Color cluster rotation

The principal component of the cloud of points is computed as follows. First, the center of the cloud is obtained by computing the center of gravity of all the points. The center of gravity is of course equivalent to global space average color a, 

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Figure 6.23 Color cluster rotation. The cluster of points is first shifted to the origin. Then, the major axis of the cluster is aligned with the gray vector. This is done by rotating the cluster around a vector that is perpendicular to the gray vector and also perpendicular to the major axis of the cluster. Finally, the cluster is shifted to maintain the original average intensity.

Figure 6.24 Results obtained with color cluster rotation. The algorithm performs well given a uniform illumination. It is not able to handle images with multiple illuminants.

Figure 6.25 Results obtained with color cluster rotation where the cloud of points is shifted to the center of the color cube and all points are rescaled by the inverse of the square root of the largest eigenvalue.

Random recognition rate Full range per band White patch retinex Gray world assumption Simplified hom Gamut constraint 3D Gamut constraint 2D Color cluster rotation Comprehensive normalization Risson (2003)... 

Color cluster rotation, which is described in Section 6.6, views pixels of the input image as a cloud of points. A principal component analysis is done to determine the main axis of this cloud of points. The main axis is rotated onto the gray vector. For the input data in Helson s experiments, there are only two different colors sensed by the sensor. The two colors line up along the axis ei, which is defined by the illuminant. 

Color cluster rotation, original average intensity is maintained. 

Color cluster rotation, color cloud is centered and then rescaled to fill color cube. 

Paulus D, Csink L and Niemann H 1998 Color cluster rotation Proceedings of the International Conference on Image Processing (ICIP), pp. 161-165. IEEE Computer Society Press. 

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