Optimal nonnegative color scanning filters

A Mathematical Investigation into the Design of Prefilters That Make Cameras More Colorimetric

By placing a color filter in front of a camera we make new spectral sensitivities. The Luther-condition optimization solves for a color filter so that the camera’s filtered sensitivities are as close to being linearly related to the XYZ color matching functions (CMFs) as possible, that is, a filter is found that makes the camera more colorimetric. Arguably, the more general Vora-Value approach solves for the filter that best matches all possible target spectral sensitivity sets (e.g., any linear combination of the XYZ CMFs). A concern that we investigate here is that the filters found by the Luther and Vora-Value optimizations are different from one another. In this paper, we unify the Luther and Vora-Value approaches to prefilter design. We prove that if the target of the Luther-condition optimization is an orthonormal basis—a special linear combination of the XYZ CMFs which are orthogonal and are in unit length—the discovered Luther-filter is also the filter that maximizes the Vora-Value. A key advantage of using the Luther-condition formulation to maximize the Vora-Value is that it is both simpler to implement and converges to its optimal answer more quickly. Experiments validate our method.

Spectral sensitivity estimation of trichromatic camera based on orthogonal test and window filtering

The three-channel spectral sensitivity of a trichromatic camera represents the characteristics of system color space. It is a mapping bridge from the spectral information of a scene to the response value of a camera. In this paper, we propose an estimation method for three-channel spectral sensitivity of a trichromatic camera. It includes calibration experiment by orthogonal test design and the data processing by window filtering. The calibration experiment was first designed by an orthogonal table of the 9-level and 3-factor. A rough estimation model of spectral sensitivity is established on the data pairs of the system input and output in calibration experiments. The data of rough estimation is then modulated by two window filters on frequency and spatial domain. The Luther-Ives condition and the smoothness condition are introduced to design the window, and help to achieve the optimal estimation of the system spectral sensitivity. Finally, the proposed method is verified by some comparison experiments. The results show that the estimated spectral sensitivity is basically consistent with the measured results of the monochromator experiments, the relative full-scale errors of the RGB three-channel is obviously lower than the Wiener filtering method and the Fourier band-limitedness method. The proposed method can estimate the spectral sensitivity of the trichromatic digital camera very well, which is of great significance for the colorimetric characterization and evaluation of imaging systems.

Fast model-based multispectral imaging using nonnegative principal component analysis

Estimation of the spectral reflectance of a scene is a critical problem in image processing and computer vision applications. Model-based multispectral imaging, one of the spectral reflectance estimation methods, can effectively reconstruct the full spectrum using a small number of camera shots. However, it is based on iterative optimization and, thus, is computationally too intensive. In this Letter, we modify the iterative optimization problem to a closed-form problem using nonnegative principal component analysis. The proposed method can substantially reduce the computational cost while maintaining the accuracy.

Selection of optimal spectral sensitivity functions for color filter arrays

A color image meant for human consumption can be appropriately displayed only if at least three distinct color channels are present. Typical digital cameras acquire three-color images with only one sensor. A color filter array (CFA) is placed on the sensor such that only one color is sampled at a particular spatial location. This sparsely sampled signal is then reconstructed to form a color image with information about all three colors at each location. In this paper, we show that the wavelength sensitivity functions of the CFA color filters affect both the color reproduction ability and the spatial reconstruction quality of recovered images. We present a method to select perceptually optimal color filter sensitivity functions based upon a unified spatial-chromatic sampling framework. A cost function independent of particular scenes is defined that expresses the error between a scene viewed by the human visual system and the reconstructed image that represents the scene. A constrained minimization of the cost function is used to obtain optimal values of color-filter sensitivity functions for several periodic CFAs. The sensitivity functions are shown to perform better than typical RGB and CMY color filters in terms of both the s-CIELAB ∆E error metric and a qualitative assessment.

Noise robustness of a colorimetric evaluation model for image acquisition devices with different characterization models

Colorimetric evaluation of an image acquisition device is important for evaluating and optimizing a set of sensors. We have already proposed a colorimetric evaluation model [J. Imaging Sci. Technol. 49, 588-593 (2005)] based on the Wiener estimation. The mean square errors (MSE) between the estimated and the actual fundamental vectors by the Wiener filter and the proposed colorimetric quality (Qc) agree quite well with the proposed model and we have shown that the estimation of the system noise variance of the image acquisition system is essential for the evaluation model. In this paper, it is confirmed that the proposed model can be applied to two different reflectance recovery models, and these models provide us an easy method for estimating the proposed colorimetric quality (Qc). The influence of the system noise originates from the sampling intervals of the spectral characteristics of the sensors, the illuminations and the reflectance and the quantization error on the evaluation model are studied and it is confirmed from the experimental results that the proposed model holds even in a noisy condition.

A subspace matching color filter design methodology for a multispectral imaging system

In this paper, we present a methodology to design filters for an imaging system to improve the accuracy of the spectral measurements for families of reflective surfaces. We derive the necessary and sufficient conditions that the sensor space of the system must obey in order to measure the spectral reflectance of the surfaces accurately. Through simulations, we show how these conditions can be applied to design filters using a set of sample spectral data acquired from extracted teeth. For this set of data, we also compare our results to those of Wolski's method, a conventional filter design method which produces filters that recover tristimulus values of surfaces accurately under several illuminants. We show that our method produces filters that capture the spectral reflectance better given the same number of measurements. The errors in predicting the color of the sample data are much lower under every test illuminant when the filters designed with our method are used.

Recovery of spectral reflectances of objects being imaged without prior knowledge

Prior knowledge of the noise present in a color image acquisition device is very important in estimating colorimetric values or in recovering the spectral reflectances of pixels of objects being imaged, since these values are greatly influenced by the noise. In this paper, a new model is proposed for the determination of the noise variance of a multispectral color image acquisition system and experimental results to demonstrate its accuracy are presented. It is demonstrated that the noise variance of an actual multispectral color image acquisition system computed by the proposal agrees fairly well with the variance which minimizes the mean-square error of the recovered reflectances by the Wiener filter. As an application of the proposal, it is shown that spectral reflectances of an art painting are recovered accurately by the use of sensor responses without prior knowledge of objects being imaged and noise present in an image acquisition system.

Spectral characterization of a color scanner based on optimized adaptive estimation

A scanner characterization method is proposed to estimate spectral reflectance from scanner responses by using an optimized adaptive estimation method. In contrast to our previous study [J. Opt. Soc. Am. A21, 1125 (2004)], this method considers the weighting of training samples. It is demonstrated that the color accuracy of this method is only slightly affected by the number of training samples and can provide more accurate reflectance estimation.

Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra

Nonnegative color analysis filters are obtained by using an invertible linear transformation of characteristic spectra, which are orthogonal vectors from a principal component analysis (PCA) of a representative ensemble of color spectra. These filters maintain the optimal compression properties of the PCA scheme. Linearly constrained nonlinear programming is used to find a transformation that minimizes the noise sensitivity of the filter set. The method is illustrated by computing analysis and synthesis filters for an ensemble of measured Munsell color spectra.

Using reflectance models for color scanner calibration

We examine the use of linear spectral reflectance models for calibrating a color scanner to generate device-independent CIE XYZ values from scanner vectors. Polynomial regression approaches to color scanner calibration use parameterized functions to approximate the calibration mapping over a set of training colors. These approaches can perform poorly if the parameterized functions do not accurately model the structure of the desired calibration mapping. Several studies have shown that linear reflectance models accurately characterize a wide range of materials. By viewing color scanner calibration as reflectance estimation, we can incorporate linear reflectance models into the calibration process. We show that in most cases linear models do not constrain the calibration problem sufficiently to allow exact recovery of X, Y, Z from a scanner vector obtained with three filters. By examining a series of methods that exploit information about reflectance functions, however, we show that reflectance information can be used to improve the accuracy of calibration over that of standard methods applied to the same set of inputs.

Color categories revealed by non-negative matrix factorization of Munsell color spectra

Non-negative matrix factorization (NMF, Nature 401 (1999) 788-791) is a method to derive non-negative basis functions for sets of data that are inherently non-negative, such as color spectra. We applied NMF to Munsell color spectra and investigated the color names associated with the non-negative basis functions. NMF yields basis functions compatible with established color naming categories.

System design for accurately estimating the spectral reflectance of art paintings

Accurately estimating the spectral reflectance of art paintings from low-dimensional multichannel images requires that both image-acquisition hardware with appropriate spectral characteristics and appropriate estimation software be applied to the captured multichannel image. In this study, a system that incorporates both factors is designed and developed on the basis of the minimum-mean-square error criterion. The accuracy of spectral estimation by use of this system is evaluated, and the system's high performance is demonstrated.

Color device calibration: a mathematical formulation

The mathematical formulation of calibrating color image reproduction and recording devices is presented. This formulation provides a foundation for future research in areas of characterization of devices and display of color images. The importance of calibration is demonstrated by real examples. The procedure outlined in this paper should become standard for displaying color images for the image processing community.

Figures of merit for color scanners

In the design and evaluation of color scanners and cameras, it is useful to have a single figure of merit that closely agrees with perceived color accuracy. In the past, several measures of goodness for color scanning filters have been proposed to fulfil such a requirement. Most of the proposed measures have had shortcomings in that they are either based on error metrics in color spaces that are not perceptually uniform, or in that they do not take into account the effects of measurement noise. An extension of the most promising measure, based on linearized CIELAB space, is proposed to obtain a new figure of merit that has a high degree of perceptual relevance and also accounts for the varying noise performance of different filters. The paper also provides a common framework for the different figures of merit and a comprehensive comparison of their computational complexity and reliability.