Logo PTB

Improved reconstruction of spatially resolved color spectra


Spectral color measurement is a fundamental application in many fields of industry. Common procedures employ spot color measurement devices by which a complete spectral determination of object surfaces is possible only with large effort. Multispectral line scan cameras offer, however, the potential to record the complete reflectance spectrum of a measurement surface in real time with the aid of a suitable algorithm. The wide application of this measuring concept in industry has so far not been possible due to the lack of a robust and validated reconstruction procedure.

Within the scope of the MNPQ project "Reconstruction of spatially resolved color spectra from continuous line scan camera measurements" and in cooperation with the company Chromasens GmbH, a two-stage Bayesian reconstruction approach has been developed which includes available prior knowledge about spectral content. This procedure yields analytical expressions for a fast and efficient deconvolution which supports, in particular, a direct evaluation. In addition to the reconstructed color spectra, the procedure also provides their underlying probability distribution which allows the calculation of uncertainties and standard deviations. A simulation study showed that the reconstruction quality of empirical procedures which use so-called kernel functions can be clearly improved with the Bayesian approach. In particular, color spectra which are not captured by training data and which can, therefore, be estimated only insufficiently by empirical procedures, can be better reconstructed by the developed method.

Scientific publication:

M. Dierl, T. Eckhard, B. Frei, M. Klammer, S. Eichstädt, C. Elster:
Improved estimation of reflectance spectra by utilizing prior knowledge.
J. Opt. Soc. Am. A, 33(7), 1370-1376, 2016.
[DOI: 10.1364/JOSAA.33.001370]

Root-mean-square error (RMSE) between reconstruction and reference spectrum as a func-tion of the prior standard deviation. Corresponding results of the empirical method with linear and Gaussian kernel are marked by horizontal lines.


Opens window for sending emailM. Dierl, Opens window for sending emailS. Eichstädt, Opens window for sending emailC. Elster,
Department 8.4 Mathematical Modelling and Data Analysis