Compression of Reflectance Curves by the use of Fundamental Color Stimuli (original) (raw)
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Optical Review, 2008
The classical principal component analysis technique is enhanced for reconstruction of reflectance spectra of surface colors from the corresponding tristimulus values under a given set of viewing conditions, i.e., D65 illuminant and 1964 standard observer. In this paper, the number of implemented eigenvectors has been virtually extended from three to six by estimation of another set of tristimulus values under illuminant A and 1964 standard observer. The second set of colorimetric data was predicted by the conventional non-linear regression method and used in the spectral reconstruction to produce a fully determined system in the case of six eigenvectors. The improvement obtained from the proposed modification was examined for the recovery of the reflectance spectra of Munsell color chips as well as ColorChecker DC samples. The performance is evaluated by the mean, maximum and standard deviation of color difference values under other sets of light sources. The values of mean, maximum and standard deviation of root mean square (RMS) errors between the reproduced and the actual spectra were also calculated. Results are compared with those obtained from traditional methods using the principal component analysis (PCA) routine. All metrics show that the suggested method leads to considerable improvements in comparison with the standard PCA approach.
Surface Reflectance Estimation Using the Principal Components of Similar Colors
Journal of Imaging Science and Technology, 2007
The sensor response of a camera can be represented as the stimulus multiplied by the spectral distribution of an ambient illuminant, the surface reflectance of an object, and camera sensitivity. Surface reflectance is one of the most significant factors that indicates an object's color; therefore its estimation has received widespread attention. Among conventional methods for estimating surface reflectance, principal component analysis (PCA) has an advantage because it uses only one set of principal components for an entire reflectance population. There are limitations, however, in estimating all reflectance using this PCA method with only one set of principal components. In this article, an algorithm is proposed to estimate surface reflectance by using principal components determined by subgroups with similar colors, which are classified from the entire reflectance population. In order to compose a subgroup with similar colors, the Macbeth ColorChecker is utilized to obtain initial representative surface reflectance values for an entire reflectance population; then the Munsell chips are divided into subgroups with different principal components. Moreover, initial representatives have to be modified to avoid biased representations for the population because the Macbeth ColorChecker does not provide optimal representations for the entire reflectance population, even though it is evenly spaced in the CIELAB color space. Therefore, the mean value of each subgroup is used to obtain new representatives, and the new subgroups of reflectance are composed by using the Lloyd quantizer design algorithm. Then, the PCA method is applied for the principal components of the subgroup including surface reflectance. To evaluate its performance, the proposed estimation method was compared with that of a conventional three-band principle component analysis. The proposed method provided better results in its performance.
Reconstruction of reflectance spectra using weighted principal component analysis
Color Research and Application, 2008
The weighted principal component analysis technique is employed for reconstruction of reflectance spectra of surface colors from the related tristimulus values. A dynamic eigenvector subspace based on applying certain weights to reflectance data of Munsell color chips has been formed for each particular sample and the color difference value between the target, and Munsell dataset is chosen as a criterion for determination of weighting factors. Implementation of this method enables one to increase the influence of samples which are closer to target on extracted principal eigenvectors and subsequently diminish the effect of those samples which benefit from higher amount of color difference. The performance of the suggested method is evaluated in spectral reflectance reconstruction of three different collections of colored samples by the use of the first three Munsell bases. The resulting spectra show considerable improvements in terms of root mean square error between the actual and reconstructed reflectance curves as well as CIELAB color difference under illuminant A in comparison to those obtained from the standard PCA method. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 360–371, 2008
Two stage principal component analysis of color
Image Processing, IEEE Transactions on, 2002
We introduce a two-stage analysis of color spectra. In the first processing stage, correlation with the first eigenvector of a spectral database is used to measure the intensity of a color spectrum. In the second step, a perspective projection is used to map the color spectrum to the hyperspace of spectra with first eigenvector coefficient equal to unity. The location in this hyperspace describes the chromaticity of the color spectrum. In this new projection space, a second basis of eigenvectors is computed and the projected spectrum is described by the expansion in this chromaticity basis. This description is possible since the space of color spectra as conical. We compare this two-stage process with traditional principal component analysis and find that the results of the new structure are closer to the structure of traditional chromaticity descriptors than traditional principal component analysis.
Spectral-reflectance function recovery for improved colour-constancy experiments
Displays, 2002
A set of symmetric memory-matching data is presented to analyse some implications of long-term memory factors within classical colourconstancy paradigms and separation algorithms. Using simulated Mondrian-type colour surrounds on a CRT monitor, subjects make a series of colour matches between a test and a matching surface; the surfaces are rendered under the same standard illuminant (equal-energy illuminant). The 16 test surfaces used were categorised into four apparent-hue collections. The analysis of the colour differences show that subjects maintained good mental representations of the surfaces, although a shift in luminance was found. With these results, we investigated how errors in remembering surface colours might be translated into errors in reconstructing surface reflectances. Thus, a description of the remembered surfaces is provided, and the spectral differences are analysed via a goodness-of-fit coefficient (GFC). As it is derived from colour-differential thresholds and GFC values, the analysis of the recalled spectral-reflectance functions shows little loss of information in the observer's task, despite imperfect mathematical recovery of the surfaces. The similarities between test and matching surfaces suggest that colour-constancy algorithms could benefit of memory matches when an illuminant change takes place, and use spectral-tolerance bands defined over the surfaces comprising a scene to improve their implementation. q
An adaptive-PCA algorithm for reflectance estimation from color images
2008 19th International Conference on Pattern Recognition, 2008
This paper deals with the problem of spectral reflectance estimation from color camera outputs. Because the reconstruction of such functions is an inverse problem, stabilizing the reconstruction process is highly desirable. One way to do this is to decompose reflectance function on a basis functions like PCA. The present work proposes an algorithm making PCA adaptive in reflectance estimation from a color camera output. We propose to adapt the PCA basis derivation by selecting, for each sample, the more relevant elements from the training set elements. The adaptivity criterion is achieved by a likelihood measurement. Finally, the spectral reflectance estimation results are evaluated with the commonly used goodness-of-fit coefficient (GFC) and ∆E color difference, and prove the reliability of the proposed methods.
Reconstruction of reflectance data by modification of Berns' Gaussian method
Color Research & Application, 2009
Berns' method for the synthesis of spectral reflectance curve from the tristimulus color coordinates is modified. Firstly, the Gaussian bell shape red primary is replaced with a sigmoidal one to solve the dissimilarity between the spectral curves at the end region of spectrum. Secondly, three predetermined Gaussian primaries used in the original Berns' method are replaced by the adaptive ones which their half-height bandwidths vary with the tristimulus values of the desired color. The mentioned modifications are applied for the recovery of the reflectance curves of 1409 surface colors (including 1269 Munsell color chips and 140 samples of Colorchecker SG) and also 204 textile samples. Results of recovery are evaluated by the mean and the maximum color difference values under other standard light sources. The mean as well as the maximum of root mean squares between the reconstructed and the actual spectra are also calculated. The modifications are compared with the common principal component analysis (PCA) as well as Hawkyard's methods for recovery of reflectance factor. Although the PCA leads to the best results, the modifications significantly improve the recovery outcomes in comparison with the original Berns method.
Reconstruction of reflectance data using an interpolation technique
Journal of the Optical Society of America a Optics Image Science and Vision, 2009
A linear interpolation method is applied for reconstruction of reflectance spectra of Munsell as well as Col-orChecker SG color chips from the corresponding colorimetric values under a given set of viewing conditions. Hence, different types of lookup tables (LUTs) have been created to connect the colorimetric and spectrophotometeric data as the source and destination spaces in this approach. To optimize the algorithm, different color spaces and light sources have been used to build different types of LUTs. The effects of applied color datasets as well as employed color spaces are investigated. Results of recovery are evaluated by the mean and the maximum color difference values under other sets of standard light sources. The mean and the maximum values of root mean square (RMS) error between the reconstructed and the actual spectra are also calculated. Since the speed of reflectance reconstruction is a key point in the LUT algorithm, the processing time spent for interpolation of spectral data has also been measured for each model. Finally, the performance of the suggested interpolation technique is compared with that of the common principal component analysis method. According to the results, using the CIEXYZ tristimulus values as a source space shows priority over the CIELAB color space. Besides, the colorimetric position of a desired sample is a key point that indicates the success of the approach. In fact, because of the nature of the interpolation technique, the colorimetric position of the desired samples should be located inside the color gamut of available samples in the dataset. The resultant spectra that have been reconstructed by this technique show considerable improvement in terms of RMS error between the actual and the reconstructed reflectance spectra as well as CIELAB color differences under the other light source in comparison with those obtained from the standard PCA technique.