Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 314

Initialize

K = cluster size, ε = distortion threshold,
C 0 = { C k , k =1, 2, … , K } = initial cluster centroids,
Set m = 0 and D 0 >> 1 (a large positive number =
1000), A 1 = A 2 = … = A K = empty set
i =15 E =0

Update K partition sets A 1 , A 2 , …, A K

Enter N = number of
training samples from the
database
[ u 1 , u 2 , …, u N ]
[ y 1 , y 2 , …, y N ]

1. Compute J = arg min D = arg min d ( y i , C k )
k k

where d is the Euclidian distance
2. Accumulate y i into A J

3. Compute distortion E = E + D min
where D min = minimum of d obtained in part (1)

i = i + 1

Is i = N ?

No

Yes

1. Find the centroid of each cluster

Σ L k

L k

A k ( i )

i = 1

, L k = number of vectors in A k

C k =

E

2. Compute average distortion D m =

m = m +1
E= 0

N

Store new
centroids { C k , k = 1, 2, …, K }
Also calculate the centroids for CMYK
space using the color indices for each
cluster and store them

Is

Yes No

D m -1 - D m

< ε?

D m

FIGURE 7.6 Flowchart of the centroid and cluster assignment in L*a*b* space.
Note: The training database vectors y 1 , y 2 ,...,y N are used for centroid and cluster assignments
in L*a*b* space. If the same is required in CMYK space, then use training database vectors
u 1 , u 2 ,..., u N .