Multi-dimensional look up tables (LUTs) are widely employed for color transformations due to its high accuracy and general applicability. Using the LUT model generally involves the color measurement of a large number of samples. The precision and uncertainty of the color measurement will be mainly represented in the LUTs, and will affect the smoothness of the color transformation. This, in turn, strongly influences the quality of the reproduced color images. To achieve high quality color image reproduction, the color transformation is required to be relatively smooth. In this study, we have investigated the inherent characteristics of LUTs' transformation from color measurement and their effects on the quality of reproduced images. We propose an algorithm to evaluate the smoothness of 3D LUT based color transformations quantitatively, which is based on the analysis of 3D LUTs transformation from RGB to CIELAB and the second derivative of the differences between adjacent points in vertical and horizontal ramps of each LUT entry. The performance of the proposed algorithm was compared with a those proposed in two recent studies on smoothness, and a better performance is reached by the proposed method.

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