Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.
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Transcript of Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.
![Page 1: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/1.jpg)
Quaternion Colour Texture
By Lilong Shi and Brian FuntPresented by: Lilong Shi
![Page 2: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/2.jpg)
Motivation
Quaternion Representation of Colour
How effective is it?
![Page 3: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/3.jpg)
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
![Page 4: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/4.jpg)
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
![Page 5: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/5.jpg)
Problem
Best texture segmentation features?Hoang suggests combining
Colour informationSpatial structure information
Quaternion texture Integrates colour and structure
Single representation
![Page 6: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/6.jpg)
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
kbjgirq
kajaiaaa 3210
1
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Quaternions
A picture of quaternionsQuaternion axes in 4D space
Pure quaternion for colour
reali
kj
i
kj
Orthogonal in 4D
“pure” = zero real part
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Quaternions
Recently proposed QSVD/QPCA Sangwine[ICIP03], Pei[ICIP03]Generalization of complex PCA
QPCA for dimension reductionSimilar to PCA for real numbers
Quaternion texture can be described in low dimensional space
![Page 9: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/9.jpg)
Colour Texture
Why quaternions?Motivation
Unified representation of colourApplicable 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
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Colour Texture
Hoang’s colour textureLocal Gabor filters In wavelength-Fourier domainPCA for feature dimension reduction
Quaternion colour textureNicely integrates colour and structureQuaternions help unify the representation
![Page 11: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/11.jpg)
Colour Image Segmentation
Feature ExtractionQPCA based features
Texture ClusteringK-means clustering
Region MergingReduction of the number of regions
Post-processingBoundary removal
![Page 12: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/12.jpg)
Colour Image Segmentation
Feature ExtractionQPCA based features
Texture ClusteringK-means clustering
Region MergingReduction of the number of regions
Post-processingBoundary removal
![Page 13: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/13.jpg)
Texture Feature Extraction
Training
QPCA
Image-specific quaternion texture basisSampled sub-windows
Surprisingly, need only the first basis texture element
![Page 14: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/14.jpg)
Feature Extraction
Texture Representation
Single quaternion
A texture patch
1st QPCA Basis texture element
magnitude
real layerred layer
green layerblue layer
T
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Feature Extraction
Feature imagemagnitude
real layer i layer j layer k layer
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Colour Image Segmentation
Feature ExtractionQPCA based features
Texture ClusteringK-means clustering
Region MergingReduction of the number of regions
Post-processingBoundary removal
![Page 17: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/17.jpg)
Texture Clustering
Cluster quaternion pixels k-means
K > expected number of regions E.g., k=15
Every pixel is classified
![Page 18: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/18.jpg)
Colour Image Segmentation
Feature ExtractionQPCA based features
Texture ClusteringK-means clustering
Region MergingReduction of the number of regions
Post-processingBoundary removal
![Page 19: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/19.jpg)
Region Merging
Similar regions are merged Image is over-segmented (k = 15)Merge 2 most similar regions until
< 3 segmentsThreshold is reached
![Page 20: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/20.jpg)
Colour Image Segmentation
Feature ExtractionQPCA based features
Texture ClusteringK-means clustering
Region MergingReduction of the number of regions
Post-processingBoundary removal
![Page 21: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/21.jpg)
Post-processing
Misclassification is inevitable near region boundaries
Misclassified area • small region• straddles two regions
Boundaries removed
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Results
Quaternion method Hoang’s method
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Results
![Page 24: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/24.jpg)
Results
![Page 25: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/25.jpg)
The Quaternion Advantage
Hoang’s Method
QuaternionMethod
![Page 26: Quaternion Colour Texture By Lilong Shi and Brian Funt Presented by: Lilong Shi.](https://reader037.fdocuments.us/reader037/viewer/2022102907/56649d395503460f94a13afb/html5/thumbnails/26.jpg)
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