1. Quaternion Colour Constancy
Quaternions and
Quaternion Colour Constancy

2. Quaternions Quaternions …
Are a member of hypercomplex numbers
Are a generalization of complex numbers
Has one real part and three imaginary parts
i.e.
A RGB colour is represented by a pure quaternion

3. 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

4. Quaternion PCA QPCA is a generalization of complex PCA
QPCA for dimension reduction
Similar to PCA for real numbers
Quaternion-valued Texture can be described in low dim. space

5. Quaternion PCA Eg. QPCA For Image Compression
Each row of the image is a input variable
QPCA on all rows
(a) (b) (c) (d)
Figure 13: QPCA based image compression. (a) –(d) are the reconstructed images with k(# of basis vectors)=3,16,50,255. Note that (d) is the perfect reconstruction of the original image

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

7. Feature Extraction Feature Deduction T Single quaternion
1st QPCA Basis texture element
Single quaternion
A texture patch

8. Classification Textures Images based on content
By classifying their extracted quaternion features
Images based on content
By recognizing the class of textures they contain
Images based on illumination
By identifying the kind of illuminations of textures they contain

9. Colour Texture Histogram
An image contains colour textures
Colour Texture Histogram
It counts different colour textures
Quaternion texture can be used to build colour histogram
An extension of colour histogram when each pixel is consider as a texture

10. Quaternion For Colour Constancy
SVR uses colour histograms
Colour Histogram
Contains colour information only
Texture Histogram
Contains structural information only
Colour Texture Histogram
Integrates both colour and structure info
A new representation of images
Can SVR do better by Colour Texture Histogram?

11. for Training Set Reduction
K-Medians Clustering
for Training Set Reduction

12. Function Estimation
Define a function(curve) that minimizes the energy function controlled by all training data points
Use this function to estimate new data
SVR, TPS

13. Control Point Reduction
Problem
Training set too large to fit into memory
Long processing time
Reduce training set using k-medians
Partition n control points into k clusters
Keep k medians of these clusters
Reduce n control points to k

14. k-Medians k-medians clustering:
Given: N points (x1… xN) in a metric space
Find k points C = {c1, c2, …, ck} that minimize Σ d(xi, C) (the assignment distance)
In the example above, only 4 control points are needed to define the curve

15. k-Medians k-medians Median as the best representative for each cluster
Less sensitive to outliers
k can be determined based on memory and training time requirement