1. Reducing Artifacts in Surface Meshes Extracted from Binary Volumes R. Bade, O. Konrad and B. Preim efficient smoothing of iso-surface meshes Plzen - WSCG 2007 - Feb. 1st

2. Reducing Artifacts in Surface Meshes – Ragnar Bade2/16 CONTENT Motivation State of the Art Reconstruction of Volume Data Information Constrained Artifact Reduction Conclusion

3. Reducing Artifacts in Surface Meshes – Ragnar Bade3/16 discrete image resolution binary segmentation MOTIVATION Artifacts in Surfaces of Binary Volumes

4. Reducing Artifacts in Surface Meshes – Ragnar Bade4/16 STATE OF THE ART Reduction of Artifacts at: voxel level mesh extraction mesh level binary segmentation filtering of binary volume mesh extractionmesh filtering voxel-levelmesh-level

5. Reducing Artifacts in Surface Meshes – Ragnar Bade5/16 Taubin λ/μ-filter STATE OF THE ART Smoothing of Surface Meshes smoothing may not remove artifacts but may remove relevant details smooth but still correct surfaces are needed Gauss-kernel 5x5x5

6. Reducing Artifacts in Surface Meshes – Ragnar Bade6/16 ALGORITHM IDEA terraces stairs properties of the binary volume are still inherent in extracted surfaces reconstruction of volume properties (cell size, center and edges) mesh smoothing constrained to volume data properties

7. Reducing Artifacts in Surface Meshes – Ragnar Bade7/16 SURFACE EXTRACTION Marching Cubes for Binary Volumes cell based approach linear interpolation on cell edges

8. Reducing Artifacts in Surface Meshes – Ragnar Bade8/16 RECONSTRUCTION Cell Size Determination  cell size influences distance between vertices MC only creates vertices at cell edges cell size corresponds to vertex distance in each dimension

9. Reducing Artifacts in Surface Meshes – Ragnar Bade9/16 RECONSTRUCTION Cell Center Determination  by identifying one defined cell case detect vertex with minimal x,y,z position compute cell center derive cell center for another vertex from its distance to the found cell center

10. Reducing Artifacts in Surface Meshes – Ragnar Bade10/16 RECONSTRUCTION Cell Edge Determination detect the edge of the cell a vertex is located on vertices are located at three orthogonal planes simple sign check of distance from center c

11. Reducing Artifacts in Surface Meshes – Ragnar Bade11/16 RECONSTRUCTION Drawbacks skewed, rotated, and other arbitrary manipulated meshes can not be processed correctly Opportunities reconstruction of binary volume constrained smoothing of the surface mesh

12. Reducing Artifacts in Surface Meshes – Ragnar Bade12/16 CONSTRAINED MESH SMOOTHING Cell Size Constraint constrain vertex movement to ±½(∂x, ∂y, ∂z) -incorrect representation +max displacement equals cell diagonal

13. Reducing Artifacts in Surface Meshes – Ragnar Bade13/16 CONSTRAINED MESH SMOOTHING Cell Edge Constraint constrain vertices to remain on cell edges +correct representation -less smoothing

14. Reducing Artifacts in Surface Meshes – Ragnar Bade14/16 DIAMOND CONSTRAINED SMOOTHING Diamond Constraint keep vertices inside a diamond-shaped area diamond axes size corresponds to cell size

15. Reducing Artifacts in Surface Meshes – Ragnar Bade15/16 RESULTS Dataset#Faces#VerticesTimeIterationsmax HDV in % sphere 35k17k1.3 sec760.4199.2 cube 43k21k1.3 sec260.4899.7 aneurysma 53k26k2.6 sec590.4997.1 pelvis104k52k7.4 sec1100.5098.3 bromchial tree165k82k12.5 sec520.4994.4 Pentium 4 processor, 3 GHz | smoothing stopping threshold 0.002

16. Reducing Artifacts in Surface Meshes – Ragnar Bade16/16 CONCLUSION Artifact Reduction in Surface Meshes Extracted from Binary Volumes reconstruction of volume data diamond constrained smoothing reduce artifacts at an earlier stage combine MC and diamond constrained smoothing for surface extraction

17. Thank you for your attention