Surface reflectance estimation by the dichromatic model

A method is described for estimating the surface-spectral reflectances of glossy objects when the color signal is a mixture of diffuse reflections, specular reflections, and interreflections. The objects are inhomogeneous dielectric materials, and the reflected light is measured using a spectroradiometer. We first describe the main idea; the color signals, reflected from two closely apposed surfaces with a single interreflection between them, can be expressed by a linear combination of the illuminant spectrum and two diffuse spectral reflection functions. We introduce a representation in which each of these three terms is projected onto a point on a unit sphere. Estimation of the diffuse reflection functions is then reduced to finding the vertices of the spherical triangle. Next, an algorithm is described to estimate the locations of the vertices of diffuse reflectance functions from the measured samples. The reliability of the algorithm is demonstrated in an experiment using two plastic objects with glossy surfaces. © 1996 John Wiley & Sons, Inc.     

Methods of selecting a small reflectance set as a transfer standard for correcting spectrophotometers

The present article concerns the use of software and transfer standards of reflectance to correct a fielded spectrophotometer so that it behaves closely like a reference instrument. A method is described to choose from a large set of reflectances the best subset of a few reflectances to act as a transfer standard. A reflectance set is generated from the algorithm using each of two alternative metrics for instrument closeness: CIELAB ΔE* and a weighted sum of absolute differences over wavelength. Both metrics yield transfer standards that conspicuously exclude BCRA reflectances and also show improvement over the BCRA reflectances currently used for this purpose. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 13–17, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20169     

Waypoint shift manifolds for object color evaluation and comparison

Variability in object appearance is common in everyday experience and this variability can generally be attributed to the relationships between viewing conditions and the composition of an object's spectral reflectances. This paper proposes that objects, illuminants, and observers can be evaluated using a Wpt (Waypoint) shift manifold (WSM), which is defined as a set of Wpt points associated with one or more objects, observers, and/or illuminants. Since spectral reflectances of an object can be decomposed to three components (a wavelength invariant nonselective component, a characteristic reflectance, and a metameric black reflectance), WSMs of any object for an observing condition is composed of three Wpt vectors associated with a perfect reflecting diffuser, the characteristic reflectance, and the metameric black reflectance of the object. Material shift potential (MSP) can be defined as shapes and orientations of object WSMs for evaluation and comparison of object colors. Experimental results show that MSP are dramatically influenced by Wpt vectors associated with the characteristic reflectance and the metameric black reflectance for an object rather than the Wpt vectors associated with nonselective reflectance. Thus, MSP can be preserved for objects having similar characteristic reflectances and metameric black reflectances. In other words, spectral reflectances that have been manipulated to have similar overall shapes exhibit similar color inconstancy.     

Linear bases for spectral reflectance functions of acrylic paints

A linear model for representing reflectances has been developed from a group of 5574 samples of acrylic paint on paper. Using acrylic paints makes easy the generation of a large variety of samples by mixing, due to the high miscibility among these kinds of pigments: this point was the key to achieve a great spatial homogeneity in our samples. Besides, these kinds of paints keep their chromatic properties stable over time. The first 7 vectors of the so-called overall linear basis were sufficient for a more than adequate mathematical representation of the spectral-reflectance curves. A study by hue groups of the mathematical properties of these curves indicates that the use of a hue basis of representation implies, on the average, a reduction in 1 or 2 of the number of vectors needed in order to achieve results analogous to those of the overall basis. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 39–45, 1998     

Colorimetric calibration of a video digitizing system: Algorithm and applications

In principle, digitized color video images should be rich and convenient sources of colorimetric information. In practice, these advantages are offset by the difficulty of reliably translating the video camera's output into colorimetric variables. A solution to this problem is outlined here, one which exploits the fact that spectral reflectances of many natural materials vary slowly in the visible. A characteristic vector analysis of reflectances for a set of such materials leads to an algorithm that gives colorimetrically accurate spectral reflectances from the red-green-blue output of a video digitizing system. Prior knowledge about the illumination leads to chromaticity and luminance information, which can be comparable in quality to that obtained from a spectrora-diometer. Some sample retrievals are shown for the algorithm. Since it is designed to correct color biases that are unknown initially, the algorithm has the advantage that images from many sources can be analyzed.     

Comparison of real colour gamuts using a new reflectance database

A large set of data, comprising the spectral reflectances of real surface colours, has been accumulated. The data comprise 16 groups with different materials and include 85,879 measured spectra. From these data, CIELAB colorimetric coordinates were calculated under CIE illuminant D50 and the CIE 1931 standard colorimetric (2°) observer. Several published colour gamuts including those developed by Pointer and ISO reference colour gamut [ISO Graphic Technology Standard 12640‐3:2007] were compared using the present data set. It was found that the Pointer gamut is smaller than the new real data in most of the colour regions. The results also showed that the ISO reference colour gamut is larger than the new real accumulated data in most regions. The present finding indicates that there is a need to derive a new colour gamut based on the newly accumulated data for common applications. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 442–451, 2014     

Spectral reflectance reconstruction from RGB images based on weighting smaller color difference group

A method to reconstruct spectral reflectance from RGB images is presented without priori knowledge of camera's spectral responsivity. To obtain the spectral reflectance of a pixel or region in images, this method assumes that reflectance is a weighted average of reflectances of samples in a selected training group, in which all samples have smaller color difference with that pixel or region. Four proposed weighting modes with different selected numbers of training samples were investigated. Among them, the inverse square weighting mode obtains the best performance, and it is not very sensitive to the selected training samples number. Experimental results show that all weighting modes outperform the traditional method in terms of root mean squared error and Goodness‐of‐Fit Coefficient between the actual and the reconstructed reflectances as well as color differences under the other light condition. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 327–332, 2017     

The principal components of reflectances

There are practical reasons to represent a set of reflectance spectra by a limited basis‐function expansion. Such an expansion is most tractable in color technology applications when it is homogenous. However, more often a true principal‐component analysis (PCA) is performed, which involves an offset of the expansion by a mean spectrum. In deference to custom, we discuss and exercise the traditional PCA on reflectances. We review the method of calculation and present tables of the principal components of 3,534 object‐color samples from three color‐order systems. Next, we describe two kinds of principal‐component coordinates of a measured reflectance spectrum, one obtained by least‐square best fit and the other by tristimulus match under one or more specified lights. Finally, we show illustrative examples, and propose some possible new uses for principal‐component analysis of reflectances. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 104–110, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10230     

Recovering neugebauer colorant reflectances and Ink‐spreading curves from printed color images

Spectral reflection prediction models, although effective, are impractical for certain industrial applications such as self‐calibrating devices and online monitoring because their calibration requires specific color‐constant calibration patches. Using the CMYK Ink‐Spreading enhanced Yule‐Nielsen‐modified Spectral Neugebauer model (IS‐YNSN), we propose a method to recover the colorant reflectances (Neugebauer primaries), the ink‐spreading curves, and the Yule‐Nielsen n‐value using only tiles extracted from printed color images. There is no prior knowledge about the reproduction device. Thanks to a set of constraints based on principal component analysis and the relationships between composed Neugebauer primaries and the ink transmittances, good approximations of the Neugebauer primaries are achieved. These approximations are then optimized, yielding an accurately calibrated IS‐YNSN model comparable to the one obtained by classical calibrations. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 216–233, 2014; Published online 23 February 2013 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/col.21800     

Absolute reflectance factor calibration for goniospectrophotometry

Currently, spectrophotometric standard reference materials are calibrated only using the CIE recommended illumination and viewing geometries. A need exists for standards that have been calibrated at many other combinations of illumination and viewing angles. The common practice has been to assume that a primary transfer standard such as BaSO₄ is Lambertian even though its non-Lambertian behavior is well documented. This study was undertaken to develop a practical standard for this type of metrology. Two diffuse materials, BaSO₄ and PTFE, were characterized goniospectrophotometrically. Bidirectional absolute spectral reflectance factors were determined for 60 combinations of illumination and view angles in a single plane. Neither material was found to be Lambertian and both failed to completely depolarize reflected radiation. The results were modeled using principal components analysis. The resulting model allows the determination of bidirectional spectral reflectances factors with a minimum effort. PTFE powder can be prepared repeatably with no significant effect on the measured reflectance properties, thus indicating that it would be a suitable primary transfer standard for goniospectrophotometry.     

Principal components applied to modeling: Dealing with the mean vector

Principal components analysis is often used to fit a population of spectral reflectances by a mean vector plus a basis‐function expansion about the mean. Certain color‐technology applications (such as color correction) are much easier if the mean is absent. If the mean of reflectance (or of another spectral function) is a linear combination of the first few principal components (such as the first three), then a linear model can fit the original data without mentioning the mean vector in the model's formulation. This idea is worked out step by step, and a realistic example is presented. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 261–266, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20021     

Numerical methods for smoothest reflectance reconstruction

Three numerical methods are presented for finding the smoothest reflectance curve associated with a given triplet of tristimulus values. The methods differ in how “smooth” is defined, and also differ in the domain of colors over which they are applicable. The first method is very quick and applies to any tristimulus values, but sometimes can yield reflectance curves with portions that fall outside the range 0 to 1. The second method applies to colors within the spectral locus (real colors) and guarantees that the reflectances produced are positive. The third method applies to colors within the object color solid (object colors) and guarantees that the reflectances fall within the range 0 to 1. The methods are shown to create reflectances that closely resemble those of real colors (natural and synthetic). Focus is given to implementing the numerical methods in very short MATLAB/Octave functions and to understanding the numerical behavior of the methods near the limits of their respective domains of applicability in terms of matrix conditioning and discretization artifacts.     

Using color to separate reflection components

In computer vision, the goal of which is to identify objects and their positions by examining images, one of the key steps is computing the surface normal of the visible surface at each point (“pixel”) in the image. Many sources of information are studied, such as outlines ofsuifaces, intensity gradients, object motion, and color. This article presents a method for analyzing a standard color image to determine the amount of interface (“specular”) and body (“diffuse”) reflection at each pixel. The interface reflection represents the highlights from the original image, and the body reflection represents the original image with highlights removed. Such intrinsic images are of interest because the geometric properties of each type of reflection are simpler than the geometric properties of intensity in a black-and-white image. The method is based upon a physical model of reflection which states that two distinct types of reflection–interface and body reflection–occur, and that each type can be decomposed into a relative spectral distribution and a geometric scale factor. This model is far more general than typical models used in computer vision and computer graphics, and includes most such models as special cases. In addition, the model does not assume a point light source or uniform illumination distribution over the scene. The properties of tristimulus integration are used to derive a new model of pixel-value color distribution, and this model is exploited in an algorithm to derive the desired quantities. Suggestions are provided for extending the model to deal with diffuse illumination and for analyzing the two components of reflection.     

On the colours dichromats see

Dichromatic colour vision is commonly believed to be a reduced form of trichromatic colour vision (referred to as the reductionist principle). In particular, the colour palette of the dichromats is believed to be a part of the colour palette of the trichromats. As the light‐colour palette differs from the object‐colour palette, the dichromatic colour palettes have been derived separately for light‐colours and object‐colours in this report. As to light‐colours, the results are in line with the widely accepted view that the dichromatic colour palettes contain only two hues. However, the dichromatic object‐colour palettes have proved to contain the same six component colours which constitute the trichromatic object‐colour palette (yellow, blue, red, green, black and white). Moreover, all the binary and tertiary combinations of the six component colours present in the trichromatic object‐colour palette also occur in the dichromatic object‐colour palettes. Yet, only five of the six component colours are experienced by dichromats as unitary (unique) object‐colours. The green unitary colour is absent in the dichromatic object‐colour palettes. The difference between the dichromatic and trichromatic object‐colour palettes arises from the fact that not every combination of the component‐colour magnitudes occurs in the dichromatic object‐colour palettes. For instance, in the dichromatic object‐colour palettes there is no colour with the strong green component colour. Furthermore, each achromatic (black or white) component colour of a particular magnitude is combined with the only combination of the chromatic components. In other words, the achromatic component colours are bound with the chromatic component combinations in dichromats. © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 112–124, 2014     

Wavelength sensitivity of AATCC Blue wool lightfastness standards under light radiation

The fading characteristics of the AATCC Blue Wool L2 and L4 lightfastness standards were examined from the standpoint of wavelength sensitivity. Experiments were carried out by exposing a specimen to a narrow monochromatic band isolated from the dispersed polychromatic light emitted by a Xe lamp source. The wavelength sensitivity characteristics of Blue wool L2 and L4 lightfastness were determined on a radiant energy basis. Both Blue Wool Standards displayed peak maxima at 245 and 294 nm. The results indicated that UVA and UVB had a significant fading effect, whereas visible light caused fading to a small extent. Specific wavelengths caused Blue wool to significantly fade, suggesting that the total irradiated UV energy may not be an appropriate index. In addition, their spectral reflectances did not directly explain these characteristics of the standards.     

The coefficient of variation as a measure of spectrophotometric repeatability

The mean color difference from the mean (MCDM) is a standard measure of spectrophotometric repeatability. This article proposes a supplementary measure: the coefficient of variation (CoV), which is the ratio of the standard deviation of the measured reflectances to their mean. The CoV is calculated from the same repeated sample measurements as the MCDM. Unlike the MCDM, the CoV depends only on physical quantities, and not on perceptual quantities; furthermore, a CoV is defined for each wavelength. This article analyzes data from six different spectrophotometer–sample combinations. An important empirical result is that the CoV is nearly constant across wavelengths, except when the reflectance at a particular wavelength is less than about 5%, in which case, measurement variability is markedly greater. Because the MCDM tends to lose this fact through averaging, the CoV is recommended as an adjunct to the MCDM for spectrophotometer analysis and development. The CoV analysis also provides evidence that samples’ surface geometry is a major factor in measurement variability. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 571–579, 2016     

Color mixing and color separation of pigments with concentration prediction

In this study, we propose a color mixing and color separation method for opaque surface made of the pigments dispersed in filling materials. The method is based on Kubelka–Munk model. Eleven different pigments with seven different concentrations have been used as training sets. The amount of concentration of each pigment in the mixture is estimated from the training sets by using the least‐square pseudo‐inverse calculation. The result depends on the number and type of pigments selected for calculation. At most we can select all pigments. The combinations resulted with negative concentrations or unusual high concentrations are discarded from the list of candidate combination. The optimal pigment's set and its concentrations are estimated by minimizing the reflectance difference of given reflectance and predicted reflectance. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 461–469, 2008     

The properties of multiple CMF determinations using alternative primary sets part I: Evidence and modeling

This article concerns William Thornton's single‐observer colour matching functions (CMFs). Alternative “prime colour” (or PC), “non‐prime” (or NP), and “anti‐prime” (or AP) wavelengths were used, and the measurements appear to challenge the basis on which conventional colorimetry predicts metameric colour matches. An analysis of Thornton's visual match data for alternative‐primary CMFs is presented. Using conventional colorimetric calculations, Thornton's articles establish failures of linear transformability between experimental data sets, failures of tristimulus sum prediction, and differences in CIE chromaticity for a set of strongly metameric stimuli that all match the same neutral reference stimulus. Error analysis using an optimization model is first used to confirm that Thornton's data represent a significant challenge to the standard colorimetric model. Thornton's assertion is supported that spectral power appears to be visually subadditive at NP and AP wavelengths compared with spectral power at the PC wavelengths. It is next shown that each of the individual failures of prediction can be eliminated by relatively minor adjustments to the relevant CMFs. However, each instance of failure required a different adjustment. Multiple and significantly incompatible linear adjustments of the CMFs are apparently needed to explain Thornton's results. The implication is that the visually additive value of the spectral stimuli used in the matches varies not only with wavelength but also as a nonlinear function of stimulus power. The implied variations in visual additivity become significant only at certain wavelengths. Thus a small and specific subset of strongly metameric light‐source matches, such as those chosen by Thornton, are required to reveal significant variations. Such spectrally localized variations have a minimal overall effect in the tristimulus sum predictions for surface‐colour matches using broadband stimuli. A detailed analysis of the central assumptions concerning additive colour mixing is given. It suggests that any super and subadditive visual effects revealed by Thornton's measurements can be accommodated within the standard colorimetric model by extending the model rather than by modifying the CMFs. An extension is proposed in which any possible super‐ or subadditive phenomena are modeled by a redefinition of the units of visual additivity, using a spectral‐level precursor transform. Its intent is to equate the additive properties of all possible incident stimuli numerically, prior to manipulation using the Standard Model. An appropriate methodology is also described for confirming measuring and classifying any spectrally distinct super and subadditive effects. Under The Heading for Prediction Failures the methods described are applied to Thornton's data. They reveal consistent evidence of additivity differences that are both wavelength and stimulus power dependent. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 273–284, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20022     

Dimensionality determined microwave absorption properties in ferrite/bio-carbon composites

Composition and structural design play a very influential role in the microwave absorption (MA) manipulation of ferrite/carbon composites. Here, by carefully choosing the dimensionality of the bio-carbon materials, the interfacial geometries and MA properties of ferrite/bio-carbon composites have been controlled effectively. The one dimensional (1D), two dimensional (2D), and three dimensional (3D) biomass-based carbon materials decorated with ZnFe₂O₄ (ZFO) particles were obtained respectively from carbon fibers (1D), tree leaves (2D), wheat straw (2D), peanut shell (3D) and orange peel (3D) by a simple two-step synthesis method. With increasing the bio-carbon's dimensionality from 1D, 2D to 3D, the ferrite/carbon composite's MA properties are promoted and the minimum reflection loss is enhanced from −9 dB to −45 dB. By changing the ZFO/3D-bio-carbon samples' thickness, a broad absorption range from 4 to 18 GHz can be covered. Moreover, the effective absorption bandwidth for ZFO/3D-bio-carbon can be modified up to 7.1 GHz, which covers the whole Ku band. These observations identified the important roles of the ferrite/carbon interface and dimensionality of carbon materials and provided an effective and low-cost route to design microwave absorption materials based on biomass-industrial waste composites.     

Uniform-scale chromaticity diagrams: Opponent-chromatic responses as logarithms of the cone-activation ratios

Chromatic-response functions and a uniform-scale chromaticity diagram are derived by assuming that normal trichromatic vision is obtained by combining tritanopic and deuteranopic vision. Two different opponent-chromatic mechanisms can be related to these two dichromatic visions. The chromatic-response functions obtained are the logarithms of proper cone-activation ratios (CAR). Each opponent-chromatic mechanism consists of two parts separated by a properly defined neutral point that depends on the surround chromaticity. The Abney-hue shift, the wavelength discrimination for trichomats, deuteranopes, and tritanopes, and the threshold purity are well reproduced. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 27–38, 1998