Quality Characterization and Classification of Engineered Stone

Article pubs.acs.org/IECR

Quality Characterization and Classification of Engineered Stone Countertops Using a Soft-Sensor Based on Image Analysis Seongkyu Yoon,† Hae Woo Lee,† and J. Jay Liu‡,* †

Department of Chemical Engineering, University of Massachusetts Lowell, Lowell, Massachusetts 01854, United States Department of Chemical Engineering, Pukyong National University, Busan 608-739, Korea

‡

ABSTRACT: An image analysis-based soft sensor is designed and applied to the automatic quality classification of product appearance with color-textural characteristics. In this work, multiresolutional multivariate image analysis (MR-MIA) is used in order to analyze product images with color as well as texture. Partial least-squares-discriminant analysis (PLS-DA) is also used as a supervised learning method for automatic classification. The use of PLS-DA, one of the latent variable methods, enables not only classification of product appearances into distinct classes, but also estimation of product appearance with continuous variations, and analysis of of the appearance characteristics. This approach is successfully applied to the automatic quality classification of intermediate and final products in the industrial manufacturing of engineered stone countertops.

1. INTRODUCTION The visual appearance of manufactured products is one of the important factors when classifying product quality: it is an essential discriminating factor for quality estimation, especially in cases where those products make up the exterior part of other manufactured products, or if they are used mainly for display purposes. A few examples of products with special emphasis on visual appearances include TFT-LCD (thin film transistor liquid crystal display) of TV screens or computer monitors and its core components, polarizer and glass substrate. Intermediate and final inspections of these products aim to monitor and control the visual appearances, as well as their physical and mechanical features, against the desired level of quality. Yet, automatic monitoring of product aesthetics has rarely been successful in related industries, with only a limited application of machine vision available for product quality control. The flotation froth process is one of the few areas where machine vision has been successfully adopted;1,2 yet, this application has rarely been actively extended to other industries where the aesthetic quality of product appearance has been screened solely by the judgment of experienced human operators. In most cases, product inspection by human operators is performed only in the final screening for picking out defective products. Two of the shortcomings when one depends on human operators for quality inspection are that it is time-consuming and costly to train and maintain skillful human operators. Furthermore, quality screening by skilled human operators is limited and open to discrepancy; this inconsistency in human judgment has yet to be resolved in order to secure reliable and solid quality control.3 Lack of shared information and/or collective knowledge is another critical issue when depending on human judgment in quality control. It is difficult to implement consistent classification criteria among operators for deciding on accepted versus defected products.3 In most cases, the operator’s judgment is exercised randomly based on personal experience rather than on shared decisive factors and criteria of the product appearances under inspection. A main reason for this © 2013 American Chemical Society

limitation in the process industry is that the scene of a product image is nondeterministic in nature and does not allow for any concrete assumptions and/or interpretation of the image in question.3 To resolve these limitations, a soft sensor based on multiresolutional-multivariate image analysis (MR-MIA) has been proposed and applied for the monitoring of product appearance based on the product images.3 MR-MIA is an improved version of MIA (multivariate image analysis)4 proposed by Liu and MacGregor, and it has been designed to estimate both color and textural properties of the product images by combining both MIA and wavelet texture analysis.5 It has proven to be promising for quantitatively estimating the visual aesthetics of manufactured products and could easily be adapted for other purposes as well.6,7 On the basis of this consideration, this work extends the MRMIA by combining it with partial least-squares-discriminant analysis (PLS-DA). Specifically, MR-MIR is first used for analyzing the color-textured stone countertop images; then, PLS-DA is adopted for automatic classification of the product appearance based on the signatures obtained from MR-MIA. The results obtained by the combined use of MR-MIA and PLS-DA are comprehensively evaluated in order to prove its versatility and scalability in responding to the specific industrial needs in stone countertop manufacturing. This paper is organized as follows: In section 2, a new analysis method for textural properties is proposed, which combines MR-MIA and PLS-DA in order to analyze both color and textural information of an image; section 3 discusses the application of this method for automatic classification of a product appearance in both intermediate and final inspections; summary and conclusion follow in section 4. Special Issue: John MacGregor Festschrift Received: Revised: Accepted: Published: 12337

December 14, 2012 January 16, 2013 January 24, 2013 January 24, 2013 dx.doi.org/10.1021/ie303442r | Ind. Eng. Chem. Res. 2013, 52, 12337−12345

Industrial & Engineering Chemistry Research

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image (N × K × Q) X is the combined Q stacks of the (N x K) images, and this X can be efficiently analyzed by using principal component analysis (PCA) as follows:

2. ANALYSIS OF COLOR-TEXTURED IMAGES 2.1. Multiresolutional Multivariate Image Analysis (MR-MIA). Product appearance depends on color and/or textural properties of a product surface as shown in Figure 1.

A

X̲ =

∑ Ta ⊗ pa + E̲ a=1

(1)

here the underscore denotes a 3D matrix, Ta (N × K) is the score matrix, pa (Q × 1) is the loading vector, ⊗ is the Kronecker product, and E (N × K × Q) is the residual matrix, respectively. While MIA is known to be effective in extracting color or spectral information with a range of successful applications found in literature,8−11 it has limited performance when extracting spatial information that is closely related to the textural properties.12 Although a few solutions have been suggested to relax this limitation, they still have a limited capability and a narrow range of application.13,14 In contrast, multiresolutional analysis (MRA) provides a simple and straightforward way to extract the spatial properties of an image. This can be realized by the successive decomposition of a signal using a complete and orthonomal set of wavelet basis functions which have a different spacefrequency representation. As a result, a resultant high frequency image can give detailed information about the local differences in the spatial structure of the scene, while a low frequency image provides only a big picture of the scene from a larger angle.15 According to the definition of MRA,16 the subimages of a univariate image transformed by MRA are congruent to each other and can make up a new multivariate image which can be ideally analyzed by MIA. Therefore, in MR-MIA, univariate images are first transformed into multivariate images via MRA, and then those multivariate images are analyzed though MIA. A theoretical study on MR-MIA for gray scale images has proven that it yields the same results as wavelet texture analysis.3 In cases dealing with multispectral images rather than a univariate one, MRA with the discrete wavelet transform (DWT) and a decomposition level of J generates 3J+1 new multivariate images, thus MIA is again employed for each of the multivariate images in order to obtain the spectral information at each

Figure 1. Four sample images of the countertop samples with labels. The meaning of the alphabet letters in the image labels are as follows: “G”, good quality; “Q”, questionable quality (following expert graders’ evaluations); “S”, after surface polishing; “U”, before polishing. The two digit numbers denote slab numbers. In sections 3 and 4, original images are subdivided two smaller images as shown in slab Q-02-S considered as within-batch products.

To extract color as well as textural information of a product from the image, MR-MIA is employed throughout this study. MR-MIA is an enhanced method that combines the advantages of MRA (multiresolutional analysis) and MIA to analyze both color and textural features of a product at the same time. Therefore, it has many advantages when compared to conventional wavelet-based textural feature analysis for grayscale image analysis in that it can be extensively used for RGB (red/green/blue) or even the multispectral images. In this paper, only the key features of MR-MIA will be provided, and more extensive details on this method can be found in literature.5 Let us assume that a multivariate image can be considered as a stack of congruent images4 as shown in Figure 2: it is a threeway data array that has two-dimensional geometric coordinates and one-dimensional spectral coordinates. Thus, a multivariate

Figure 2. A multivariate image is a stack of congruent images measured from different variables (for example, 512 × 512 congruent images at four different wavelength bands, λ1−λ4). Then, it is the same as a three-way data array and each pixel is represented by a multivariate vector as shown above. Reprinted with permission from ref 27. Copyright McMaster University, 2004. 12338

dx.doi.org/10.1021/ie303442r | Ind. Eng. Chem. Res. 2013, 52, 12337−12345


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resolution. Therefore, MR-MIA enables one to analyze both spectral and textural information at the same time, and this principle can be applied equally to any of the MRA methods which are based on the DWT wavelet packet transform. In the present study, MR-MIA was used to analyze countertop images with color. When supposing that the image has Q channels, MRA generates Q(3J+1) images by DWT with J decompositions. For further details and a theoretical overview, refer to ref 5. 2.2. Partial Least-Squares-Discriminant Analysis (PLSDA). The human visual system can perform selective feature extraction on an image and simply compress the extracted information for interpretation.3 To achieve the ultimate goal of providing a reliable method for the automatic classification of engineered stone countertops, PLS-DA is adopted as a supervised learning method for projecting the textural and color information extracted from the image into a latent variable subspace. When the feature vector, x (x ∈ 9 d) and the class label, y (y ∈ 9 c) are present, where d and c represent the number of features and classes, respectively, PLS-DA projects the feature vector onto a low dimensional latent variable space, where the optimal number of latent variables, A, is usually much smaller than the dimension of the original data space.17 A main difference between PLS-DA and principal component analysis (PCA), which is another popular projection method, is that PLS-DA finds the latent variable space that maximizes the covariance between x and y, while PCA mainly identifies the lower dimensional space that maximally describes the variation in x only.18 Here, PLS-DA was utilized as a main supervised learning method for the classification, while PCA was employed as a complementary tool to reveal the unsupervised clustering patterns of the countertop images themselves providing additional information. Let us assume that a set of samples, X (M × d) with the known class label, Y (M × c) is given, PLS-DA model can be given by

Note that, in this study, only the two-class problem was considered for the classification of the countertop images. Thus, in PLS-DA, the binary class membership, y = {yi ∈ {1,0}} was created and a threshold of 0.5 was used to assign each sample into the estimated class.

3. DATA SETS AND IMAGE COLLECTION The dimension of manufactured countertop slabs examined in this work is approximately 20.4 cm × 12.9 cm × 1.3 cm (L × W × H). The countertops are manufactured through the process described in the ref 3. For sample preparation, 17 batch runs with different recipes and different operating conditions were selected and one countertop slab per each batch was collected giving 17 slab samples with enough variations in countertop patterns. The images of the countertops were collected by using a color scanner, and these 8-bit, 300DPT images were saved in bitmap format without compression. Then, the original samples were trimmed to be 2300 × 1400 color images for analysis. The actual list of the 29 images is provided in Table 1. Among 29 Table 1. List of 29 Samples and Corresponding Quality Evaluations by Experts

A

X=

∑ tapaT + E = X̂ + E a=1

(2)

A

Y=

∑ taq aT + F = Ŷ + F a=1

evaluation

Q-01-S Q-02-S Q-03-S Q-04-S G-S-05 G-06-S G-07-S G-08-S Q-09-S G-10-S G-11-S G-12-S Q-13-S G-14-S G-15-S G-16-S G-17-S

questionable questionable questionable questionable good good good good questionable good good good questionable good good good questionable

image ID

evaluation

Q-03-U Q-04-U G-05-U G-06-U G-07-U G-08-U

questionable questionable good good good good

G-10-U G-11-U G-12-U Q-13-U G-14-U

good good good questionable good

G-16-U

good

samples, 12 samples were obtained from the product before surface polishing and the corresponding 12 samples after the polishing were also included in Table 1 with the same image numbers in their labels. All the countertop samples were manufactured under different manufacturing conditions except for each of the 12 pairs of countertops that were obtained before and after the surface polishing operation.

(3)

where ta (M × 1) is the score vector, pa (d × 1) and qa (c × 1) are the loading vectors, E (M × d) and F (M × c) are the residual matrices of X and Y, respectively. Here, the optimal number of latent variables A is usually determined by crossvalidation to provide highest predictive power for the resultant PLS-DA model.17,19 At the same time, the model parameters are typically computed by using the nonlinear iterative partial least-squares (NIPALS) algorithm. Alternately, it can be also shown that the PLS-DA weight vector, wa (i.e., ta = Xwa) corresponds to the first eigenvector of the eigenvalue problem for the covariance matrix of XTYYTX as follows:20 XTYYTXwa = λ wa

image ID

4. AUTOMATIC CLASSIFICATION OF THE VISUAL QUALITY OF MANUFACTURED STONE COUNTERTOPS 4.1. Inspection of Raw Countertop Images. Figure 3 depicts the actual images of the countertops before and after surface polishing, which is one of the countertop manufacturing steps. In this figure, it can be easily recognized that there exists a noticeable difference in the visual quality of the products before and after the surface polishing. Currently, experienced operators are using the after-polishing products when classifying the product quality, since the sample countertop images after polishing have higher contrast and sharper tones. Without the expertise of experienced operators, however, it is

(4)

Once the PLS-DA model is identified, each observation can be assigned into its own classes according to their estimated values of Ŷ .21 Then, the classification accuracy can be also quantitatively quantified by misclassification rate, sensitivity, specificity, or area under the receiver operating characteristic curve (AUC) from cross-validation or external validation.22 12339



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Figure 3. A schematic diagram of the unit operations in the countertop manufacturing and a comparison of the color and textural properties of the countertops before and after the surface polishing operation.

Figure 4. t1−t2 score plot obtained from PCA of the MR-MIA features for all countertops including the polished and unpolished ones.

difficult to discriminate between the products with “good” and “questionable” quality from these images. Furthermore, the quality inspection of the countertops before the polishing is more challenging even for experienced personnel due to the low contrast of the images. In Table 1, the list of countertop samples is shown together with their quality evaluations made by the experts. Here, both the products before and after polishing are included, so that the effects of the polishing operation on the classification performance of the MR-MIA based soft-sensor could be evaluated, as will be shown in the next sections. Note that if there exists a reliable way to classify the unpolished products at an earlier stage, it would significantly reduce the water and chemical consumptions. 4.2. Estimation of Visual Quality of Manufactured Countertops. To investigate the feasibility of MR-MIA, all the images were analyzed together without differentiating between the products in terms of polishing operation. For this, the original images were converted into two, noncongruent, low resolution (1150 × 1400) images in order to increases the number of observations. Then, the 2D discrete wavelet transform was applied to the RGB (red, green, and blue) images of countertops using the Coiflet filter. Here, a decomposition level of 5 was employed, generating 3(3 × 5 + 1) = 48 subimages from each of the original images. These choices (the number of decomposition levels and the wavelet function) were made by trial and error following some guidelines.23,24 The number of decomposition levels was found according to our experience such that the size of the 2D wavelet coefficients should be greater than 10 × 10 and this criterion is conformable to that of Chang and Kuo.23 Then, the energy for each of the approximations and the details level was computed to convert each image into a feature vector with 48 dimensions. The data set X (48 × 58), consisting of 58 samples with 48 features, was analyzed using PCA. Figures 4 and 5, and Table 2 represent the results obtained from the PCA model of the converted MR-MIA features. In this model, three principal components were sufficient to describe the variation in the countertop images before and after polishing, as shown in Table 2. In addition, it can be observed that the products with and without the polishing operation clustered into separate classes clearly in the PCA score plot of Figure 4, illustrating that MR-MIA features successfully extracted the color-textural information from the corresponding countertop stone images. Therefore, even with the unsupervised learning of PCA, the products at different manufacturing

stages can be easily discriminated between one another. Figure 5 shows the first two loading vectors, p1 and p2, whose values and sign represent the contribution of each of the wavelet decomposition levels (1 approximation and 5 detail levels for each RGB channels) in the PCA model. In general, the energy of the 2D wavelet coefficients represents the grayscale intensity of each subimage.3 In addition, the subimages at the approximation level represent the full content of an image including the image background, while the subimages at the detail levels provide distinctive local features in the specified frequency bands.15 On the basis of these general assumptions, it could be observed in Figures 4 and 5 that the differences between the polished and unpolished products were mainly described by the first PC, t1 and p1. At the same time, the polished products had a higher contrast in color in that their score, t1, and their loading values, p1, for the approximation and detailed levels were the same sign. The higher contrast in those products can easily be explained by the enhanced boundary between the quartz and resin in the countertop surface after the polishing operation. On the other hand, the second principal component mainly explained the color variation among the products within each class (polished vs unpolished). Thus, the loading, p2, exhibited a different magnitude and sign for the approximation and details at the RGB color channels. Note that if the extracted features of MR-MIA are only related to textural information, the loadings at the different RGB channels should be identical, which was not the case in this study indicating that the MR-MIA employed here could successfully capture both the color and texture-related information from the given images of the engineered countertops. 4.3. Automatic Classification of the Aesthetic Quality of the Polished Countertops. In this section, the automatic classification of the stone countertops was conducted from the acquired product images to discriminate the countertops with good and questionable quality. To this end, a supervised learning model of PLS-DA was adopted as a soft-sensor and used to classify the countertops on the basis of the image feature obtained from MR-MIA. At the same time, its results were compared to the MR-MIA combined with PCA3 to demonstrate the superiority of the proposed method. Note that here the classification models were constructed separately for each of the polished and unpolished countertops, since the characteristics of their images were much different from each other as illustrated before. 12340



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Figure 5. p1 and p2 loadings of the PCA model for all countertops including the polished and unpolished ones. Error bars were calculated from the cross-validations.

Table 2. Cumulative R2 and Q2 of the PCA Model of MRMIA Features of All Countertops Including Both Polished and Unpolished Ones no. of PCs

R2 (%)

Q2(%)

1 2 3

97.5 98.9 99.3

97.4 98.4 99.1

variation among the different countertops (data are not shown), indicating that the corresponding PCA model with MR-MIA features could consistently capture the color and textural characteristics of the given countertop images without any bias. However, as can be seen in the score plot of Figure 6a, PCA could not discriminate the countertops with two different qualities (i.e., questionable vs good), resulting in severe overlap between two classes in the corresponding principal component space. Although a further detailed investigation revealed that the third principal component, which only explained 7.5% of total variance in the data, was partially correlated with the countertop quality (r = −0.63 with p-value = 0.0001 between t3 and Y), it was not sufficient to discriminate the different stone countertops reliably according to their aesthetic qualities. Then, to complement the limitations of PCA, the PLS-DA model was constructed using the same set of the MR-MIA features as X and the augmented class labels for each

First, the PCA model constructed on the MR-MIA features of the polished countertop images was investigated in Figure 6a, where the corresponding score plot of the first two principal components was shown. In this PCA model, six principal components were selected as optimum and they explained 95.4% of total variance in the data. In addition, the original image of each countertop was divided into two separate images as stated before, and the examination of the variation within the identical countertop revealed that it was much smaller than the

Figure 6. t1−t2 score plot obtained for the polished stone countertops: (a) PCA, (b) PLS-DA. 12341



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Table 3. Classification Accuracy of the PLS-DA Model in Discriminating the Countertops with Different Qualitiesa calibration

a

cross-validation

no. of LVs

overall

class 1: good

class 2: questionable

overall

class 1: good

class 2: questionable

polished

9

1.00 (34/34)

1.00 (20/20)

1.00 (14/14)

0.94 (32/34)

0.95 (19/20)

0.93 (13/14)

unpolished

6

1.00 (24/24)

1.00 (18/18)

1.00 (6/6)

0.92 (22/24)

0.89 (16/18)

1 (6/6)

Values in parentheses represent (the number of correctly classified samples)/(the total number of samples) in the corresponding class.

had negative contributions for almost all frequency bands of the detail levels at three different color channels. Hence, it indicated that the poor contrast of the polished countertop surface in the localized frequency bands could be attributed to the bad quality observed for the corresponding countertop, which was in line with the judgment made by the experienced operator. On the other hand, an investigation of the variable importance in projection (VIP)25 in the given PLS-DA model provided more systematic information on the influence of each MR-MIA feature on the overall separation among the products with different qualities. Figure 9a represents the VIP scores calculated for each image feature obtained from distinct frequency bands and at different color channels. Here, one could see that the detail images at the moderate frequency scales, such as dh(3), dd(4), dv(3) and dd(3) at R channel and dh(3), dd(4) and dv(3) at G channel, generally had high influences on the discriminations capability of the PLS-DA model, indicating that these features might be employed as simple and robust image markers to develop a more parsimonious PLS-DA model for classifying the polished countertops. Note that, in Figure 9a, the variables, whose VIP values were higher than 1, were represented by a different color, since they were generally regarded as the important ones in describing the variation in X as well as the covariance between X and Y.25,26 4.4. Automatic Classification of the Aesthetic Quality of the Unpolished Countertops. To further validate the proposed scheme of combining MR-MIA with PLS-DA, the classification performance of the soft-sensor was evaluated for the unpolished countertops using the identical methodology implemented in the previous section. Figure 10 represents the corresponding score plots for the first two latent variables obtained from PCA and PLS-DA models. Four principal components and six latent variables were identified in the given PCA and PLS-DA models, respectively. The unpolished countertops with different qualities could be well discriminated in both models as can be seen in Figure 10, thus exhibiting similar discriminating powers. However, in the PCA model, the most valuable information on the class differences was mainly identified by the second principal component, and other score plots with different combinations of the scores did not produce any clear separations between the classes. In contrast, the PLSDA could capture the class differences mostly by the first latent variables and, at the same time, a similar degree of separation between the classes could be equally found in the multiple score plots with combinations of other scores. Therefore, the PLS-DA was more preferable to the PCA for the given task of discriminating the unpolished countertops. Table 3 summarized the classification accuracy obtained from the PLS-DA model for the unpolished countertops. The PLSDA correctly classified all the samples into questionable and good qualities during the model training, and only two samples with good quality were misclassified during the cross-validation.

countertop images as Y. In this PLS-DA model, nine latent variables were identified as optimum by the leave-one-out cross-validation, which was relatively large and possibly indicates the complexity of the given classification problem. However, in the score plot of the corresponding PLS-DA model (Figure 6b), it can be clearly seen that, even with first two latent variables, the polished countertops having two different qualities could be separated into two distinct clusters although there existed a slight overlap between two classes. This was a great improvement compared to the previously obtained PCA model, illustrating the superiority of the proposed method. Another advantage of PLS-DA was that it can explicitly classify each of the countertops in a quantitative manner by inspecting the estimated values of Ŷ . Therefore, its classification accuracy was examined in Table 3, where the classification accuracy for the entire polished countertops as well as within each of the classes was summarized. Here, the classification accuracy of PLS-DA was defined as the ratio of the correctly assigned countertops in the given set of observations, and it was quantified in both the model training and cross-validation steps.17 In this table, one could see that all the countertops were correctly assigned into their own classes during the model training. At the same time, only two countertops (one from the good and one from the questionable quality) were misclassified during the cross-validation, demonstrating the potential of the PLS-DA with MR-MIA as an automatic soft-sensor tool in countertop manufacturing. To further demonstrate the usefulness of the PLS-DA in interpreting the differences in the aesthetic quality of the polished countertops, two sample images, which had different qualities with extreme distance between them in the score plot of Figure 6b, were illustrated in Figure 7. It was evident from this figure that the discrimination of these two images in conjunction with their aesthetic quality might be challenging for the inexperienced personnel. However, the score contributions in the PLS-DA for these two countertop images (Figure 8) clearly revealed that the countertop with bad quality

Figure 7. An example of two polished countertop images with extreme differences in their aesthetic quality. 12342



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Figure 8. The score contribution in PLS-DA for two polished countertops, Q-17-S_B and G-15-S_B. Here, the score contribution of Q-17-S_B were subtracted by the score contribution of G-15-S_B.

Figure 9. VIP scores obtained from PLS-DA models: (a) polished countertops, (b) unpolished countertops. Error bars were calculated from the cross-validations.

Figure 10. t1−t2 score plot obtained for the unpolished stone countertops: (a) PCA, (b) PLS-DA.

were coming from the several localized image features characterized at the detail levels by the MR-MIA, which was similar to the previous cases of the polished countertops. In

In addition, the VIP scores in the corresponding PLS-DA model of Figure 9b revealed that the most discriminating powers for the unpolished countertops with different qualities 12343



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fact, the comparison of the VIP profiles for the polished and unpolished countertops showed that several image components at the moderate to high frequency scales, such as dd(4), dh(3), dv(3), dd(3) and dv(4) at R channel, dd(4), dh(3), dv(3), and dv(4) at G channel and dd(1) at B channel, were identically selected as the most influential ones in both models, confirming that these overlapping frequency bands might be the key factors in determining the overall aesthetic quality of the engineered stone countertop products. In general, the results obtained from the unpolished countertops were very encouraging, considering that the differentiation of the unpolished countertops at the early stage according to their qualities was a challenging task even for the experienced personnel due to the higher brightness and the lower contrast in their acquired countertop images. However, it should be also noted that a more thorough validation of the developed soft-sensor would be needed to generalize these findings.

5. CONCLUSION This research explored an image-analysis based soft sensor for the automatic classification of visual aesthetics of the manufactured countertops with both color and texture properties. To this end, MR-MIA was used to extract the color-texture information from the images of the manufactured countertops, and PLS-DA, a latent variable method, was used to automatically classify the products into two different classes of good and questionable qualities. To demonstrate the proposed approach, the soft-sensor models combining the MR-MIA with the PLS-DA were developed for both the polished and unpolished stone countertops, and their performances were compared to the conventional MR-MIA combined with the PCA. Owing to the advantages of the MR-MIA in extracting the color and textural features from the acquired digital images, and the PLS-DA in finding maximal separation among the classes in the reduced latent variable spaces, the combined use of the MR-MIA and the PLS-DA could improve the overall classification performance in discriminating the countertop products with different qualities, compared to the conventional MR-MIA with the PCA. In addition, the successful application of the proposed method to the unpolished countertops may significantly reduce the associated consumption of energy and chemicals, which poses the economic benefits to engineering stone countertop manufacturing.

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AUTHOR INFORMATION

Corresponding Author

*Address correspondence to [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Basic Science Research Program through the National Research Foundation (NRF) funded by the ministry of Education, Science and Technology (2010-00003056).

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REFERENCES

(1) Holtham, P. N.; Nguyen, K. K. On-line analysis of froth surface in coal and mineral flotation using JKFrothCam. Int. J. Miner. Proc. 2002, 64, 163−180. (2) Kaartinen, J.; Hatonen, J.; Hyotyniemi, H.; Miettunen, J. Machine-vision-based control of zinc flotation-A case study. Control Eng. Pract. 2006, 14 (12), 1455−1466. 12344



Article

(27) Liu, J. J. Machine vision for process industries: Monitoring, control, and optimization of visual quality of processes and products. Dissertation. McMaster University, Ontario, Canada, 2004.

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Quality Characterization and Classification of Engineered Stone

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