Spatial Subdivision Techniques

SAMPL Group PresentationBy Gerald Dalley

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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)

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Correspondence Searching in Range Image Registration:

Range Image Registration

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Correspondence Searching in Range Image Registration:

Range Image Registration (cont.)

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Correspondence Searching in Range Image Registration:

Correspondence Search

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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

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Spatial Subdivision Techniques:

Uniform Subdivision

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Spatial Subdivision Techniques:

Octrees (shown as a Quadtree)

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Spatial Subdivision Techniques:

k-D Trees

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Spatial Subdivision Techniques:

Binary Space Partitioning (BSP) Trees

1

2l

2r

3rl3lr

3rr

3ll

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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