Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L*a*b*. In the present report we survey some of the most important methods of scattered data interpolation in two-dimensional and in three-dimensional spaces. We review both single-valued cases, where the underlying function has the form f:R #R, and multivalued cases, where the underlying function is f:R . The main methods we review include linear triangular (or tetrahedral) interpolation, cubic triangular (Clough--Tocher) interpolation, triangle based blending interpolation, inverse distance weighted methods, radial basis function methods, and natural neighbor interpolation methods. We also review one method of scattered data fitting, as an illustration to the basic differences between scattered data interpolation and scattered data fitting.

Color device calibration is traditionally performed using one-dimensional (1-D) per-channel tone-response corrections (TRCs). While 1-D TRCs are attractive in view of their low implementation complexity and efficient real-time processing of color images, their use severely restricts the degree of control that can be exercised along various device axes. A typical example is that per separation (or per-channel), TRCs in a printer can be used to either ensure gray balance along the C=M=Yaxis or to provide a linear response in delta-E units along each of the individual (C M and Y) axis, but not both. This paper proposes a novel two-dimensional color correction architecture that enables much greater control over the device color gamut with a modest increase in implementation cost. Results show significant improvement in calibration accuracy and stability when compared to traditional 1-D calibration. Superior cost quality tradeoffs (over 1-D methods) are also achieved for emulation of one color device on another.

ABSTRACT Flatbed scanners and digital cameras have become established and widely used color imaging devices. If colorimetrically calibrated, these trichromatic devices can provide fast color measurement tools in applications such as printer calibration, process control, objective print quality measurements and color management. However, in calibrations intended to be used for color measurements on printed matter, the media dependency must be considered. Very good results can be achieved when the calibration is carried out on a single media and then applied for measurements on the same media, or at least a media of a very similar type. Significantly poorer results can be observed when the calibration is carried out for one printer-substrate combination and then applied for measurements on targets produced with another printer-substrate combination. Even if the problem is restricted to the color calibration of a scanner or camera for different paper media printed on a single printer, it is still tedious work to make a separate calibration for each new paper grade to be used in the printer. Therefore, it would be of interest to find a method where it is sufficient to characterize for only one or a few papers within a grade segment and then be able to apply a correction based on measurable optical paper properties. However, before being able to make any corrections, the influence of measurable paper properties on color characterizations must be studied and modeled. Fluorescence has been mentioned 1-3 as a potential source of error in color calibrations for measurements on printed matter. In order to improve paper whiteness, producers of printing paper add bluish dye and fluorescent whitening agents (FWA) to the paper 4 . In this study, the influence of FWA in printing paper on the color calibration of a digital camera for color measurements on printed targets is discussed. To study the effect of FWA in the paper, a set of papers with varying additions of FWA but otherwise identical, were produced on a smallscale experimental paper machine. Firstly, the impact on the color calibration when the amount of FWA in the paper varies was studied. Secondly, the situation where the printed substrate has FWA-content, and illuminations having different contents of ultraviolet (UV) light were used in the camera and reference spectrophotometer measurements respectively. The results show that for some combinations of illuminations used in the calibration, very large errors are induced by the variation of FWA in the printed substrate.

and diagnostics applications

Digital imaging is a rapid growing area with the developments in computer technology. Digital color use has become a conventional tool in many disciplines, such as cartography remote sensing and photogrammetry. The need for better color quality enforces digital imaging industry to produce devices with less color distortions. Despite the today’s advanced level of technology, it is known that input and output devices cause color distortions, which depends on the quality of the device itself. Scanners, being peripheral devices that capture the image of an object, are mostly used input devices in digital imaging. In this study color accuracy of desktop scanners is handled. A method based on polynomial transformation, which makes possible to map device dependent colors to device independents ones, is introduced. Tests on five different desktop scanners show the evident applicability of the method. 1.

Abstract. We propose a novel scanner characterization approach for applications requiring color measurement of hardcopy output in calibration, characterization, and diagnostics applications. The method is advantageous for common practical color printing systems that use more than the minimum of three colorants necessary for subtractive color reproduction; printing with cyan (C), magenta (M), yellow (Y), and black (K) is the most prevalent example we use in our description. The proposed method exploits the fact that for the scenarios in consideration, in addition to the scanner RGB values for a scanned patch, the CMYK control values used to print the patch are also available and can be exploited in characterization. An indexed family of 3D scanner characterizations is created, each characterization providing a mapping from scanner RGB to CIELAB for a fixed value of K, the latter constituting the index for the characterization. Combined together, the family of 3D characterizations provides a single 4D characterization that maps scanner RGB obtained from scanning a patch and the K control value used for printing the patch to a colorimetric CIELAB measurement for the patch. A significant improvement in the robustness of the method to variations in printing is obtained by modifying the K index to utilize the scanned output for a black-only patch printed with the corresponding K value instead of directly utilizing the control K value used at the printer. Results show that the proposed 4D scanner characterization technique can significantly outperform standard 3D approaches in the target applications. © 2007 SPIE and IS&T. �DOI: 10.1117/1.2803833� 1