The problem of device independent color in color management systems is abstracted as that of involving a set of transformations from device space to a reference space (normalization), reference space to a reference space (gamut compression), and from reference space to a device space (rendering). Issues of color management such as color calibrations, corrections, matching, and soft proofing can then be addressed in terms of this frame work.Pentahedral type multidimensional interpolations are applied in this paper for both LUT estimation from calibration data and for color space transformations/conversions. Efficient discrimination schemes are developed for locating a point of interest with in a Pentahedral volume. The structure of a decision scheme depend on its corresponding space partition. Decision schemes that can be implemented with tree structures are very fast. Complexity of storage and computations are discussed for interpolating at a given point. Efficient storage schemes for lookup table contents that permit high speed color space transformations implementations are presented. Switching between different types of volume partitions minimizes the artifacts and maintains the continuity of the estimated variables.Methods are also developed in the paper for the estimation of LUTs for transformations between different devices and color spaces. Pentahedral type multidimensional interpolations and grid search based optimizations are applied for constructing LUTs from colorometric calibration data. Pentahedral type formulations provide unique estimates for inverse problems involving m -> m variable transformations/conversions. For inverse problems with n -> m variables transformations, constrained optimization schemes are developed for estimating LUTs. Gamut mapping is also addressed in the estimation of LUTs.The algorithms are applied for a number of electronic imaging applications and the evaluation results are presented.