Hierarchical Isocontours Extraction and Compression Thomas Lewiner 1

Hierarchical Isocontours Extraction and Compression Thomas Lewiner 1, 2, Luiz Velho 3, Hélio Lopes 1, Vinícius Mello 3 1 PUC-Rio — Departamento de Matemática 2 INRIA — Géométrica Project (France) 3 IMPA — Laboratório Visgraf SIBGRAPI - SIACG 2004 9/15/2020

2 Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Encoding an isocontour is cheaper than encoding the whole image Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

3 Outline Hierarchical Extraction : Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction • Regular Binary Multi-Triangulation • Geometry and Topology Controls Progressive Compression : • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

4 Prior Work: Hierarchical Extraction • Implicit domain in multi-resolution : quad-trees (Lopes et al, 2002) Motivation Prior Works Hierarchical Extraction • Curve simplification: Douglas-Peucker 1973, Wu-Márquez 2003. • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 → Binary Multi-Triangulation: Mello et al. 2003. Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

5 Prior Work: Progressive Compression • Signal Map + vector displacement: Bossen, Le Buhan and Ebrahimi 1997 Motivation Prior Works Hierarchical Extraction • Chain Code: Freeman 1974 • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 → Encode the signal along the multiresolution curve Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

6 Extraction Regular Binary Multi-Triangulation Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Regular data set Irregular data set Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

7 Hierarchy Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Multi-Triangulation → Multiresolution curve Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

8 Geometry Control Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control No control Distortion Control Curvature Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Curvature Control Distortion Control Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

9 Topology Control Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction No control Topology Control Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

10 Progressive Compression • Encodes only the tubular neighbourhood Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control • Encodes along with the curve Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

11 Uniform coarser Resolution Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction 59 bits (8 bytes) Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

12 Adaptive coarser resolution 40 bytes Compression Decompression Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

13 Refinements Compression +16 bytes Decompression Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

14 Prediction Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Parabola fitting on the decoder's points. Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

15 Results Motivation Prior Works Hierarchical Extraction • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

16 Extensions Motivation Prior Works Hierarchical Extraction • • • Isosurfaces n. D level sets Enhance prediction Improve arithmetic encoder Automatic tuning • Geometry Control • Topology Control Progressive Compression • Coarser Resolution • Refinements • Prediction Results SIBGRAPI - SIACG 2004 Hierarchical Isocontours Extraction and Compression – T. Lewiner, L. Velho, H. Lopes and V. Mello

Thank you! SIBGRAPI - SIACG 2004 9/15/2020