loss of generality in a set of sampling points for the device color space the sampling points are scaled such that the range in each channel is 0 1 for example if the color device accepts 8 bit data as input then one would normalize the values by 255 furthermore in a 3d lut there are three 1d sampling grids the number of steps in each channel n a n b and n c may not be the same moreover the lut must be u201c complete u201d in the sense that every point a i b j c k i 1 n a j 1 n b k 1 n c must also be present in the samples this type of lut is sometimes called non uniform lut if there is any chance of confusion in addition the condition that a 1 b 1 c 1 0 a n a b n b c n c 1 is imposed this is not a serious restriction and if it is not satisfied it means some part of the device space is not sampled something that should be avoided in the design of targets having described a 3d lut 108 and the requirements for the sampling points 106 the goal of the data processing system 104 is then given a set of sample points s 106 find a 3d lut 108 in the sense above with n a n b n c as large as possible fig2.