Optimization of sensor response functions for colorimetry of reflective and emissive objects

Design of non-Gaussian multispectral shortwave infrared filters assessed by surface spectral reflectances on the ECOSTRESS library

This paper addresses the multispectral filter design problem for spectral ranges where a viewing subspace is not defined. The methodology of color filter design is extended to this case, which allows the optimization of custom filter transmittance that meets the physical constraints of available fabrication methods. Multispectral shortwave infrared filters are then designed for two scenarios: spectral reconstruction and false-color representation. The Monte Carlo method is used to verify the filter performance degradation due to deviations in fabrication. The results obtained indicate that the proposed method is useful for designing multispectral filters to be fabricated using generic processes without any additional constraints.

Filter design and color correction for the X-cube prism 3CCD camera

For the X-cube prism three-charge-coupled-device (3CCD) camera, the spectra of the designed dichroic films in the X-cube prism shift with changes in the angle of incident light, producing non-uniformity of color on the image plane. We considered the influence of the incident angle on color performance in filter design and directly optimized the thin film to improve color consistency. An optical model was constructed to calculate the distribution of camera spectral sensitivity and independently correct the non-uniform color on the image plane. Results showed that the optimization and correction methods could significantly improve the color performance of the X-cube prism 3CCD camera.

Designing Color Filters That Make Cameras More Colorimetric

When we place a colored filter in front of a camera the effective camera response functions are equal to the given camera spectral sensitivities multiplied by the filter spectral transmittance. In this article, we solve for the filter which returns the modified sensitivities as close to being a linear transformation from the color matching functions of the human visual system as possible. When this linearity condition - sometimes called the Luther condition- is approximately met, the 'camera+filter' system can be used for accurate color measurement. Then, we reformulate our filter design optimisation for making the sensor responses as close to the CIEXYZ tristimulus values as possible given the knowledge of real measured surfaces and illuminants spectra data. This data-driven method in turn is extended to incorporate constraints on the filter (smoothness and bounded transmission). Also, because how the optimisation is initialised is shown to impact on the performance of the solved-for filters, a multi-initialisation optimisation is developed. Experiments demonstrate that, by taking pictures through our optimised color filters, we can make cameras significantly more colorimetric.

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.

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.

Estimation of spectral reflectance of object surfaces with the consideration of perceptual color space

Due to the nonlinear transform from spectral reflectance to CIELAB values, the solution obtained by minimizing reflectance error in traditional spectral characterization methods will not be optimal when evaluated by colorimetric error. We propose a reflectance estimation method with consideration of perceptual color space. It combines two approaches, i.e., colorimetric-based spectral calculation and weighted spectral calculation. The experimental results show that the proposed method performs better than previous methods in terms of color difference with very slight degradation in spectral accuracy.

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.

Spectral-reflectance reconstruction in the near-infrared region by use of conventional charge-coupled-device camera measurements

Our aim is to develop a method for obtaining the reflectance spectra of samples in the near-infrared (NIR) region (800-1,000 nm) by using a small number of measurements performed with a conventional CCD camera (multispectral imaging). We experimentally determined the spectral sensitivity of the CCD camera in the NIR range, used a method based on principal component analysis to reconstruct the spectral reflectance of the samples, and analyzed the number and shape of the filters that need tobe used to apply this method. Finally we obtained the reflectance spectra of a set of 30 spectral curves by numerical simulation. The small amount of errors in the spectral reconstruction shows the potential of this method for reconstructing spectral reflectances in the NIR range.

Inner products and orthogonality in color recording filter design

We formalize ideas of orthogonality and inner products implicit in the development of a number of figures of merit (FOM) of color recording filters. We show that, in negligible measurement noise, the data dependence of each FOM based on linear color correction is equivalent to a choice of inner product (and hence of orthogonality). Further, we show that optimal sensors with respect to noise sensitivity are simply defined as orthogonal with respect to this inner product. We also develop the idea of a generalized Q-factor by generalizing the Euclidean inner product to include all inner products. Simulations demonstrate the utility of our analytical results.

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.

Optimal nonnegative color scanning filters

In this correspondence, the problem of designing color scanning filters for multi-illuminant color recording is considered. The filter transmittances are determined from a minimum-mean-squared orthogonal tristimulus error criterion that minimizes the color error in estimates obtained from noisy recorded data. Nonnegativity constraints essential for physical realizability are imposed on the filter transmittances. In order to demonstrate the significant improvements obtained, the resulting filters are compared with suboptimal filters reported in earlier literature.

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.

Digital color imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented using vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided.