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. We’re testing quaternion colour representation on texture segmentation
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 QPCA for dimension reduction
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 Quaternion 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. Texture Feature Extraction
Surprisingly, need only the first basis texture element
Training
Image-specific quaternion texture basis
QPCA
Sampled sub-windows

14. Feature Extraction Texture Representation T Single quaternion
1st QPCA Basis texture element
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 Quaternion colour
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