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Characterization of different blue using a custom-design multispectral imager Asylbek Kulmyrzaev, Dominique Bertrand, Éric Dufour

To cite this version:

Asylbek Kulmyrzaev, Dominique Bertrand, Éric Dufour. Characterization of different blue cheeses using a custom-design multispectral imager. Dairy Science & Technology, EDP sciences/Springer, 2008, 88 (4-5), pp.537-548. ￿hal-00895793￿

HAL Id: hal-00895793 https://hal.archives-ouvertes.fr/hal-00895793 Submitted on 1 Jan 2008

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Dairy Sci. Technol. 88 (2008) 537–548 Available online at: c INRA, EDP Sciences, 2008 www.dairy-journal.org DOI: 10.1051/dst:2008021 Original article

Characterization of different blue cheeses using a custom-design multispectral imager

Asylbek Kulmyrzaev1*, Dominique Bertrand2,ÉricDufour1

1 Unité de Recherches Typicité des Produits Alimentaires, ENITA Clermont-Ferrand, Marmilhat, BP 35, 63370 Lempdes, France 2 Unité de Sensiométrie et de Chimiométrie, ENITIAA-INRA, BP 82225, 44322 Nantes, France

Abstract – The present study was conducted to determine whether multispectral imagery combined with chemometrics could accurately distinguish and classify different blue cheeses. The images of the pre-packed PDO Bleu d’Auvergne (n = 12) and Fourme d’Ambert (n = 23) blue cheeses were acquired using a custom-design multispectral imager. The image acquisition was conducted in the ultraviolet (360 nm, 370 nm and 400 nm), visible (470 nm, 568 nm and 625 nm) and near- infrared (875 nm and 950 nm) spectral regions. The spectral functions of image texture based on the Fourier spectrum and image weights were extracted from the raw multivariate images using an image processing tool and a method of simultaneous decomposition of covariance matrices, respectively. Principal component analysis (PCA) and partial least squares discriminant analysis (PLSDA) of the spectrum functions showed a reliable discrimination of the Bleu d’Auvergne and Fourme d’Ambert blue cheeses. Examination of the image weights using PLSDA allowed the pre- diction of the producers of the blue cheeses. Our data demonstrated the ability of the multispectral imagery combined with chemometrics to characterize the quality and identity of the blue cheeses in a rapid and inexpensive manner. blue / characterization / multispectral imagery / image texture / chemometrics

摘要 – 利用特制的多谱段成像仪描述蓝纹干酪的性质。本研究目的是为了确定是否可以 用多谱段图像结合化学统计学来准确识别和分类不同的蓝纹干酪。使用自行设计的多谱段 成像仪对预先包装好的原产地保护产品 Bleu d’Auvergne 干酪 (n = 12) 和 Fourme d’Ambert 干酪 (n = 23) 在紫外光 (360 nm、370 nm、400 nm), 可见光 (470 nm、568 nm、625 nm) 和近 红外光 (875 nm 和 950 nm) 光谱区域分别采集图像。基于傅立叶光谱和图像权重而建立的 图像纹理光谱函数是从经图像处理工具和同步分解协方差矩阵方法处理的原始多元图像中 推算出来的。频谱函数主成分分析 (PCA) 和偏最小二乘判别分析 (PLSDA) 结果显示, 该方 法能可靠的区分 Bleu d’Auvergne 和 Fourme d’Ambert 蓝纹干酪。而且使用 PLSDA 检验图 像权重还能预测蓝纹干酪的生产商。实验表明, 多谱段图像结合化学统计学方法是一种快 速、经济的描述蓝纹干酪特性和鉴定蓝纹干酪的方法。

蓝纹干酪 / 特征 / 多谱段图像 / 图像纹理 / 化学统计学

Résumé – Caractérisation de différents fromages à pâte persillée par imagerie multispec- trale. Cette étude avait pour objectif de déterminer le potentiel de l’imagerie multi-spectrale cou- plée à la chimiométrie, à discriminer et à classer correctement des fromages à pâte persillée. Les images de portions de fromages AOC Bleu d’Auvergne (n = 12) et Fourme d’Ambert

* Corresponding author (通讯作者): [email protected]

Article published by EDP Sciences 538 A. Kulmyrzaev et al.

(n = 23) pré-emballés ont été enregistrées au moyen d’un banc d’imagerie multi-spectrale déve- loppé par nos laboratoires. Les images ont été acquises sur une plage spectrale incluant l’ultra- violet (360, 370 et 400 nm), le visible (470, 568 et 625 nm) et le proche infrarouge (875 et 950 nm). Les fonctions spectrales issues de transformées de Fourier et caractérisant la texture de l’image et les poids des images ont été extraites des images multi-spectrales au moyen, respectivement, d’un algorithme d’analyse d’image et d’une méthode de décomposition simultanée des matrices de co- variances. L’analyse en composantes principales (ACP) et l’analyse discriminante par partial least squares (AD-PLS) des fonctions spectrales mettent en évidence une bonne discrimination des fro- mages Bleu d’Auvergne des Fourme d’Ambert. L’analyse de la matrice de données sur les poids des images par AD-PLS permet de prédire le producteur des fromages. Nos résultats montrent le poten- tiel de l’imagerie multi-spectrale couplée à la chimiométrie pour caractériser la qualité et l’identité de fromages à pâte persillée de manière rapide et peu coûteuse. fromage à pâte persillée / caractérisation / imagerie multi-spectrale / texture des images / chimiométrie

1. INTRODUCTION squares discriminant analysis (PLSDA), factorial discriminant analysis, common Continuously growing production of components and specific weights anal- cheeses requires novel rapid and nonde- ysis (CCSWA), and others considerably structive analytical techniques to analyze increases the yield of useful information. quality and safety of cheeses. In addition to This approach has been applied to study- meeting compositional, flavor and aroma ing melting temperature and content of standards, cheese must also meet standards solid fat in cream [4], protein structure and for body, texture, color and appearance. protein interaction during Control of origin of cheeses is also im- [15], measurement of milk composition portant so consumers can purchase authen- [17, 18], effect of homogenization and tic cheeses with confidence. Each sort of heat treatment on the physicochemical cheese has individual texture, color appear- properties and quality of milk [3, 13], ance, and formed as a result of a specific cheese rheology [11], cheese identity and cheese-making technology. Consequently, structure [6], and geographical origin of these attributes are used to distinguish milk and cheeses [9, 10]. between great varieties of cheeses. It is a common practice when skilled experts Classical spectroscopy yields informa- evaluate quality and origin of cheeses. tion on a single point or small region However, evaluation of cheese quality by a of a sample at a time. A relatively new panel of experts is time-consuming and re- technology called multispectral imaging quires experienced specialists with specific combines spectroscopic and imaging tech- knowledge and strong sensory capabilities. niques to collect spectral and spatial infor- Therefore, this kind of cheese analysis is mation simultaneously. The data collected unsuitable for rapid and precise prediction can be represented as a three-dimensional of cheese quality on the industrial scale. data cube, or images formed by adding Fluorescence and infrared spectro- two-dimensional spatial information to the scopies have been investigated extensively one-dimensional spectral information at as rapid and nondestructive alternative each pixel. Therefore, multispectral imag- techniques for the analysis of food ing dramatically increases the amount of properties and constituents [12]. Cou- usable information content. Imaging tech- pling spectroscopy with multivariate nology and image analysis have success- chemometric methods such as principal fully been used to study muscles and component analysis (PCA), partial least have been proposed as an effective on-line Multispectral imaging of blue cheeses 539 technique for monitoring the quality of the ability of the technique to distinguish beef and pork [7, 8, 14, 16]. cheeses depending on cheese producer, 3 A large number of cheeses (Roquefort, to 9 slices were cut off from one cheese Stilton, , Fourme d’Ambert, and each slice was analyzed as an inde- Bleu d’Auvergne, Cabrales, etc.) are pendent sample. The Fourme d’Ambert grouped under the category of blue cheeses were manufactured by three dif- cheeses. All blue cheeses share the same ferent dairy companies, coded A (n = 24), flavor-producing agent, the mould Penicil- B(n = 6) and C (n = 18). The manufac- lium roquefortii. Despite similarities, the turers of three Bleu d’Auvergne cheeses blue cheeses exhibit differences, i.e. ori- were identified and coded A (n = 6), gin of the milk (cow’s, ewe’s), shape B(n = 9) and C (n = 19). The producers of cheeses, strains of the of several Bleu d’Auvergne cheeses were roquefortii, and color of the blue veins. not identified from the product labels and Fourme d’Ambert and Bleu d’Auvergne therefore these samples were considered are Protected Designation of Origin (PDO) as “Supplementary” and coded S (n = 10). cheeses both produced from cow’s milk All cheeses were stored at 4 ◦Cbefore to a limited extent in Auvergne (France). conducting experiments. PDO is a guarantee for consumers of the uniqueness of a food product, particularly cheeses, and an effective marketing tool for 2.2. Multispectral imaging the producers. To guarantee the authentic- ity of the PDO cheeses, it is necessary to Cheese images were recorded using a develop analytical techniques to enable au- custom-design multispectral imaging sys- thorities and producers to control correct tem presented elsewhere [1]. Briefly, the description and labeling of cheeses. imaging system consisted of a dark enclo- This paper presents a study on the abil- sure with a sample holder. The dark enclo- ity of the multispectral imaging technique sure was built as a box with a round open- to characterize different pre-packed blue ing on the top, through which the camera cheeses, particularly Fourme d’Ambert was mounted facing downwards. The il- and Bleu d’Auvergne. Combining multi- lumination source of the system was also spectral imaging with multivariate statis- mounted in the dark enclosure and con- tical tools allowed differentiation of the sisted of 8 sets of light-emitting diodes cheeses depending on the cheese type and (LED) (Roithner LaserTechnik GmbH, cheese producer. Vienna, Austria) emitting light in the ul- traviolet (360 nm, 370 nm and 400 nm), visible (470 nm, 568 nm and 625 nm) and 2. MATERIALS AND METHODS near-infrared (875 nm and 950 nm) spec- tral ranges. The images of the cheese sam- 2.1. Cheese collection ples were captured with a highly sensitive cooled CCD color camera (DX20, KAPPA Pre-packed pieces of 12 Bleu Opto Electronics, Gleichen, Germany) d’Auvergne and 23 Fourme d’Ambert with a zoom lens (focal length of 5.6– blue cheeses were obtained from different 32 mm, COMPUTAR, Bioblock, Illkirch, supermarkets in Clermont-Ferrand and France) and a Peltier air-cooling system. Nantes (France). The dairy companies The imaging system was connected to a manufacturing the blue cheeses were PC and controlled by a custom design identified for the majority of the samples frame-acquiring program written in Matlab from product labels. In order to prove 7.5.0.342 (R2007b) (MathWorks, Natick, 540 A. Kulmyrzaev et al.

z

Computing: Correction against 1. image covariance; « white reference » 2. decomposition z of image covariance p Chemometrics n Image cube Computing: 1. spectrum features of image texture n×p Refolded Unfolded image cube image cube

Figure 1. Procedures developed for image processing.

MA, USA). The imaged area of each sam- wavelength dimension (z = 21 channels) ple was about 5 × 4 cm and each im- was built using the images of each sam- age formed a matrix dimensioned 480 × ple. The final cube images were then ob- 660. Twenty-four images (8 illumination tained as a logarithm of the ratio “white wavelength × 3 (RGB) channels of the reference/image cube” (Fig. 1). This trans- camera) corresponding to different spectral formation was carried out for every pixel conditions were collected on each sample. and every spectral condition. Twenty-one images were selected for fur- In total, 141 image cubes were analyzed ther analysis after removing three images using two approaches. containing no information. First, spectral functions of image tex- ture based on the Fourier spectrum were extracted for each channel of an image 2.3. Image analysis cube [5]. Extracted image spectral func- tions were expressed as the spectrum in po- Spectral images are multivariate and can lar coordinates applied to an image (Fig. 2) be regarded as a three-way data structure, yielding a function S(r, θ),whereS is the a ‘cube’. They are interpreted as a stack of spectrum function, and r and θ are the ra- images or as one image of pixel vectors [2]. dial and the angular coordinates, respec- Considering pixels as vectors of spectral tively. One-dimensional functions S θ(r)for data independently of the spatial relation- each θ and S r(θ) for each r were computed ship occurring in the image scene is equiv- and a global description was obtained by alent to unfolding each image into a single these functions as [5]: vector, i.e. unfolding the three-way mul- π tivariate image into a usual two-way data S (r) = S θ (r) matrix (Fig. 1). The two-way data matrix θ=0 is then much more convenient for mathe- and matical treatment. R = 0 An image cube with two spatial (n S (θ) = S (θ) = r 480 pixels and p 660 pixels) and one r=1 Multispectral imaging of blue cheeses 541

Figure 2. A coordinate system applied to the cheese images for computing the spectrum function S(r, θ)(r is the radial coordinate, θ is the angular coordinate, R0 is the radius of a circle centered at the origin). The computation yields the 1-D functions S θ(r)andS r(θ).

where R0 is the radius of a circle cen- decomposed into score images ta and load- tered at the origin. Functions S (r)and ing vectors pa using PCA (Fig. 3). In order S(θ) constitute a spectral-energy descrip- to speed up computation, the cross-product tion of texture for an image region un- matrix XX is subjected to SVD. Thus, the der consideration. The idea behind this ap- model of decomposition is [2]: proach is that the behaviors of functions A S (r)andS(θ)differ from one image to an-   X(k) X(k) = λ(k)p p other, which could make it possible to dis- a a a = tinguish between the studied cheeses. The a 1 code “specxture” developed previously [5] where X(k) is the unfolded matrix derived st was applied to computing the two preced- from the k image cube, pa is the load- ing image texture measurements. (k) ings, and λa is the specific weights of the The second approach is based upon pro- latent dimension a for the kst image cube. jecting the images into an appropriate fac- In the present study image weights were torial space, which is carried out using a computed for 10 dimensions, which was method of simultaneous decomposition of assumed to provide reliable discrimination covariance matrices. This method allows of the cheese samples. the extraction of components common to The spectral functions of image texture each image and reveals their specificities and image weights were computed using through specific weights. It is assumed that algorithms programed in Matlab 7.5.0.342 common loading vectors exist that can be (R2007b). weighted differently for each multivariate The image analysis results were orga- image [2]. Singular value decomposition nized into three matrices. The first one con- (SVD) of X, an unfolded image cube, is tained the values of S θ(r) computed with illustrated in Figure 3. X is obtained by the increment of r equal to 1 pixel. The unfolding the image cube X and is then first column and the first row of this matrix 542 A. Kulmyrzaev et al.

z z

z

p = +++... n

n×p n×p X Xt1 p1 t2 p2 E

Figure 3. Singular value decomposition of an unfolded image (X is an image cube, X is an unfolded matrix, ta is score images, pa is loading vectors and E is the noise part of the decomposition).

contained cheese sample names and values Matlab 7.5.0.342 (R2007b) were utilized of r, respectively. The structure of the sec- in the statistical data treatment. ond matrix was similar to that of the first one and contained the values of S r(θ)com- puted with the increment of θ equal to 1◦. 3. RESULTS AND DISCUSSION The third matrix was built of the computed (k) image weights λa , in which the first col- 3.1. Analysis of spectrum features umn represented the cheese sample names, while the first row represented the dimen- PCA and PLSDA of the spectrum fea- sions (10). tures showed that the function S θ(r)com- puted from images is more useful in dis- crimination of the blue cheeses than the function S (θ). When applying PCA to 2.4. Multivariate statistical analysis r the function S θ(r) it was possible to ob- serve evident differences between the Bleu Principal component analysis (PCA) d’Auvergne and Fourme d’Ambert blue and partial least squares discriminant anal- cheeses. Figure 4 shows a PCA scatter- ysis (PLSDA) written by the authors were plot view of the Bleu d’Auvergne and applied to the computed image features. Fourme d’Ambert blue cheeses in respect The objective of the statistical processing to their scores in the first two principal was to derive relevant information from components (PC1 and PC2). The image the image data allowing the discrimination patterns (e.g., shapes of blue veining) of and classification of the blue cheeses. In the two cheeses are very similar, which PLSDA a “leave-one-out” cross-validation makes it difficult to differentiate between process was used for validation, that is, the cheeses visually. The results of PCA leaving one sample of the calibration set demonstrated that spectral features of the at a time for prediction. The custom-design images are appropriate indicators for dif- versions of PCA and PLSDA programed in ferentiation of blue cheeses. As shown in Multispectral imaging of blue cheeses 543

4

2

0

−2 PC2 (7.6%)

−4 BA FA −6 −10 −8 −6 −4 −20246810 PC1 (36.1%)

Figure 4. Discrimination of the blue cheeses using PCA applied to the spectrum function S θ(r)(BA is the Bleu d’Auvergne blue cheeses and FA is the Fourme d’Ambert blue cheeses).

Figure 4, despite some samples of the Bleu the spectrum along the radial direction on d’Auvergne and Fourme d’Ambert blue an image, it was assumed that this infor- cheeses overlapping, two separate groups mation should be of spectral origin. In of the cheeses can be easily distinguished. order to verify this hypothesis, the func- Figure 5 shows a score plot of a PLSDA tion S θ(r) for the cheese samples was an- classification of the Bleu d’Auvergne and alyzed. In Figure 6 an example plot of Fourme d’Ambert blue cheeses based on S θ(r) in the 30 pixels distance from the the function S θ(r) computed from the origin along the radial direction computed cheese images. The PLSDA model took for a Bleu d’Auvergne and a into account five variables. Most of the Fourme d’Ambert blue cheese is presented. Bleu d’Auvergne cheeses were assigned These two cheese samples marked with cir- positive scores regarding dimension D1, cles in Figure 5 are in opposition to each while the majority of the Fourme d’Ambert other, which points out considerable dif- cheeses were scored negative. Cheese sam- ference in the texture of the correspond- ples were classified according to the group ing images. The difference between these for which they had the best match. This can two cheeses can be characterized by the be expressed in terms of the percentage of notable shift of the corresponding peaks in the samples assigned to the correct class. the functions S θ(r)(Fig.6). Thus, it can The classification success of the cheeses is be concluded that the classification of the presented in Table I. Bleu d’Auvergne and Fourme d’Ambert Since the source of information for the blue cheeses derived using PCA (Fig. 4) identification of cheeses was the function and PLSDA (Fig. 5) is based upon the S θ(r), which characterizes the behavior of spectral features of the cheese images. 544 A. Kulmyrzaev et al.

1e+6 BA FA 8e+5

4e+5

0 D2

−4e+5

−8e+5

−1e+6 −1e+6 −5e+5 0 5e+5 1e+6 D1

Figure 5. Score plot of the classification of the blue cheeses resulting from PLSDA applied to the spectrum function S θ(r) (BA is the Bleu d’Auvergne blue cheeses and FA is the Fourme d’Ambert blue cheeses).

Table I. Results of the PLSDA classification of the blue cheeses obtained using the spectral mea- surements of the cheese image texture.

Bleu d'Auvergne Fourme d'Ambert Classification success (%) Bleu d'Auvergne 61 3 95.3 Fourme d'Ambert 8 69 89.6

3.2. Analysis of cheese image weights data table by means of PLSDA. It should be noted that the best results were ob- It was intended to analyze whether the tained when PLSDA was performed sepa- image weights could be a reliable indica- rately on the Bleu d’Auvergne and Fourme tor to distinguish between the blue cheeses d’Ambert blue cheese image weights. Fig- according to the cheese producer. Initially, ure 7 presents a factorial map determined (k) the image weights λa were projected in the by the first and second dimensions pro- space determined by the first and second duced by the PLSDA applied to the image latent variables, which were more present weights of the Bleu d’Auvergne cheeses. It in the multivariate images compared with can be seen that the cheeses from the pro- other latent variables. The discrimination ducer coded C were widely separated from of the cheeses observed on this kind of plot the rest, and there was some overlap of the was poor (data not shown). Therefore, in cheeses produced by the A and B cheese- order to distinguish the cheeses better, it makers and supplementary S cheeses (un- was decided to analyze the image weights known producer). All the C cheeses had Multispectral imaging of blue cheeses 545

0.16 0.14 BA FA 0.12 0.10 0.08 A.U. 0.06 0.04 0.02 0.00 0 5 10 15 20 25 30 Radial coordinate (pixel)

Figure 6. Examples of the spectrum function S θ(r) computed for the Bleu d’Auvergne cheese (BA) and Fourme d’Ambert cheese (FA) marked with circles in Figure 4.

0.002

0.001

0.000 D2 −0.001

S −0.002 A B C −0.003 −0.12 −0.08 −0.04 0.00 0.04 0.08 D1

Figure 7. Discrimination of the Bleu d’Auvergne blue cheeses according to the cheese producer, resulting from PLSDA of the image weights (A, B, C and S denote different cheese producers). 546 A. Kulmyrzaev et al.

Table II. Results of the PLSDA classification of the Bleu d’Auvergne blue cheeses according to the cheese producer obtained using the image weights (A, B, C and S denote different cheese producers; see Materials and Methods).

A B C S Classification success (%) A4200 66.7 B2601 66.7 C20151 83.3 S 1 5 0 12 66.7

0.002 A B 0.001 C

0.000 D2 −0.001

−0.002

−0.003 −0.06 −0.04 −0.02 0.00 0.02 0.04 0.06 D1

Figure 8. Discrimination of the Fourme d’Ambert blue cheeses according to the cheese producer, resulting from PLSDA of the image weights (A, B and C denote different cheese producers). negative scores according to the first di- by means of PLSDA, considering a model mension (D1), while the A, B and S with 5 dimensions, is presented in Table II. cheeses had positive scores, meaning the The best performance was obtained for image features of the C cheeses differed to the C cheeses (83.3%), and the A, B and a considerable extent from those of the re- S cheeses were predicted with lower accu- maining cheeses (Fig. 7). The image pat- racy (66.7%). The data in Table II prove terns such as shapes and sizes of blue vein- that the A, B and S cheeses were char- ing and pixel intensities observed on the acterized with more homogeneous image blue cheese pieces are greatly influenced weights, which caused more problematic by the cheese-making conditions. The dis- classification. tribution of the cheeses observed in Fig- Better performance was demonstrated ure 7 might suggest that the production for the Fourme d’Ambert blue cheese dif- conditions of the cheeses coded A, B and ferentiation and classification. In Figure 8, S were similar. The accuracy of classi- the cheeses were well separated into three fication of the Bleu d’Auvergne cheeses groups according to the dimension D1 in Multispectral imaging of blue cheeses 547

Table III. Results of the PLSDA classification of the Fourme d’Ambert blue cheeses obtained using the image weights (A, B and C denote different cheese producers; see Materials and Methods).

A B C Classification success (%) A164 4 66.7 B060 100 C 4 1 13 72.2 relation to three producers, A, B and C. polar coordinates, S(r, θ)(Fig.2), were Cheeses A, B and C were classified as ac- shown to be a good image feature to dis- curately as 66.7%, 100% and 72.2%, re- tinguish between the Bleu d’Auvergne and spectively (Tab. III). Good classification of Fourme d’Ambert blue cheeses. This re- the Fourme d’Ambert blue cheeses indi- sult was yielded when the spectrum func- cated the greater difference in their image tion was analyzed using PCA and PLSDA. patterns, which could be the effect of pro- On the other hand, the image weights de- duction conditions, i.e. the contribution of rived using the method of simultaneous native microflora from the local milk and decomposition of covariance matrices ap- environment to the cheese ripening, differ- plied to the unfolded image cube (Fig. 3) ing from one producer to another. and submitted to the PLSDA procedure Consequently, results from PLSDA re- allowed the discrimination of the blue vealed that image weights could be an ef- cheeses by the cheese producer. In sum- fective indicator to differentiate the blue mary, this study demonstrated the capacity cheeses with respect to the production of multispectral imagery to classify differ- origin. ent blue cheeses in spite of the visual sim- ilarity of their structure and appearance. It is reasonable to expect that as an an- 4. CONCLUSION alytical technique, multispectral imagery combined with chemometrics will offer a Application of chemometric tools to an- rapid and relatively inexpensive method alyzing multivariate images obtained by for monitoring cheese quality and identity. means of the simple multispectral imager ff ff o ers an e ective tool for distinguish- Acknowledgements: The financial contribu- ing and classifying different blue cheeses. tion of the European Commission to this As the present study has demonstrated, project is acknowledged (Project MIF1-CT- the advantage of multispectral imaging in 2005-021890). cheese quality studies is that by applying a large number of illuminating light wave- lengths specific to different cheese con- REFERENCES stituents it is possible to obtain multivari- ate images containing useful information [1] Chevallier S., Bertrand D., Kohler A., for identification of the blue cheeses. An Courcoux P., Application of PLS-DA in mul- tivariate image analysis, J. Chemometr. 20 important point in the multivariate image (2006) 1–9. processing is extraction of appropriate im- age features, which contain information [2] Courcoux P., Devaux M.F., Bouchet B., of interest. Spectral measurements of im- Simultaneous decomposition of multivari- ate images using three-way data anal- age texture based on the Fourier spectrum ysis. Application to the comparison of and expressed as the spectrum function in cereal grains by confocal laser scanning 548 A. Kulmyrzaev et al.

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