A procedure for creating efficient reflectance spectra from CIE tristimulus colour values is described using a modified linear model. By fixing certain criteria based on colour difference values, the proposed technique preliminarily selects a series of suitable samples from a main data set containing the reflectance values of a large number of different coloured samples, based on the colour specifications of a given sample. In this way, a series of different databases containing the reflectance values of confirmed samples relating to the particular samples are formed. Then, a well‐known principal components linear model is applied using three basis functions. This operation yields higher cumulative variances in comparison with the original database, having the same number of basis vectors. The performance of the proposed method is evaluated using a different collection of samples and the resulting spectra show considerable improvements in terms of root mean square error as well as colour difference values under different illuminants.

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K/S and reflectance graphs are essential tools in characterizing the dyeing behavior. In textile coloration, estimating the dye concentration is poor using the Kubelka-Munk model due to its low scalability and deviation of the reflectance function from linearity after low dye concentrations, particularly in the wavelengths where the gradient of K/S against dye concentration is noticeable. This paper focused on extending the validity of the Kubelka-Munk function, which originates from the linearity of reflectance function against higher dye concentration. A data set of dyed polyester specimens with three disperse dyes in a dye concentration range was prepared. At the present work, K/S was analyzed by describing the scalability property, and the suitable wavelengths in the visible spectrum where K/S benefits from minor deviation from linearity were also discussed. It was observed that the K/S function is not always scalable and deviates in λ max after a specific dye concentration for K/S > 17. Accordingly, the wavelengths other than λ max were found that could be as important as λ max. For the K/S values > 25, no practical region was achieved.

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