1. Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi

2. Motivation Quaternion Representation of Colour How effective is it?

3. Quaternion Colour • Quaternions for color representation • Very nice theoretically • Sangwine [Electronics Letters 98] • Previous quaternion colour uses • Simple colour image filtering and edge detection, correlation, compression(Sangwine [ICIP 2000, EUSIPCO2000, ICIP’99], Pei[ICIP03]) We’re testing quaternion colour representation on texture segmentation

4. Problem • Segment images containing • Regions of different colour • Regions of different structure • Our focus is more on colour representation than texture • Texture as a testbed

5. Problem • Best texture segmentation features? • Hoang suggests combining • Colour information • Spatial structure information • Quaternion texture • Integrates colour and structure • Single representation

6. Quaternions • Quaternions … • Type of hypercomplex number • Generalization of complex numbers • Have one real part and three imaginary parts • i.e. • An RGB colour is represented by a pure quaternion

7. Quaternions • A picture of quaternions • Quaternion axes in 4D space • Pure quaternion for colour real i Orthogonal in 4D j k i “pure” = zero real part j k

8. Quaternions • Recently proposed QSVD/QPCA • Sangwine[ICIP03], Pei[ICIP03] • Generalization of complex PCA • QPCA for dimension reduction • Similar to PCA for real numbers Quaternion texture can be described in low dimensional space

9. Colour Texture • Why quaternions? • Motivation • Unified representation of colour • Applicable to different colour spaces • E.g. (R,G,B) or (L,M,S) • Sangwine’s methods have been useful • Interesting to try quaternions for texture

10. Colour Texture • Hoang’s colour texture • Local Gabor filters • In wavelength-Fourier domain • PCA for feature dimension reduction • Quaternion colour texture • Nicely integrates colour and structure • Quaternions help unify the representation

11. Colour Image Segmentation • Feature Extraction • QPCA based features • Texture Clustering • K-means clustering • Region Merging • Reduction of the number of regions • Post-processing • Boundary removal

12. Colour Image Segmentation • Feature Extraction • QPCA based features • Texture Clustering • K-means clustering • Region Merging • Reduction of the number of regions • Post-processing • Boundary removal

13. Surprisingly, need only the first basis texture element QPCA Image-specific quaternion texture basis Texture Feature Extraction • Training Sampled sub-windows

14. 1st QPCA Basis texture element Feature Extraction • Texture Representation T Single quaternion A texture patch

15. Feature Extraction • Feature image

16. Colour Image Segmentation • Feature Extraction • QPCA based features • Texture Clustering • K-means clustering • Region Merging • Reduction of the number of regions • Post-processing • Boundary removal

17. Texture Clustering • Cluster quaternion pixels • k-means • K > expected number of regions • E.g., k=15 • Every pixel is classified

18. Colour Image Segmentation • Feature Extraction • QPCA based features • Texture Clustering • K-means clustering • Region Merging • Reduction of the number of regions • Post-processing • Boundary removal

19. Region Merging • Similar regions are merged • Image is over-segmented (k = 15) • Merge 2 most similar regions until • < 3 segments • Threshold is reached

20. Colour Image Segmentation • Feature Extraction • QPCA based features • Texture Clustering • K-means clustering • Region Merging • Reduction of the number of regions • Post-processing • Boundary removal

21. Post-processing • Misclassification is inevitable near region boundaries • Misclassified area • small region • straddles two regions Boundaries removed

22. Results Quaternion method Hoang’s method

23. Results

24. Results

25. The Quaternion Advantage Hoang’s Method Quaternion Method

26. Conclusion • Explored quaternion colour representation • Texture segmentation as a testbed • Results comparable to more complex methods • Quaternion colour • Elegant representation • Colour as a unit instead of 3 independent channels • Shown to be effective in practice