INTERPOLATION AND EXTRAPOLATION IN COLOR

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 speci cation 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 fcig on a regular grid and the corresponding set of color speci cation values ftig obtained from data collection, nd the fcgg for di erent ftgg on a grid in the color speci cation space. This grid should be ne enough so that simple interpolation is adequate to obtain control values for color speci cation values that are not in the table. The grid is obtained from a relatively sparse data set with an appropriately de ned interpolation scheme. This interpolation scheme can be very complex since it is used only once to compute the grid. This regular ner grid can be used in real-time to obtain the control value for any color speci cation value located inside a given color gamut. Two interpolation schemes are evaluated in this thesis. One of the problems with constructing the ne 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 ne 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 modi ed 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 di erent 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 ful llment of the requirements for the Degree of Master of Science Department of Electrical and Computer Engineering Raleigh May 1994 Approved By: H.J. Trussell G.L. Bilbro S.A. Rajala Chairman of Advisory Committee ii For my parents and my brother, whose love, support and encouragement have made this possible. iii Biography Atish P. Kakodkar, was born in Panaji, India on April 19, 1970. He completed the Indian Certi cate for Secondary Education (equivalent to the 10th Grade) in 1986, at Mount St. Mary's School, New Delhi, India. He went on to complete his Higher Secondary School Examination (equivalent to the 12th grade) in 1988 at Dhempe College of Arts & Science, Panaji, India. Following this, he continued his studies at the Indian Institute of Technology, Madras, India, where he was awarded a Bachelor of Technology in the eld of Electronics & Electrical Communication Engineering in 1992. He was a Research Assistant with the Center for Communications and Signal Processing at North Carolina State University from August 1992 to June 1994. He is also a recipient of the National Talent Search Examination (NTSE) Scholarship awarded by the Government of India to the most promising students of science in the country. Acknowledgements I would like to thank Professor Sarah A. Rajala for acting as my advisor and giving me the opportunity to pursue a graduate degree at NCSU. I would also like to immensely thank Professor H. Joel Trussell for his guidance and help throughout the course of this work. Thanks must also be given to Dr. Gri L. Bilbro for being a member of my committee. To my colleagues, Dr. Poorvi Vora, Dr. Mike Vrhel and Gaurav Sharma, I owe my gratitude for the exchange of ideas and information which were of great help. A special mention must be made of John Co e who not only helped me take some of the measurements for my research work, but also proved to be a supportive and helpful friend. I would also like to thank my other friends and colleagues Valerie La, Ahmet Akyamac, Manish Kulkarni and Christophe Grard. Lastly, I would like to thank some of my friends who in their own special way made all the work worthwhile Mary Easo, for being such a wonderful person and an understanding friend, Anadi Srivastava, whose immense knowledge never ceases to amaze me, Jayashri Deshmukh, for giving me a di erent perspective to life, Paritosh (Lapi) Dikshit, who kept me smiling, and Rajika Bhandari, for teaching me the art of stretching my dollar.