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Spatial Subdivision Techniques

Spatial Subdivision Techniques. SAMPL Group Presentation By Gerald Dalley. Presentation Overview. Motivation Correspondence Searching in Range Image Registration Nearest-Neighbor Searches in Matching What’s Wrong with Brute Force? Spatial Subdivision Techniques

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Spatial Subdivision Techniques

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  1. Spatial Subdivision Techniques SAMPL Group Presentation By Gerald Dalley

  2. 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) Spatial Subdivision Techniques

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

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

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

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

  7. 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 Spatial Subdivision Techniques

  8. Spatial Subdivision Techniques:Uniform Subdivision Spatial Subdivision Techniques

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

  10. Spatial Subdivision Techniques:k-D Trees Spatial Subdivision Techniques

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

  12. For Further Information… • Foley, van Dam, Feiner, Hughes. Computer Graphics: Principles and Practice. Addison-Wesley. 2nd 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 Spatial Subdivision Techniques

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