Diagnosing and Correcting Systematic Errors in Spectral-Based Digital Imaging

A digital imaging system containing a calibration target, an image capture device, and a mathematical model to estimate spectral reflectance factor was treated as a spectrophotometer and as such subject to systematic and random errors. The systematic errors considered were photometric zero, photometric linear and nonlinear scale, wavelength linear and nonlinear scale, and bandwidth. To diagnose and correct the systematic errors in a spectral imaging system, a technique using multiple linear regression as a function of wavelength was employed, based on the measurement and image based estimating of several image verification targets. Based on the stepwise regression technique, the most significant diagnosed systematic errors were photometric zeros, photometric linear scale, wavelength linear scale, and bandwidth errors. The performance of spectral imaging after correction of the estimated spectral reflectance, based on the modeling result, was improved on average 25.3% spectrally and 16.7% colorimetrically. This technique is suggested as a general method to improve the performance of spectral imaging systems. Introduction The accuracy of a spectral imaging system is dependent upon several parameters including the image capture device, the calibration target, and the mathematical method to estimate spectral reflectance factor. Since the total system generates spectral reflectance factor, the errors associated with conventional spectrophotometry can be considered for spectral imaging. Spectrophotometric errors can be divided into systematic and random errors. Systematic errors include errors resulting from wavelength, bandwidth, detector linearity, nonstandard geometry, and polarization. Totally, systematic errors are caused by characteristics of the instrument that are the same for all measurements. Measurement of systematic errors is the evaluation of accuracy of the measurements. Random errors are caused by inability to control the instrument. That might be caused from drift, electronic noise, and sample presentation. But it is not limited to these error sources. Random errors, by definition, are discussed in terms of probabilities. A standard deviation indicates the probability of the existence of random error. Based on error propagation theory, the random errors can propagate through several steps of a calibration process and finally can be a parameter to calculate systematic error. Hence, it is not true to say that the accuracy of a spectrophotometer is affected just by the systematic errors. Berns and Petersen have developed a technique based on the use of multiple linear regression to model systematic spectrophotometric errors and subsequently correct spectral measurements based on the modeling result. The developed technique is currently used in industrial environments. Berns’ method was first described by Robertson, who demonstrated its utility in diagnosing photometric zero and linear photometric scale errors in a General Electric Recording Spectrophotometer. To improve the instrument performance, the first step is to diagnosis the errors and the second step is to correct an instrument’s systematic errors. To determine which error parameters are statistically significant, stepwise regression was suggested. In this research, it was presumed that a combination of a calibration target, image capture device, and the mathematical model to estimate spectral reflectance factor was equivalent to a typical spectrophotometer. The systematic errors, including photometric zero, photometric linear and nonlinear scale, wavelength linear and nonlinear scale and bandwidth were considered as the possible errors in the spectral imaging system. The systematic errors were modeled by a series of equations and minimized using the multiple linear regression technique. It was assumed that the random errors were negligible. Calibration and Verification Targets A set of common targets included the GretagMacbeth ColorChecker Color Rendition Chart (CC), the GretagMacbeth ColorChecker DC (CCDC), and the Esser TE221 scanner Test Chart (Esser) along with two targets containing typical artist’s paints using Gamblin Conservation Colors were used as targets to both diagnose and correct the systematic errors in a spectral imaging system. The Gamblin and EXP target contain 63 and 14 colors, respectively. The EXP target was developed based on analysis the Gamblin Conservation Colors using Kubelka-Munk turbid media theory. All the targets were measured using a GretagMacbeth Color XTH, integrating sphere specular component excluded in the wavelength range of 360 to 750 nm in intervals of 10 nm with a small aperture. The instrument was the reference spectrophotometer and by definition, assumed to be error-free. Spectral Image Acquisition Images of the targets and a uniform grey background were captured using a modified Sinarback 54 digital camera in its ′′fourshot′′ mode. The Sinarback 54 is a three channel digital camera that incorporates a Kodak KAF-22000CE CCD with a resolution of 5440×4880 pixels. This camera has been modified by replacing its IR cut-off filter with clear glass and fabricating two filters used sequentially, resulting in a pair of RGB images. For 13th Color Imaging Conference Final Program and Proceedings 25 this experiment, a pair of Elinchrom Scanlite 1000 tungsten lights was used, producing a correlated color temperature of 2910 K. All images were digitally flat fielded using the grey background followed by image registration. Spectral reflectance factor was estimated from linear photometric camera signals by a matrix transformation: