Quaternion Colour Texture

By Lilong Shi and Brian FuntPresented by: Lilong Shi

Motivation

Quaternion Representation of Colour

How effective is it?

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

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

Problem

Best texture segmentation features?Hoang suggests combining

Colour informationSpatial structure information

Quaternion texture Integrates colour and structure

Single representation

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

Quaternions

A picture of quaternionsQuaternion axes in 4D space

Pure quaternion for colour

reali

kj

i

kj

Orthogonal in 4D

“pure” = zero real part

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

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

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

Colour Image Segmentation

Feature ExtractionQPCA based features

Texture ClusteringK-means clustering

Region MergingReduction of the number of regions

Post-processingBoundary removal

Colour Image Segmentation

Feature ExtractionQPCA based features

Texture ClusteringK-means clustering

Region MergingReduction of the number of regions

Post-processingBoundary removal

Texture Feature Extraction

Training

QPCA

Image-specific quaternion texture basisSampled sub-windows

Surprisingly, need only the first basis texture element

Feature Extraction

Texture Representation

Single quaternion

A texture patch

1st QPCA Basis texture element

magnitude

real layerred layer

green layerblue layer

T

Feature Extraction

Feature imagemagnitude

real layer i layer j layer k layer

Colour Image Segmentation

Feature ExtractionQPCA based features

Texture ClusteringK-means clustering

Region MergingReduction of the number of regions

Post-processingBoundary removal

Texture Clustering

Cluster quaternion pixels k-means

K > expected number of regions E.g., k=15

Every pixel is classified

Colour Image Segmentation

Feature ExtractionQPCA based features

Texture ClusteringK-means clustering

Region MergingReduction of the number of regions

Post-processingBoundary removal

Region Merging

Similar regions are merged Image is over-segmented (k = 15)Merge 2 most similar regions until

< 3 segmentsThreshold is reached

Colour Image Segmentation

Feature ExtractionQPCA based features

Texture ClusteringK-means clustering

Region MergingReduction of the number of regions

Post-processingBoundary removal

Post-processing

Misclassification is inevitable near region boundaries

Misclassified area • small region• straddles two regions

Boundaries removed

Results

Quaternion method Hoang’s method

Results

Results

The Quaternion Advantage

Hoang’s Method

QuaternionMethod

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