spatial subdivision techniques sampl group presentation by gerald dalley
TRANSCRIPT
Spatial Subdivision Techniques
SAMPL Group PresentationBy Gerald Dalley
6 Feb 2001 2Spatial 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)
6 Feb 2001 3Spatial Subdivision Techniques
Correspondence Searching in Range Image Registration:
Range Image Registration
6 Feb 2001 4Spatial Subdivision Techniques
Correspondence Searching in Range Image Registration:
Range Image Registration (cont.)
6 Feb 2001 5Spatial Subdivision Techniques
Correspondence Searching in Range Image Registration:
Correspondence Search
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6 Feb 2001 6Spatial Subdivision Techniques
Nearest-Neighbor Searches in Matching
Images from http://avalon.viewpoint.com/
Feature X
Featu
re
Y
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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
6 Feb 2001 8Spatial Subdivision Techniques
Spatial Subdivision Techniques:
Uniform Subdivision
6 Feb 2001 9Spatial Subdivision Techniques
Spatial Subdivision Techniques:
Octrees (shown as a Quadtree)
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Spatial Subdivision Techniques:
k-D Trees
6 Feb 2001 11Spatial Subdivision Techniques
Spatial Subdivision Techniques:
Binary Space Partitioning (BSP) Trees
1
2l
2r
3rl3lr
3rr
3ll
6 Feb 2001 12Spatial Subdivision Techniques
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