ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

A Two-Stage Bayesian Approach for the Analysis of Multispectral Camera Measurements

12 September 2016, 12:10 – 12:30


Submitted by
Marcel Dierl
Marcel Dierl (Physikalisch-Technische Bundesanstalt), Timo Eckhard (Chromasens GmbH), Bernhard Frei (Chromasens GmbH), Maximilian Klammer (Chromasens GmbH), Sascha Eichstädt (Physikalisch-Technische Bundesanstalt), Clemens Elster (Physikalisch-Technische Bundesanstalt)
Estimation of spectral reflectance from responses of multispectral imaging systems is important for numerous applications in imaging science and several reconstruction principles have been proposed to this end. These principles have in common that the calculation of spectral reflectance from measurement data requires the solution of an ill-posed inverse problem. In many practical situations appropriate prior knowledge is available that should be utilized in the reconstruction procedure for regularization. However, this is not straightforward for many of the data analysis methods currently applied in spectral measurement, and it is often realized by using suitable training data and special kernel functions.

Here we present a two-stage Bayesian approach that allows us to incorporate prior knowledge about spectral content. Such prior knowledge can originate from previous monochromator or spectrophotometer measurements. For the Bayesian analysis we apply truncated normal distributions that ensure the physical constraint of positivity and use special designed prior covariance matrices to provide smooth recovered spectra. In the first step, called calibration stage, spectral sensitivity curves for each camera channel of the multispectral imaging system are determined that connect camera responses with spectral reflectances. In the subsequent measurement stage these results are used for the estimation of the reflectance spectrum from the camera’s response. The approach yields analytical expressions for a fast and efficient estimation of spectral reflectance and is thus suitable for real-time applications. Besides point estimates, also probability distributions are obtained which completely characterize the uncertainty associated with the reconstructed spectrum.

We demonstrate the performance of our approach by using simulated data for the camera responses and spectral curves. It is shown that through incorporation of prior knowledge the Bayesian treatment yields improved reconstruction results for a wide range of standard deviations of the prior compared to methods that resort to training data only. Reflectance spectra which are not fully captured by training data can also be well estimated with our approach.
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