Adaptive Simplification of 3D Models using Multiresolution Analysis

1. Adaptive Simplification of 3D Modelsusing Multiresolution Analysis Michaël Roy

2. Outline • Introduction • Multiresolution Analysis • Multiresolution decomposition • Attribute analysis • Model Characterization • Adaptive Simplification • Conclusion and Future Work

3. Motivation • Acquisition of high quality models representing the real world • High density meshes • High resolution textures • Visualization and storage of these models • Geometric simplification of the meshes • Conservation of the “relevant information” Introduction

4. Exemple of High Quality Model Texture 3D mesh + 184 429 faces 16 MB storage (VRML) 256 x 512 pixels 22 KB storage (JPG) Introduction Model “Jared”: courtesy Brad Grinstead

5. Previous Work in literature • Geometric driven simplification • Many algorithms (Cignoni 1998) • Global simplification • User guided simplification (Kho & Garland 2003) • Attribute driven simplification • Works great for colors • Doesn't manage texture content • Toubin's adaptive simplification of range images • Manage texture content Introduction

6. Level of detail representation Detail extraction Localisation of relevant information Segmentation Adaptive Simplification Framework 3D model with attributes Multiresolution Analysis Characterization Adaptive simplification 3D simplified model Introduction

7. Outline • Introduction • Multiresolution Analysis • Multiresolution decomposition • Attribute analysis • Model Characterization • Adaptive Simplification • Conclusion and Future Work

8. Multiresolution Analysis • Widely used for signal and image • Recently adapted for 3D irregular meshes • Level of detail decomposition • Frequency content assessment • Applications • Filtering, compression, feature detection,.... Multiresolution Analysis

9. V0 V1 W1 Synthesis (Reconstruction) Analysis (Decomposition) V2 W2 V3 W3 Vi Approximation Wi Details Multiresolution Analysis Scheme Multiresolution Analysis

10. Multiresolution Mesh Analysis • Decompose a mesh into different resolution levels • Detail extraction 5 3 0 high low Detail magnitude Multiresolution Analysis

11. Downsampling / Upsampling • We need: • downsampling operator for decomposition • upsampling operator for reconstruction Edge contraction Vertex split Multiresolution Analysis

12. Resolution Level Construction • We use a global downsampling method to define different levels of resolution • Select an independent set of vertices • Remove them using edge contractions Multiresolution Analysis

13. Example of Global Downsampling level 1 level 2 level 3 level 0 Green points: locked vertices composing the next level (even vertices) Red points: selected vertices to be removed (odd vertices) Multiresolution Analysis

14. Detail Computation • To compute the details of each level, we need to predict the odd vertices of the next finer level • The details are the difference between the initial odd vertices and the predicted ones • The odd vertices are predicted using a non-uniform subidivision • We can think of the details as frequencies and of the levels of details as frequency bands • The coaser the level, the lower the frequencies Multiresolution Analysis

15. Prediction of Odd Vertices • We use a relaxation operator minimizing the normal curvature of the odd vertices i,j i,j Multiresolution Analysis

16. Prediction of the Attributes • We can predict the attributes of the odd vertices by extending the relaxation operator • Attributes are relaxed according to the surface normal curvature

17. Outline • Introduction • Multiresolution Analysis • Multiresolution decomposition • Attribute analysis • Model Characterization • Adaptive Simplification • Conclusion and Future Work

18. low high Detail magnitude Localisation of Relevant Information • Details with high magnitude represent relevant information Geometry Texture 432 Texture 751 Model Characterization

19. Segmentation of Details • Detail thresholding Initial details Relevant information Thresholded details Model Characterization

20. Outline • Introduction • Multiresolution Analysis • Multiresolution decomposition • Attribute analysis • Model Characterization • Adaptive Simplification • Conclusion and Future Work

21. Principles • Relevant information are locked and will not be removed • Multiresolution analysis creates a pyramid of nested levels • Vertex hierarchy can be represented as a binary tree (called vertex forest) • The vertex forest allows dynamic adaptive simplification (for visualization purpose) Adaptive Simplification

22. Vertex Forest Simplification Adaptive Simplification

23. Result 131 242 faces (6.8 MB) 36 772 faces (1.9 MB) Adaptive Simplification

24. Outline • Introduction • Multiresolution Analysis • Multiresolution decomposition • Attribute analysis • Model Characterization • Adaptive Simplification • Conclusion and Future Work

25. Conclusion • Multiresolution analysisis sensible to noise, which leads to an improper simplification • Need a better segmentation to remove isolated and special cases (usage of morphological operators solve this issue in part) • Need automatic detail thresholding • Simplification using vertex forest still unstable Conclusion and Future Work

26. Future Work • Improve the detail segmentation • Combine geometric and texture details • Extend the scheme to adaptive visualization • Publication on Wavelet Applications in Industrial Processing, part of the SPIE International Symposium on Photonics Technologies for Robotics, Automation, and Manufacturing Conclusion and Future Work

27. Adaptive Simplification of 3D Modelsusing Multiresolution Analysis Michaël Roy