nearest-Neighbor Searches in Matching What’s Wrong with Brute Force? Spatial Subdivision Techniques n Uniform Subdivision -- O(1) to O(N) Octrees -- n k-D Trees -- n BSP Trees -- n O(log N) O(log 6 Feb 2001 N) Spatial Subdivision Techniques 2

Correspondence Searching in Range Image Registration: Range Image Registration 6 Feb 2001 Spatial Subdivision Techniques 3

Correspondence Searching in Range Image Registration: Range Image Registration (cont. ) 6 Feb 2001 Spatial Subdivision Techniques 4

Correspondence Searching in Range Image Registration: Correspondence Search ? ? ? ? ? 6 Feb 2001 Spatial Subdivision Techniques 5

Nearest-Neighbor Searches in Matching Feature Y Feature X Images from http: //avalon. viewpoint. com/ 6 Feb 2001 Spatial Subdivision Techniques 6

Spatial Subdivision Techniques: Why Bother? O(N) vs. O(log N) Nearest-neighbor searches n n n Range Image Registration DAGSI and Billion-Point Data High-dimensional feature-based object/image matching Ray-object intersections n n Range Image Registration Ray tracing Volumetric object representations 6 Feb 2001 Spatial Subdivision Techniques 7

Spatial Subdivision Techniques: Uniform Subdivision 6 Feb 2001 Spatial Subdivision Techniques 8

Spatial Subdivision Techniques: Octrees 6 Feb 2001 (shown as a Quadtree) Spatial Subdivision Techniques 9

Spatial Subdivision Techniques: k-D Trees 6 Feb 2001 Spatial Subdivision Techniques 10

Spatial Subdivision Techniques: Binary Space Partitioning (BSP) Trees 3 rl 3 lr 2 r 2 l 3 rr 3 ll 1 6 Feb 2001 Spatial Subdivision Techniques 11

For Further Information… Foley, van Dam, Feiner, Hughes. Computer Graphics: Principles and Practice. Addison-Wesley. 2 nd Ed. 1992. (newer edition available too) n n 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. n k-D Trees Michael Abrash’s Graphics Programming Black Book. n BSP Trees 6 Feb 2001 Spatial Subdivision Techniques 12