V. Ostromoukhov, R.D. Hersch, C. Peraire, P. Emmel, I. Amidror
IS&T/SPIE Symposium of Electronic Imaging: Science and Technology, Conf. on Device Independent Color Imaging, SPIE Vol. 2170, 1994, pp. 133-142
In the present paper we study two different table-based approaches for the calibration of electronic imaging systems. The first approach, which is the classical one, uses the device independent CIE-XYZ colorimetric space as an intermediate colorimetric standard space. Input and output devices such as scanners, displays and printers are calibrated separately with respect to the objective CIE-XYZ space. The second approach, the so-called closed-loop approach, calibrates directly scanner- printer pairs, without any reference to an objective colorimetric space. Different theoretical and practical issues of both approaches are discussed: approximation techniques, error analysis, complexity, duration of a typical calibration cycle and domains of applicability.
For the first approach, the only assumption made about the characteristics of input and output devices is that the 3D relationships between the RGB space and CIE-XYZ space as well as between the CIE-XYZ and the output CMY space can be approximated by a set of locally linear transformations. In order to obtain 3D calibration tables, two algorithms are explored. In the first algorithm, the measured samples (learning set) are used for splitting the colorimetric space into Voronoi polyhedra separating each sample from its neighbours. The learning set allows for each polyhedron computing a linear transformation between input values and output values. The two-step transformation between scanned RGB to CIE-XYZ and between CIE-XYZ to CMY provides, for each new RGB sample, its equivalent CMY values. This method however produces some discontinuities at boundaries of Voronoi cells and is therefore not suitable for exact calibration. The problem is overcome with the second algorithm, which is based on the segmentation of the colorimetric input spaces into Delaunay tetrahedra whose vertices are given by elements of the learning set. For each new RGB sample, three-linear interpolation within the corresponding tetrahedron is applied, first in the RGB space in order to obtain its XYZ values, and then in the XYZ space in order to obtain its CMY values. This solution provides perfect continuity at the boundaries of the Delaunay tetrahedra and offers within the printer's gamut a highly predictable result. The remaining discrepancy between the original image and the resulting one may be reduced by updating the calibration tables through an iterative process.
The second approach, the closed-loop approach, establishes a direct 3D relationship between the input device's RGB space and the output device's CMY space. Printed samples are directly scanned, thus enabling a first order local characterization of the RGB space with respect to the output CMY space of a given scanner-printer pair. This first order characterization is used to produce a new set of samples which is reinjected in the calibration process, thus producing the second order characterization, and so forth. After a certain number of iterations, the process converges and produces a stable result for samples located within the printer's gamut. The present paper defines the set of conditions which must be respected to make such reference-free calibration feasible. This method uses the same 3D interpolation technique within Delaunay tetrahedra as in the first approach. For error analysis, a relationship to CIELAB is established and errors are estimated in the perceptually uniform colorimetric space.
We conclude that both methods described in the article can be applied with success in slightly different contexts: the two step method using the device-independent CIE-XYZ space as an intermediate space can be used for calibrating complex multi-device systems, while the closed-loop method is a good candidate for building dedicated calibrated scanner-printer pairs permitting the use of a quick and efficient calibration procedure.
Download the full paper: PDF 128 KB