A mathematical approach to best luminance maps.

An algorithm to calculate the best global mapping from color to grayscale is presented. We assert that the best mapping minimizes the difference between the multi-channel local tensor and the tensor of the resultant mono-chromatic image. To minimize the objective function, we represent the grayscale image as a weighted sum of the RGB channels, three channels and their second-order polynomial and three channels and their root polynomial. The optimization searches for the best weights to combine the linear, polynomial, and root polynomial functions. Our results show that the optimal weights can half the root mean square difference between the color gradients and those achieved by the conventional luminance transformation. Further improvement is achieved by adding the squared and root squared channels to the solution. The improvements are also visually evident.

Robust metric for the evaluation of visual saliency algorithms.

In this paper, we analyzed eye fixation data obtained from 15 observers and 1003 images. When studying the eigen-decomposition of the correlation matrix constructed based on the fixation data of one observer viewing all images, it was observed that 23% of the data can be accounted for by one eigenvector. This finding implies a repeated viewing pattern that is independent of image content. Examination of this pattern revealed that it was highly correlated with the center region of the image. The presence of a repeated viewing pattern raised the following question: can we use the statistical information contained in the first eigenvector to filter out the fixations that were part of the pattern from those that are image feature dependent? To answer this question we designed a robust AUC metric that uses statistical analysis to better judge the goodness of the different saliency algorithms.

Optimal bases for convex color mixture.

Partitive color mixing is the process by which the human eye integrates different neighboring colors to result in a single uniform surface. This process is convex: The perceived color is the weighted average of a small set of basis colors, and given that the weights represent the relative area of each color, they must sum to one. We present an efficient algorithm that generates a small number of new, natural bases such that a large set of spectra can be adequately expressed as a convex combination of these bases. Our results show that 9-11 bases are sufficient to represent a set of 1269 Munsell surfaces within the convex model.

Metamer sets without spectral calibration.

The set of metamers for a given device response can be calculated given the device's spectral sensitivities. Knowledge of the metamer set has been useful in practical applications such as color correction and reflectance recovery. Unfortunately, the device sensitivities of a camera or scanner are not known, and they are difficult to estimate reliably outside the laboratory. We show how metamer sets can be calculated when a device's spectral sensitivities are not known. The result is built on two observations: first, the set of all reflectance spectra consists of convex combinations of certain basic colors that tend to be very bright (or dark) and have high chroma; second, the convex combinations that describe reflectance spectra result in convex combinations of red-green-blue (RGB) values. Thus, given an RGB value, it is possible to find the set of convex combinations of the RGB values of the basic colors that generate the same RGB value. The corresponding set of convex combinations of the basic spectra is the metamer set.

Calibrating color cameras using metameric blacks.

Spectral calibration of digital cameras based on the spectral data of commercially available calibration charts is an ill-conditioned problem that has an infinite number of solutions. We introduce a method to estimate the sensor's spectral sensitivity function based on metamers. For a given patch on the calibration chart we construct numerical metamers by computing convex linear combinations of spectra from calibration chips with lower and higher sensor response values. The difference between the measured reflectance spectrum and the numerical metamer lies in the null space of the sensor. For each measured spectrum we use this procedure to compute a collection of color signals that lie in the null space of the sensor. For a collection of such spaces we compute the robust principal components, and we obtain an estimate of the sensor by computing the common null space spanned by these vectors. Our approach has a number of advantages over standard techniques: It is robust to outliers and is not dominated by larger response values, and it offers the ability to evaluate the goodness of the solution where it is possible to show that the solution is optimal, given the data, if the calculated range is one dimensional.