Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 316

cluster centroids C k . When Equation 7.34 is satis ed, the process stores the new

centroids C 1 , C 2 ,...,C K . These centroids are the centroids that will be used

in the clusters for the adaptation process. After the centroids are computed, a

''

nal

''

final step of accumulating the training samples into the appropriate clusters will
be performed, as shown in Figure 7.7. These centroids will be

used during the adaptation process. But, when using the models, the correspond-
ing cluster centroids in CMYK space is required. This can be computed
using Equation 7.32 in CMYK space using color indices from the

— in L*a*b* space —

final clusters or

running the flowchart of Figure 7.6 in CMYK space using training database vectors

u 1 , u 2 ,...,u N .
The cluster centroids C k from Figure 7.6 are used in the initialization step of
Figure 7.7. However, cluster centroids obtained from some other approach can also
be used here. For example, the centroids may be

for example, a
critical color in the yellow region of the gamut (colors used for controlling the
printing device) or colors from a document obtained by processing the pixels in the
document where an accurate model is desired. Again, begin, create an empty set,
A 1 , A 2 ,...,A K and set i initially at 1. Using N number of training samples, yi i is
accumulated into the appropriate cluster, that is, the cluster having the centroid
with the shortest Euclidean distance from the training sample, similar to Figure 7.6.
Repeat this process until all training samples are accumulated and stored into

'' critical colors, ''

Initialize

K = cluster size
C k , k= 1, 2, …, K = cluster centroids
A 1 , A 2 , …, A K = empty sets
i= 1

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

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

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

k k

2. Accumulate y i into A J

Is

No

i=i+ 1

i=N ?

Yes

Stop

FIGURE 7.7 Flowchart of accumulating training samples into clusters in L*a*b* space.