In this work, we address the problem of spectral reflectance recovery from both CIEXYZ and RGB values by means of a machine learning approach within the fuzzy logic framework, which constitutes the first application of fuzzy logic in these tasks. We train a fuzzy logic inference system using the Macbeth ColorChecker DC and we test its performance with a 130 sample target set made out of Artist's paints. As a result, we obtain a fuzzy logic inference system (FIS) that performs quite accurately. We have studied different parameter settings within the training to achieve a meaningful overfitting-free system. We compare the system performance against previous successful methods and we observe that both spectrally and colorimetrically our approach substantially outperforms these classical methods. In addition, from the FIS trained we extract the fuzzy rules that the system has learned, which provide insightful information about how the RGB/XYZ inputs are related to the outputs. That is to say that, once the system is trained, we extract the codified knowledge used to relate inputs and outputs. Thus, we are able to assign a physical and/or conceptual meaning to its performance that allows not only to understand the procedure applied by the system but also to acquire insight that in turn might lead to further improvements. In particular, we find that both trained systems use four reference spectral curves, with some similarities, that are combined in a non-linear way to predict spectral curves for other inputs. Notice that the possibility of being able to understand the method applied in the trained system is an interesting difference with respect to other 'black box' machine learning approaches such as the currently fashionable convolutional neural networks in which the downside is the impossibility to understand their ways of procedure. Another contribution of this work is to serve as an example of how, through the construction of a FIS, some knowledge relating inputs and outputs in ground truth datasets can be extracted so that an analogous strategy could be followed for other problems in color and spectral science.
Keywords: CIEXYZ; RGB; fuzzy logic; fuzzy logic inference systems; spectral recovery.