Two-dimensional Correlation Coefficient Research Articles

Quantitative characterization of vascular targeted photodynamic therapy efficiency for port-wine stains using image processing techniques

SignificanceVascular targeted photodynamic therapy (V-PDT) is a clinically approved therapeutic approach for treating vascular-related diseases, such as port-wine stains (PWS). For accurate treatment, various light doses are required for different lesions due to the irregularity of vascular size, shape, degree of disease, which commonly alters during different stages of V-PDT, making quantitative analysis of treatment efficiency is highly needed. ApproachLesion images before and after V-PDT treatment of patients with PWS were used to construct a quantitative method to characterize the differences among lesions. Image analysis techniques were applied to calculate Euclidean distances and two-dimensional correlation coefficients for V-PDT efficiency evaluation. ResultsAccording to the image analysis, V-PDT with good treatment efficiency resulted in a larger Euclidean distance and a smaller correlation coefficient, in comparison with the case having lower V-PDT efficiency. ConclusionsThe new method to quantify the Euclidean distances and correlation coefficients is developed, which is promising for the quantitative analysis of V-PDT efficiency for PWS.

Improved fuzzy evidential DEMATEL method based on two-dimensional correlation coefficient and negation evidence

Improved fuzzy evidential DEMATEL method based on two-dimensional correlation coefficient and negation evidence

Using Flexible and Stretchable Surface Electromyography Electrode Array to Evaluate Congenital Muscular Torticollis in Children.

Congenital Muscular Torticollis (CMT) is a neuromuscular disease in children, which leads to exacerbation of postural deformity and neck muscle dysfunction with age. Towards facilitating functional assessment of neuromuscular disease in children, topographic electromyography (EMG) maps enabled by flexible and stretchable surface EMG (sEMG) electrode arrays are used to evaluate the neck myoelectric activities in this study. Customed flexible and stretchable sEMG electrode arrays with 84 electrodes were utilized to record sEMG in all subjects during neck motion tasks. Clinical parameter assessments including the cervical range of motion (ROM), sonograms of the sternocleidomastoid (SCM), and corresponding histological analysis were also performed to evaluate the CMT. The muscle activation patterns of neck myoelectric activities between the CMT patients and the healthy subjects were asymmetric during different neck motion tasks. The CMT patients presented significantly lower values in spatial features of two-dimensional (2D) correlation coefficient, left/right energy ratio, and left/right energy difference (p < 0.001). The 2D correlation coefficient of activation patterns of neck rotation and extension in CMT patients significantly correlated with clinical parameter assessments (p < 0.05). The findings suggest that the spatial features of muscle activation patterns based on the sEMG electrode arrays can be utilized to evaluate the CMT. The flexible and stretchable sEMG electrode array is promising to facilitate the functional evaluation and treatment strategies for children with neuromuscular disease.

Two-Dimensional Clustering of Spectral Changes for the Interpretation of Raman Hyperspectra.

Two-dimensional correlation spectroscopy (2D-COS) is a technique that permits the examination of synchronous and asynchronous changes present in hyperspectral data. It produces two-dimensional correlation coefficient maps that represent the mutually correlated changes occurring at all Raman wavenumbers during an implemented perturbation. To focus our analysis on clusters of wavenumbers that tend to change together, we apply a k-means clustering to the wavenumber profiles in the perturbation domain decomposition of the two-dimensional correlation coefficient map. These profiles (or trends) reflect peak intensity changes as a function of the perturbation. We then plot the co-occurrences of cluster members two-dimensionally in a manner analogous to a two-dimensional correlation coefficient map. Because wavenumber profiles are clustered based on their similarity, two-dimensional cluster member spectra reveal which Raman peaks change in a similar manner, rather than how much they are correlated. Furthermore, clustering produces a discrete partitioning of the wavenumbers, thus a two-dimensional cluster member spectrum exhibits a discrete presentation of related Raman peaks as opposed to the more continuous representations in a two-dimensional correlation coefficient map. We demonstrate first the basic principles of the technique with the aid of synthetic data. We then apply it to Raman spectra obtained from a polystyrene perchlorate model system followed by Raman spectra from mammalian cells fixed with different percentages of methanol. Both data sets were designed to produce differential changes in sample components. In both cases, all the peaks pertaining to a given component should then change in a similar manner. We observed that component-based profile clustering did occur for polystyrene and perchlorate in the model system and lipids, nucleic acids, and proteins in the mammalian cell example. This confirmed that the method can translate to "real world" samples. We contrast these results with two-dimensional correlation spectroscopy results. To supplement interpretation, we present the cluster-segmented mean spectrum of the hyperspectral data. Overall, this technique is expected to be a valuable adjunct to two-dimensional correlation spectroscopy to further facilitate hyperspectral data interpretation and analysis.

Multinodes interval electric vehicle day-ahead charging load forecasting based on joint adversarial generation

The spatial–temporal distribution of electric vehicle (EV) charging load has strong randomness and is affected by battery capacity and user behavior. In addition, the multinode charging load in the distribution network has differential correlations. A multinode charging load joint adversarial generation interval-forecasting method considering the spatial correlation of the charging load between nodes is proposed to effectively forecast the spatial–temporal distribution of EV charging load. First, the multinode joint charging scenario is constructed. Under the spatial charging load matrix, the spatial–temporal correlation between multinode charging loads in the joint charging scenario of the forecast day and the historical day is analyzed. According to the strong-correlation historical-day multinode joint charging scenario of the forecasting day, the original multinode multiple-correlation-day joint charging scenario set, describing the charging behavior of multinode EVs, is determined. Second, a Wasserstein generative adversarial network with a gradient penalty is used to characterize the strong randomness of the spatial–temporal distribution of the charging load. A large number of joint charging scenarios with similar probability distributions but different timing distributions from the original scenario set are generated to obtain the potential spatial–temporal distribution of the multinode joint charging load. Then, based on the weighted two-dimensional correlation coefficient, the strong-correlation joint scenario set on the day to be forecast is selected from the generated multinode multiple-correlation-day joint charging scenario set. Finally, according to the strong-correlation joint scenario set on the day to be forecast, the interval-forecasting conclusion of the multinode EV charging load is obtained. To verify the effectiveness of the new multinode charging load interval-forecasting method, the simulation experiment uses the measured charging load data of 32 charging stations in a region of Zhejiang Province. The comparative experiment demonstrated that the proposed method has more-refined intervals and higher coverage than state-of-the-art interval forecasting models. Among the evaluation indexes of the charging load forecasting results of the new method, the PICP value is higher than 90.4%, and the PINAW and MAPE values are lower than 32.1% and 17.7%, respectively. The new method overcomes the limitation that the total charging load obtained by each node's charging load forecasting method is much higher than the actual demand.

Combination of Hyperspectral and Machine Learning to Invert Soil Electrical Conductivity

An accurate estimation of soil electrical conductivity (EC) using hyperspectral techniques is of great significance for understanding the spatial distribution of solutes and soil salinization. Although spectral transformation has been widely used in data pre-processing, the performance of different pre-processing techniques (or combination methods) on different models of the same data set is still ambiguous. Moreover, extremely randomized trees (ERT) and light gradient boosting machine (LightGBM) models are new learning algorithms with good generalization performance (soil moisture and above-ground biomass), but are less studied in estimating soil salinity in the visible and near-infrared spectra. In this study, 130 soil EC data, soil measured hyperspectral data, topographic factors, conventional salinity indices such as Salinity Index 1, and two-band (2D) salinity indices such as ratio indices, were introduced. The five spectral pre-processing methods of standard normal variate (SNV), standard normal variate and detrend (SNV-DT), inverse (1/OR) (OR is original spectrum), inverse-log (Log(1/OR) and fractional order derivative (FOD) (range 0–2, with intervals of 0.25) were performed. A gradient boosting machine (GBM) was used to select sensitive spectral parameters. Models (extreme gradient boosting (XGBoost), LightGBM, random forest (RF), ERT, classification and regression tree (CART), and ridge regression (RR)) were used for inversion soil EC and model validation. The results reveal that the two-dimensional correlation coefficient highlighted EC more effectively than the one-dimensional. Under SNV and the second order derivative, the two-dimensional correlation coefficient increased by 0.286 and 0.258 compared to the one-dimension, respectively. The 13 characteristic factors of slope, NDI, SI-T, RI, profile curvature, DOA, plane curvature, SI (conventional), elevation, Int2, aspect, S1 and TWI provided 90% of the cumulative importance for EC using GBM. Among the six machine models, the ERT model performed the best for simulation (R2 = 0.98) and validation (R2 = 0.96). The ERT model showed the best performance among the EC estimation models from the reference data. The kriging map based on the ERT simulation showed a close relationship with the measured data. Our study selected the effective pre-processing methods (SNV and the 2 order derivative) using one- and two-dimensional correlation, 13 important factors and the ERT model for EC hyperspectral inversion. This provides a theoretical support for the quantitative monitoring of soil salinization on a larger scale using remote sensing techniques.

An image analysis method for determining boiling front in minichannel heat exchanger

In this work a numerical method for determining boiling front in short time period of flow was presented. A non-stationary boiling in rectangular eleven minichannels (0.25 mm x 0.25 mm x 32 mm) was recorded using Phantom v1610 high speed camera with the speed of 6000 fps. In the algorithm correlation between subsequent frames was computed. Frames were divided into reference and test frames. In each iteration a part of a reference frame called ‘reference gate’ and moving part of a test frame called ‘moving gate’ were considered. A two-dimensional correlation coefficient was calculated. Such method allowed to identify the location of boiling front in each minichannel separately.

Generating electromagnetic Schell-model sources using complex screens with spatially varying auto- and cross-correlation functions

We present a method to generate any physically realizable electromagnetic Schell-model source. Our technique can be directly implemented on existing vector-beam generators that utilize spatial light modulators for coherence control, beam shaping, and relative phasing. This work significantly extends published research on the subject, where control over the partially coherent source’s cross-spectral density matrix was limited.We begin by presenting the statistical optics theory necessary to derive and implement our method. We then apply our technique, both analytically and in simulation, to produce two electromagnetic Schell-model sources from the literature. We demonstrate control over the full cross-spectral density matrices of both partially coherent beams. We compare the simulated results of these two sources to the corresponding theoretical or designed quantities to validate our approach. We find, through examination of the two-dimensional correlation coefficients, that both sources converge to their desired, ensemble (or by ergodicity, “long-time”) statistics within 500 random field instances.Our method and subsequent findings will be useful in any application where control over beam shape, polarization, and spatial coherence are important. These include but are not limited to free-space/underwater optical communications, directed energy, medicine, atomic optics, and optical tweezers.

Rapid identification of soil organic matter level via visible and near-infrared spectroscopy: Effects of two-dimensional correlation coefficient and extreme learning machine

Accurate estimation of soil organic matter (SOM) is essential in understanding the spatial distribution of SOM to identify areas that need fertilization and the required grade of those fertilizers. Visible and near-infrared spectroscopy is a promising alternative to time consuming and costly conventional soil assessment methods. However, this approach is highly dependent on selecting suitable preprocessing strategies and data mining techniques for regression analysis. In this study, 2D correlation coefficients, including ratio, difference, and normalized difference indices, were introduced to select sensitive spectral parameters. The performance of extreme learning machine (ELM) was evaluated via comparison with that of support vector machine (SVM) for SOM estimation. A total of 257 soil samples were collected from Hubei Province, Central China, with SOM contents and reflectance spectra measured in the laboratory. Five spectral pretreatments, except for the raw spectra, were applied. SVM and ELM models were calibrated on spectral parameters selected by one-dimensional and 2D correlation coefficients and subsequently applied to predict SOM. Results showed that 2D correlation coefficient can effectively highlight the detailed SOM information compared with that of one-dimensional correlation coefficient. The ELM models yielded superior predictability relative to SVM models in all eight established models. The most excellent estimation accuracy was obtained by 2D ratio index and ELM (TRI-ELM) method, with an independent validation R2 and a ratio of performance to interquartile range of 0.83 and 3.49, respectively. The SOM fertility levels of predicted SOM showed that TRI-ELM method presented the largest similarity to laboratory-measured SOM levels, and misclassified samples were all concentrated within one error level. In summary, our study indicates that the TRI-ELM model is a rapid, inexpensive, and relatively accurate method for identifying SOM fertility level.

Automated EPID-based measurement of MLC leaf offset as a quality control tool

The multi-leaf collimator (MLC) dosimetric leaf gap (DLG) offset and transmission are measured parameters which influence the dosimetric accuracy of radiation therapy treatment plans. An international consortium developed an efficient method of automatically measuring the two-dimensional MLC DLG and transmission using the electronic portal imaging device (EPID) on multiple Varian TrueBeam linacs incorporating Millennium and high definition (HD) MLCs. Quality control was implemented as part of each test. Results were compiled including comparisons to baseline measurements and between machines. Validations were accomplished using ion chambers (IC) and a 2D IC array. Sensitivity was investigated by introducing deliberate leaf position offsets, repeatability was assessed, and performance was analyzed using statistical process control methods. The EPID measured DLG (EDLG) and transmission were consistently smaller than the IC measured DLG and transmission for all machines tested. EDLG variations across two dimensions averaged more than 0.24 mm for both Millennium and HD MLCs, demonstrating that leaf-to-leaf DLG variations should be assessed for both MLC types. The two-dimensional correlation coefficient between the IC array and EPID measurements was at least 0.937. A nearly linear relationship between changes in the EPID measured leaf gap and actual leaf positions was measured, with R2 > 0.999. EDLG results were analyzed as a difference relative to a baseline EDLG measurement for each machine, a metric we labeled the leaf offset constancy (LOC). The maximum change in LOC out of the 20 repeatability tests was −0.094 mm. The LOC QC process was found to be capable (Cpk > 1) for 4 machines using a ± 0.15 mm specification limit. LOC results showed that leaves may deviate from their reference positions at a level that approaches dosimetric significance for small stereotactic and highly modulated treatment fields, with average excursions measuring up to 0.21 mm for a Millennium MLC and 0.16 mm for a HD MLC. The effects of initialization, gantry angle, and common repairs are also reported.

A New Two-Dimensional Rank Correlation Coefficient

Spearman’s rank correlation coefficient might be the best known nonparametric measure of association currently in use. It assesses the linear relationships between the ranks of monotonically related variables even if the relationship between the variables is not linear. This study presents a new method for calculating two-dimensional (horizontal and vertical) rank correlation coefficients between matrices composed of variables which are not necessarily in linear association. The matrices contain the ranks of measurements instead of raw values. The averages of all rows are used for calculating the horizontal rank correlation and the averages of all columns are used for calculating the vertical rank correlation instead of considering the averages of the whole matrices. This approach enables a separate determination of the degree of horizontal and vertical relationships between the compared data matrices by using the horizontal and vertical variance and covariance values that constitute the base of the two-dimensional correlation method. The presented method is first applied on 5 simple hypothetical matrices and then on the monthly total precipitation records of 6 stations in southwest Turkey. The results have shown that the presented rank correlation approach successfully assesses the two-dimensional associations between the hypothetical matrices and time series data like precipitation, provides a measure for exactly determining the monotonic relationships not determined by the conventional Pearson’s and Spearman’s correlation approaches, it is much more robust to outliers and normality is not a prerequisite. The software developed for calculating two-dimensional rank correlation coefficients is freely provided together with this paper.

Translational motion correction algorithm for truncated cone-beam CT using opposite projections.

Cone-beam computed tomography (CBCT) is widely used in various medical imaging applications, including dental examinations. Dental CBCT images often suffer from motion artifacts caused by involuntary rigid motion of patients. However, earlier motion compensation studies are not applicable for dental CBCT systems using truncated detectors. This study proposes a novel motion correction algorithm that can be applied for truncated dental CBCT images. We propose a two-step method for motion correction. First, we estimate the relative displacement of each pair of opposite projections by finding the motion vector that maximizes the two-dimensional correlation coefficients of the opposite projections. Second, we convert the relative displacement into the absolute coordinate motion that yields the highest image sharpness of the reconstruction image. Using the motion vectors in the absolute coordinate system, motion artifacts are then compensated by modifying the trajectory of the source and detector during the back-projection step of the image reconstruction process. In simulation, the proposed method successfully estimated the true relative displacement. After converting to the absolute coordinate motions, the motion-compensated image was close to the ground-truth image and exhibited a lower mean-square-error than that of the uncompensated image. The results from the real data experiment also confirmed that the proposed method successfully compensated for the motion artifacts. The experimental results confirmed that the proposed method was applicable to most dental CBCT systems using a truncated detector without any use of an additional motion tracking system nor prior knowledge.

Blind Steganography in Color Images by Double Wavelet Transform and Improved Arnold Transform

&lt;p&gt;Steganography is a method which can put data into a media without a tangible impact on the cover media. In addition, the hidden data can be extracted with minimal differences. In this paper, two-dimensional discrete wavelet transform is used for steganography in 24-bit color images. This steganography is of blind type that has no need for original images to extract the secret image. In this algorithm, by the help of a structural similarity (SSIM) and a two-dimensional correlation coefficient, it is tried to select part of sub-band cover image instead of embedding location. These sub-bands are obtained by 3-levels of applying the DWT. Also to increase the steganography resistance against cropping or insert visible watermark, two channels of color image is used simultaneously. In order to raise the security, an encryption algorithm based on Arnold transform was also added to the steganography operation. &lt;/p&gt;

Statistical two-dimensional correlation spectroscopy of urine and serum from metabolomics data

Statistical two-dimensional correlation spectroscopy combined with pattern recognition is demonstrated for coanalysis of NMR spectroscopic data from different sources. The urine and serum 1H NMR spectra from metabolomics datasets of diabetes and hyperthyroidism are taken as examples. The intrinsic covariance of certain molecules between urine and serum spectra is identified. The highly urine-serum-correlated metabolites are further analyzed by using the projection to latent structure discriminant analysis (PLS-DA) method. To illustrate the applicability of the method, the metabolomics datasets of diabetes and hyperthyroidism are imported separately to calculate the corresponding two-dimensional urine-serum correlation coefficient matrixes. The results show that creatinine (δ 4.08) and succinate (δ 2.45) are found to be highly correlated between urine and serum from diabetes patients, and choline (δ 3.21) and pyruvate (δ 2.33) are highly correlated between urine and serum from hyperthyroidism patients. This study offers a new angle of view for interpreting metabolomics data and demonstrates the potential of the correlation analysis of spectra from different biological sources as a new systems biology tool.

Comparison of the observed dependence of large-scale Birkeland currents on solar wind parameters with that obtained from global simulations

Abstract. Spatial distributions of the large-scale Birkeland currents derived from magnetic field data acquired by the constellation of Iridium Communications satellites have been compared with global-magnetosphere magneto-hydrodynamic (MHD) simulations. The Iridium data, spanning the interval from February 1999 to December 2007, were first sorted into 45°-wide bins of the interplanetary magnetic field (IMF) clock angle, and the dependencies of the Birkeland currents on solar wind electric field magnitude, Eyz, ram pressure, psw, and Alfvén Mach number, MA, were then examined within each bin. The simulations have been conducted at the publicly-accessible Community Coordinated Modeling Center using the University of Michigan Space Weather modeling Framework, which features a global magnetosphere model coupled to the Rice Convection Model. In excess of 120 simulations with steady-state conditions were executed to yield the dependencies of the Birkeland currents on the solar wind and IMF parameters of the coupled model. Averaged over all IMF orientations, the simulation reproduces the Iridium statistical Birkeland current distributions with a two-dimensional correlation coefficient of about 0.8, and the total current agrees with the climatology averages to within 10%. The total current for individual events regularly exceeds those computed from statistical distributions by factors of ≥2, resulting in larger disparities between observations and simulations. The simulation results also qualitatively reflect the observed increases in total current with increasing Eyz and psw, but the model underestimates the rate of increase by up to 50%. The equatorward expansion and shift of the large-scale currents toward noon observed for increasing Eyz are also evident in the simulation current patterns. Consistent with the observations, the simulation does not show a significant dependence of the total current on MA.

Coupled human erythrocyte velocity field and aggregation measurements at physiological haematocrit levels

Simultaneous measurement of erythrocyte (RBC) velocity fields and aggregation properties has been successfully performed using an optical shearing microscope and Particle Image Velocimetry (PIV). Blood at 45% haematocrit was sheared at rates of 5.4⩽γ˙⩽252s-1 and imaged using a high speed camera. The images were then processed to yield aggregation indices and flow velocities. Negligible levels of aggregation were observed for γ˙⩾54.0s-1, while high levels of aggregation and network formation occurred for γ˙⩽11.7s-1. The results illustrate that the velocity measurements are dependent on the extent of RBC aggregation. High levels of network formation cause the velocities at γ˙⩾5.4s-1 to deviate markedly from the expected solid body rotation profile. The effect of aggregation level on the PIV accuracy was assessed by monitoring the two-dimensional (2D) correlation coefficients. Lower levels of aggregation result in poorer image correlation, from which it can be inferred that PIV accuracy is reduced. Moreover, aggregation is time-dependent, and consequently PIV accuracy may decrease during recording as the cells break up. It is therefore recommended that aggregation and its effects are taken into account in future when undertaking blood flow studies using PIV. The simplicity of the technique, which requires no lasers, filters, or special pretreatments, demonstrates the potential wide-spread applicability of the data acquisition system for accurate blood flow PIV and aggregation measurement.

Two-dimensional correlation coefficient mapping in gas chromatography: Jet fuel classification for environmental analysis

We demonstrate the feasibility of using two-dimensional correlation coefficient mapping to classify gas chromatograms of environmental hazards. Correct identification and classification of the contaminants is the prerequisite for their appropriate treatment and containments. A data set consisting of 76 gas chromatograms of eight types of jet fuels, which are common sources of hydrocarbon contamination in ground water, is examined with two-dimensional statistical sample–sample correlation coefficients. Analysis demonstrates that jet fuel samples of the same type correlate strongly with each other but less significantly with other jet fuel classes. According to the magnitude of the correlation coefficients between each pair of the samples, jet fuel types of each sample in the data set can be assigned with an accuracy of 100% through a leave-one-out cross validation (LOOCV) procedure. Correlation coefficient mapping is thus a promising method to classify samples of environmental importance.

Unfolding of apomyoglobin studied with two-dimensional correlations of tryptophan, 8-anilino-1-naphthalenesulfonate, and pyrene fluorescence

Acid-induced unfolding of horse apomyoglobin is studied with fluorescence of tryptophan residues and extrinsic probes 8-anilino-1-naphthalenesulfonate (ANS) and pyrene. Two-dimensional statistical correlation coefficient analysis of tryptophan, ANS and pyrene fluorescence reveals that apomyoglobin unfolds in two steps via a folding intermediate. Both tryptophan and ANS fluorescence show microenvironment-sensitive emission maximum and fluorescence intensity. Hetero-spectral 2D correlation analysis reveals that the “red” tryptophan fluorescence correlates with the “red” ANS fluorescence, and the “blue” correlates with the “blue” in the acid-induced unfolding process. Correlation curves are established between the hydrophobicity of the probe-binding site(s) as disclosed by ANS and pyrene fluorescence and the folding extent of apomyoglobin as indicated by tryptophan fluorescence. Two anion-induced refolding intermediates of apomyoglobin: Cl −-induced A-1, and trichloroacetate (TCA)-induced I-2 do not follow the correlation trajectory in the acid-induced unfolding. This suggests that the two anion-induced intermediates do not belong to the low-salt acid-unfolding pathway of apomyoglobin.

Statistical two-dimensional correlation coefficient mapping of simulated tissue phantom data: Boundary determination in tissue classification for cancer diagnosis

Statistical correlation coefficient mapping has proven to be a useful technique in tissue classification for cancer diagnosis. The classification is achieved by comparing the correlation coefficients for an unknown to a set of selected tissue samples with known pathological conditions. Currently, the correlation coefficient threshold in the classification is empirically determined. In this paper, boundaries of statistical significance between different tissue pathological conditions are established through Bayesian analysis on the Fisher’s z-transformed Pearson’s correlation coefficients between tissue samples. Moreover, probability values are provided in assigning a tissue sample to a specific tissue clinical condition, which is more appreciable in clinical practices. The methodology is examined with a simulated tissue-phantom data set, yielding satisfactory diagnostic results.

Two-dimensional (2D) correlation coefficient analyses of heavily overlapped near-infrared spectra

Two-dimensional (2D) correlation coefficient analysis is employed to classify and characterize spectral variations among heavily overlapped near-infrared spectra of pellets and films of three kinds of polyethylene (PE), high-density (HD), low density (LD), and linear low-density (LLD) polyethylene, and five kinds of ivory signature seals. The sample-sample (SS) 2D correlation maps are used for classification while the wavenumber-wavenumber (WW) 2D correlation maps are used for determining spectral variation among the above materials. Both correlation maps are obtained by multiplying the original data with themselves. It is found that the NIR spectra of pellets and films of HD PE are clearly different from those of LD PE and LLD PE, while the NIR spectra of five kinds of ivory seals yield easily discernable squares in the SS correlation maps. The background variation is thought to be behind the differentiation of the PE samples because the WW correlation maps do not indicate appearance of new bands. The correlation results are compared with those of principal component analysis (PCA). This study is a novel application of 2D correlation coefficient analysis which reveals that a comprehensive description of demanding spectral systems is achievable by utterly simple mathematical means because 2D correlation maps are obtained via a single mathematical operation.