Interpolation and Extrapolation in Color Systems

KAKODKAR, ATISH PANDURANG. Interpolation and Extrapolation in Color Systems. (Under the direction of Prof. Sarah A. Rajala and Prof. H. Joel Trussell.) With the increased use of color in desktop publishing applications has come a desire for greater control of the color quality. Colorimetric reproduction requires calibrated color output devices. One approach to color calibration is to characterize a color output device with a three-dimensional look-up table. The look-up table maps the color specification values to the control values of the color output device. This thesis looks at the problem of obtaining the look-up table. The problem can be posed in the following manner. Given a set of control values {c.} on a regular grid and the corresponding set of color specification values {t.} obtained from data collection, find the {cg } for different {tg } on a grid in the color specification space. This grid should be fine enough so that simple interpolation is adequate to obtain control values for color specification values that are not in the table. The grid is obtained from a relatively sparse data set with an appropriately defined interpolation scheme. This interpolation scheme can be very complex since it is used only once to compute the grid. This regular finer grid can be used in real-time to obtain the control value for any color specification value located inside a given color gamut. Two interpolation schemes are evaluated in this thesis. One of the problems with constructing the fine grid of values for the LUT is the determination of values that are near the edge of the gamut of the output device. While the functions which represent the device are usually well behaved and smoothly varying, the truncation of the data can cause a problem with interpolation methods. An approach to solving the truncation problem is to extrapolate the data outside the gamut. The extrapolated points are then used in the interpolation to estimate the values for the fine grid. The use of extrapolated values permits the use of a single interpolation algorithm over the entire gamut of the device, rather than using a modified algorithm in regions near the edge of the gamut. The results of this method are comparable to other interpolation methods but it is simpler to implement. Three different extrapolation schemes are evaluated in this thesis and the best one is selected to obtain the look-up table. This thesis discusses the calibration of a thermal dye transfer color printer. Calibration is carried out initially for a mathematical model. The behaviour of this model is compared to the behaviour of the printer, both with and without the presence of noise. This can be used to determine whether the model is a good representation of the printer and can be used to predict the performance of the printer. INTERPOLATION AND EXTRAPOLATION IN COLOR SYSTEMS by Atish P. Kakodkar A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Department of Electrical and Computer Engineering