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Geometry Synthesis

This research paper explores the synthesis of new geometry that closely resembles an input geometry, using a fast matching algorithm based on distance fields. It extends the concept of texture synthesis to geometry synthesis. The paper includes results and future directions for improving mesh reconstruction and porting applications from texture synthesis to geometry synthesis.

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Geometry Synthesis

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  1. Geometry Synthesis Ares Lagae Olivier Dumont Philip Dutré Department of Computer Science Katholieke Universiteit Leuven 10 August, 2004

  2. Introduction synthesized texture example texture texture synthesis (images by Wei & Levoy, SIGGRAPH 2000)

  3. Introduction synthesized geometry example geometry geometry synthesis Given an example of input geometry, synthesize new output geometry that is perceived similar to the input geometry.

  4. Related Work • Procedural modeling • Texture synthesis • Pixel based • Patch based • Bidirectional texture function synthesis

  5. Texture Synthesis Pixel Based synthesized texture example texture copy pixel find best match Efros & Leung 1999, Wei & Levoy 2000, ...

  6. Texture Synthesis Patch Based synthesized texture example texture merge overlap copy patch find best match Liang et al. 2001, Efros & Freeman 2001, ...

  7. Design Decisions • Geometry representation ? • triangle mesh ? • Geometry representation ? • surfels ? • Geometry representation ? • voxel grid ? • Geometry representation ? • regularly sampled distance field (images by Frisken et al., SIGGRAPH 2000)

  8. Design Decisions • Geometry representation ?  regularly sampled distance field • Unit of synthesis ?  block (~ patch in texture synthesis) • Finding similar blocks ?  geometry matching algorithm

  9. System Overview example geometry synthesized geometry find best match copy block mesh distance field synthesized distance field geometry matching algorithm

  10. ... Geometry Matching Algorithm The Problem feature vector size ≈½(neighbourhood size) ² texture synthesis 40 9 x 9 size = (block size) ³ geometry synthesis 9 x 9 x 9 32 x 32 x 32 729 32768

  11. ... similarity decreases ... ... ... Geometry Matching Algorithm Key Idea similarity ?

  12. Geometry Matching Algorithm Search Tree Construction ... all possible blocks (includes overlapping blocks)

  13. Geometry Matching Algorithm Search Tree Construction ... ... ...

  14. Geometry Matching Algorithm Search Algorithm ... ... ... similarity decreases priority queue

  15. Geometry Matching Algorithm Performance • Up to ≈ 5000 times faster than a brute force linear search • Speedup is data dependent • Works very good for distance fields

  16. Geometry Construction example synthesized distance field matching ∕∕ geometry construction geometry

  17. Geometry Synthesis Results

  18. Geometry Synthesis Results

  19. Geometry Synthesis Results

  20. Geometry Synthesis Results

  21. Geometry Synthesis Results

  22. Geometry Synthesis Results

  23. Geometry Synthesis Results

  24. Geometry Synthesis Conclusion • Extended texture synthesis to geometry synthesis • Fast geometry matching algorithm using distance fields

  25. Geometry Synthesis Future Work • Better mesh reconstruction • Port applications of texture synthesis to geometry synthesis • Synthesize geometry over a mesh

  26. Thank You! • Questions ? technical report available at http://www.cs.kuleuven.ac.be/~graphics

  27. Some Numbers

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