Efficient Storage, Compression and Transmission

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1 Efficient Storage, Compression and Transmission of Complex 3D Models context & problem definition general framework & classification our new algorithm applications for digital documents

2 Mesh Decimation highly detailed meshes laser scanners iso surfaces from CT automatic meshing of CAD models transmit, render, store data reduction without quality reduction efficiency graphics hardware global system performance

3 / / / 3774 Leif Kobbelt Erlangen Nu rnberg Mesh Decimation

4 State of the Art Vertex Removal (remove + triangulate) Re Tiling (redistribute new vertices on the old mesh) Vertex Clustering (quantize space: R 3 > N 3 ) Wavelet Representations (special connectivity)

5 General Framework for Incremental Mesh Decimation topological operation(s) (complexity, flexibility) distance / error measure (conservative, economical) quality criterion performance

6 Schroeder s Mesh Decimation vertex removal error accumulation ordering (?) tri / sec

7 Hoppe s Progressive Meshes edge collapse Hausdorff distance ordering by distance + fairness tri / sec

8 Invertible Topological Operation v l t a v a e v b t b Vertex Split v l v c v r Edge Collapse v r Progressive Meshes Multi Resolution (continuous resolution, discrete resolution)

9 Garland / Heckbert s Mesh Simplification vertex contraction error quadrics ordering by distance 4500 tri / sec

10 The general framework topological operators vertex removal (free triangulation) edge collapse (free position) half edge collapse distance measures local accumulation (over estimate) error quadrics (over/under estimate) one/two sided Hausdorff distance (complex) quality criterion implicit (error tolerance) explicit (curvature energy)

11 A Knapsack Approach half edge collapse cost (binary operation) global error control capacity (one sided (!) Hausdorff distance) > candidate set fairness criteria guidance > priority queue > greedy algorithm

12 Why??? separate topology from geometry exact error tolerances (cf. scattered data interpolation) intuivite handling global error tolerance application dependent fairness smoothness for display roundness for finite elements distance for detail preservation...

13 Discrete Fairness discrete fundamental forms > discrete energy functionals optimal smoothness > minimum bending optimal stability > minimum aspect ratio equal edge length > minimum distorsion maximum detail (with fixed number of triangles) > minimum approx. error color attributes topological distance (independent set)

14

15 Computing the Hausdorff Distance maximum minimum distance (original points to current mesh) assign removed vertices to coarse triangles redistribute vertices by local sweep

16 Applications efficient storage progressive transmission (quick previews) finite elemente analysis (mesh generation, local refinement)

17 871K 6.5K 3.5K

18 continuous transmission of images: continuous transmission of 3d objects:

19 progressive transmission of images: interactive progressive transmission of 3d objects:

20 load adaptive / view dependent display:

21 Reverse Finite Element Mesh Generation...

22 operation planing system / numerical algorithms:

23 ... trade geometry for texture attributes...

24 3D Models in Interactive Applications and Digital Documents games electronic catalogs architectural walk throughs digital mock up the virtual museum electronic clinical records geometric design log books

25 G A M E S! image: courtesy Eidos

26 Electronic catalogue / commerce image: courtesy PC Chips Electronic museum Architectural walk throughs 3d object: courtesy Cytberware

27 Electronic clinical record with 3d objects

28 Car body design log book

29 Conclusion general purpose mesh decimation intuitive parameters (tolerance + fairness) exact global error control (Hausdorff) fast (> 1 K tri / sec) level of detail for arbitrary meshes efficient algorithms mesh hierarchy > interactive multi resolution modeling

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