Reconstruction of reflectance data by modification of Berns' Gaussian method (original) (raw)
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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
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.
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.
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.
A step by step recovery of spectral data from colorimetric information
Journal of Optics, 2015
In this paper, a technique named step by step progressive method is devised for recovery of spectral data from the corresponding colorimetric information. The method consists of several stages and employs different techniques, each of which is used to enhance the performance of the recovery as much as possible. The method firstly tests a series of 6 to 3 dimensional linear interpolation techniques, successively; however, there are some samples lying outside the interpolation color gamut, which is the weakest point of the interpolation method, limiting the performance of the first solution. To overcome this problem, a modified version of weighted principal component analysis (wPCA) is employed for the spectral recovery of the samples that have been failed with linear interpolation approach. The employed weighting function takes the spectral distances of the target data and the learning set into accounts. The efficiency of the method is then evaluated by the spectral and colorimetric deviations between the actual and recovered reflectance spectra and is compared with those obtained by classical 3D linear interpolation and PCA methods. As results show that the proposed progressive approach achieves significant improvement in terms of both spectral and colorimetric errors in comparison to the classical methods.
Compression of Reflectance Curves by the use of Fundamental Color Stimuli
Attempts were made for the first time to use dimensionality reduction on the fundamental color stimuli (R FCS ) .Principle component analysis (PCA) was used for such a purpose. The results showed that the reconstruction from R FCS was ideal given zero color difference under the illuminant/observer combination used for R FCS formation.
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.
Journal of The Optical Society of America A-optics Image Science and Vision, 2006
The division of Color Space into ten zones, corresponding to the ten Munsell hues, allows a good reconstruction of surface reflectance spectra using just three eigenvectors, obtained by applying principal components analysis to the reflectance spectra of the Munsell Atlas specimens (model group), although the basis vectors obtained are different for each subspace. The use of the tristimulus values from each measured spectrum, calculated with the Illuminant D65 and the Standard Observer CIE64 to obtain the principal components necessary to reconstruct the spectrum, allows a very high degree of metamerism to be attained between the two spectra (measured and reconstructed). Furthermore, this method of calculating the principal components allows reconstruction of the spectra of specimens from other sample sets that differ from the model group used in the PCA. The colorimetric accuracy obtained in the new sample sets is similar to that obtained for the model group.