sa2014.siggraph.org sponsored by. sa2014.siggraph.org sponsored by approximate pyramidal shape...

Download SA2014.SIGGRAPH.ORG SPONSORED BY. SA2014.SIGGRAPH.ORG SPONSORED BY Approximate Pyramidal Shape Decomposition Ruizhen Hu Honghua Li Hao Zhang Daniel Cohen-Or

If you can't read please download the document

Upload: daisy-oneal

Post on 25-Dec-2015

212 views

Category:

Documents


0 download

TRANSCRIPT

  • Slide 1
  • SA2014.SIGGRAPH.ORG SPONSORED BY
  • Slide 2
  • SA2014.SIGGRAPH.ORG SPONSORED BY Approximate Pyramidal Shape Decomposition Ruizhen Hu Honghua Li Hao Zhang Daniel Cohen-Or Simon Fraser UniversityZhejiang UniversityTel Aviv University
  • Slide 3
  • SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal shape 3 Terrain 2.5D Heightfield
  • Slide 4
  • SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal shape 4
  • Slide 5
  • SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 5
  • Slide 6
  • SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 6 3D layered printing
  • Slide 7
  • SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 7 3D layered printing Molding/casting
  • Slide 8
  • SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 8 3D layered printing Molding/casting Point inside/outside testing
  • Slide 9
  • SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 9 3D layered printing Molding/casting Point inside/outside testing
  • Slide 10
  • SA2014.SIGGRAPH.ORG SPONSORED BY However, 10 Many common objects are not pyramidal Pyramidal decomposition
  • Slide 11
  • SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal decomposition Exact pyramidal decomposition Minimum number of pyramidal parts 11 NP-hard NP-hard [Fekete and Mitchell 2001]
  • Slide 12
  • SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal decomposition Approximate pyramidal decomposition Parts being only approximately pyramidal Still aiming to produce as few parts as possible 12
  • Slide 13
  • SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 13 Exact Cover Problem {1234}
  • Slide 14
  • SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 14 {1234} Exact Cover Problem
  • Slide 15
  • SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 15 {1234} 1 2 3 4 Over-segmentation Candidate parts by merging segments Exact Cover Problem
  • Slide 16
  • SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 16 {1234} Pyramidal decomposition Pyramidal Final decomposition Over-segmentation Candidate parts by merging segments Exact Cover Problem
  • Slide 17
  • SA2014.SIGGRAPH.ORG SPONSORED BY Find an appropriate over-segmentation of the shape Build an appropriate set of candidate pyramidal parts Main challenge 17 Infinite possible pyramidal parts
  • Slide 18
  • SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts Minimum-sized decompositions Easier to generate 18
  • Slide 19
  • SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough 19 1 2 34 5 6
  • Slide 20
  • SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough Combination of intersections 20 1 2 34 5 6
  • Slide 21
  • SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough Combination of intersections 21 1 2 34 5 6
  • Slide 22
  • SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough Combination of intersections 22 1 2 34 5 6
  • Slide 23
  • SA2014.SIGGRAPH.ORG SPONSORED BY Algorithm overview 23 Set Collection of subsets Exact cover Intersections
  • Slide 24
  • SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Sample a set of directions Sample a set of bases along each direction 24
  • Slide 25
  • SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Capacity measure 25 Total pyramidal areas Number of decomposed parts
  • Slide 26
  • SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Capacity measure 26
  • Slide 27
  • SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Capability measure Base voting 27
  • Slide 28
  • SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Cell formation Points voted for the same set of bases 28 Estimation of intersections
  • Slide 29
  • SA2014.SIGGRAPH.ORG SPONSORED BY Block construction To further reduce the number of candidate parts Cluster cells into blocks Find the boundaries 29
  • Slide 30
  • SA2014.SIGGRAPH.ORG SPONSORED BY Candidate parts & decomposition Parts are formed by merging blocks Decomposition can be found by solving ECP 30 Blocks Decompositions Candidate parts
  • Slide 31
  • SA2014.SIGGRAPH.ORG SPONSORED BY Results Datasets 149 2D shapes 80 3D shapes 31
  • Slide 32
  • SA2014.SIGGRAPH.ORG SPONSORED BY Results 2D shapes 32
  • Slide 33
  • SA2014.SIGGRAPH.ORG SPONSORED BY Results 3D shapes 33
  • Slide 34
  • SA2014.SIGGRAPH.ORG SPONSORED BY Evaluations 2-pyramidality 25 2D shapes & 30 3D shapes 34
  • Slide 35
  • SA2014.SIGGRAPH.ORG SPONSORED BY Evaluations Comparison to greedy approach 2-pyramidality (2D shapes) 35 Ours: Greedy:
  • Slide 36
  • SA2014.SIGGRAPH.ORG SPONSORED BY Evaluations Comparison to human judgement 30 users & 20 2D shapes 36 OursUser decomposition
  • Slide 37
  • SA2014.SIGGRAPH.ORG SPONSORED BY 3D Printing 37
  • Slide 38
  • SA2014.SIGGRAPH.ORG SPONSORED BY Conclusion A relatively new and unexplored shape property. The first construction algorithm for approximate pyramidal decomposition. The key insight is to turn the problem into a exact cover problem. The bottom-up clustering-based approach is both general and versatile. 38
  • Slide 39
  • SA2014.SIGGRAPH.ORG SPONSORED BY Limitation & further work Realistic waste estimation for 3D printing Pyramidalization Minimal modification to maximally reduce the size of its pyramidal decomposition 39
  • Slide 40
  • SA2014.SIGGRAPH.ORG SPONSORED BY Set Collection of subsets Exact cover Intersections Thank you! Approximate Pyramidal Shape Decomposition Ruizhen Hu Honghua Li Hao Zhang Daniel Cohen-Or