Isosurface Similarity Map

1. Isosurface Similarity Map Eurographics/ IEEE-VGTC Symposium on Visualization 2010 Reporter: Tzu-Hsuan Wei

2. Objective • Find out salient, representative isosurfaces • Conventional method: histogram • Similarity from the frequency of isovalues • Using information-theoretic measure of mutual information based on distance field. • To investigate the similarity between individual isosurfaces directly

3. Similarity measure • mutual information is a quantity that measures the mutual dependence of two random variables. • the mutual information is equal to the uncertainty associated with the random variable, i.e. entropy

4. Entropy Calculation based on distance field • Construct a 2D histogram based on distance field • Suppose we want to find out the similarity between the isosurface which isovalue is X and Y minimum distance from the voxel to isosurface Y Dx: minimum distance from the voxel to isosurface X Dy: minimum distance from the voxel to isosurface Y Increment the value of (Dx,Dy) position by 1 in the 2D histogram (Dx,Dy) minimum distance from the voxel to isosurface X

5. Create isosurface • Use the code from Prof. Rephael Wenger's website • First, I create a GUI in Matlab in order to show two different isosurfaces.

6. Isosurface Similarity map (simulation) Similarity distribution Similarity Map

7. Revisiting Histograms and Isosurface Statistics

9. Image Order

11. Further research • Selection of salient isosurfaces algorithm • Suppose every voxel has a path to any isosurfaces (along the gradient direction) • Different distanced field methods • Mahalanobis distance: takes into account the correlations of the data set

12. Lower similarity higher similarity

13. Future work • Apply to some medical images • Data size is too large • Too slow • A 128x128x58 image takes 4 hours • Implement in CUDA

14. Any Question ?