Building Accurate and Smooth ICC Profiles by Lattice Regression

A system-optimized framework is presented for learning a multi-dimensional look-up-table (LUT) from training samples. The technique, termed lattice regression, solves for an entire LUT at once by optimizing the three-fold objective of 1) low interpolation error on training data, 2) smooth transitions between adjacent LUT outputs, and 3) a steady overall functional trend. The proposed algorithm is tested for both smoothness and accuracy against state-of-the-art for color management in printers. Introduction Controlling image appearance across diverse image displays and capture devices requires characterizing, for each device, the mapping between the device-dependent color space and a deviceindependent color space or profile connection space (PCS). The standard method to estimate this color mapping for devices that have a complicated color response, such as printers, is by empirical characterization: learn the mapping from a set of training examples (e.g. obtained by measuring CIELab outputs for a number of RGB inputs). For computational efficiency, it is standard practice to estimate the mapping only for a set of regularly-sampled color values and store this as a multidimensional look-up-table (LUT) in an ICC profile [12], which is interpolated at runtime to map image colors. However, estimating the color mapping is challenging because it can be highly nonlinear (especially for printers), and the training examples may be noisy due to device instabilities and/or measurement error. Many standard regression methods have been applied to the problem of estimating LUTs for color management. These methods generally estimate a function that fits the training samples, and then one evaluates this function at the LUT gridpoints. However, because the effect of interpolating the LUT is not taken into account when this function is estimated, the training samples (representing everything known about the desired transformation) are not guaranteed to be accurately reproduced by interpolating the LUT. This begs the question: is it possible to learn a function that is optimal with respect to the LUT interpolation in a robust manner? In this paper, we propose a framework to answer this question, termed lattice regression, that estimates LUTs by minimizing the regularized interpolation error on the training data. Next, we review some of the related work. Then we detail the proposed lattice regression and explain why we hypothesize it will estimate accurate and smooth color mappings. After that, we describe experiments comparing the proposed lattice regression to the state-of-the-art local Tikhonov regression method for an inkjet and a laser printer in terms of color management accuracy and subjective perceptual smoothness. Note that, although these methods can be applied to both forward and inverse device characterization, our experiments focus on the problem of inverse device characterization where the placement of training examples cannot be controlled directly. The paper concludes with a discussion of the results, and some conclusions and open questions.