Application Of A Fuzzy Classification Technique In Computer Grading ...

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Application of a Fuzzy Classification Technique in Computer Grading of Fish Products B.-G. Hu, R. G. Gosine, L. X. Cao, and C. W. de Silva

Abstract—This work presents the enhancement and application of a fuzzy classification technique for automated grading of fish products. Common features inherent in grading-type data and their specific requirements in processing for classification are identified. A fuzzy classifier with a four-level hierarchy is developed based on the “generalized K-nearest neighbor rules.” Both conventional and fuzzy classifiers are examined using a realistic set of herring roe data (collected from the fish processing industry) to compare the classification performance in terms of accuracy and computational cost. The classification results show that the generalized fuzzy classifier provides the best accuracy at 89%. The grading system can be tuned through two parameters—the threshold of fuzziness and the cost weighting of error types—to achieve higher classification accuracy. An optimization scheme is also incorporated into the system for automatic determination of these parameter values with respect to a specific optimization function that is based on process conditions, including the product price and labor cost. Since the primary common features are accommodated in the classification algorithm, the method presented here provides a general capability for both grading and sorting-type problems in food processing. Index Terms—Classification, food processing, fuzzy grading.

I. INTRODUCTION

I

N recent years, intelligent systems have been employed in applications of computer grading of food products [1], [8], [20]. Grading (or quality assessment) is an important operation performed routinely in food processing industries for quality control and price assignment. Considerable work related to grading, however, is still carried out manually. In view of the very high volume of product and fast throughput rates, the operations conducted by humans can be tedious, stressful, and subjective. This leads to undesirable variation in product quality control. Increased automation of food processing operations is facilitated by intelligent sensing. For example, computer vision is a useful sensing approach in automated handling of products. The main advantages of using computer vision-based grading systems in the food processing industry are: 1) it provides most of the information that is commonly used in manual grading (such as size, shape, texture, color, and the presence of defects), which will accommodate variability Manuscript received June 8, 1995; revised February 24, 1997. This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) for a core research program, by an NSERC Research Chair, and by the Science Council of British Columbia. B.-G. Hu is with C-CORE, Memorial University of Newfoundland, St. John’s, A1B 3X5 Canada. R. G. Gosine is with C-CORE and the Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, A1B 3X5 Canada. L. X. Cao and C. W. De Silva are with the Department of Mechanical Engineering, the University of British Columbia, Vancouver, V6T 1Z4 Canada. Publisher Item Identifier S 1063-6706(98)00793-0.

in raw material; 2) it is a noncontact and nondestructive method of inspection that will reduce product damage and increase recovery; 3) it improves product quality through defect detection; 4) it results in a higher degree of consistency of sorting and grading; 5) it increases yield, productivity and process efficiency; 6) it provides some flexibility and faster response time in a product changeover; and 7) it may reduce labor costs by eliminating labor intensive tasks. Table I presents example applications of computer grading for food products using various classification methods. Classification, as a key step in computer grading, involves the construction and use of decision rules that enable the assignment of a set of unlabeled observation data to a particular category. A variety of classification algorithms have been reported in the literature. The conventional statistical classifiers are described in Therrien [26] and Fukunaga [9]. Fuzzy and neural-network classifiers are given in Bezdek [3] and Pao [19], respectively. Simpson [23] presents a good discussion of several design properties of a pattern classifier. This paper concerns automated computer grading for a fish product, specifically, herring roe. We reveal the common features inherent in data that are associated with product grading problems and we discuss the processing requirements, which are usually independent of the product type in grading. The primary focus of the work is a novel application of a fuzzy classifier based on the “generalized K-nearest neighbor rules” proposed by Bezdek et al. [4]. In the present classifiers, emphasis has been placed on accommodating the common features and specific requirements of the grading-type problems. Both conventional classifiers and fuzzy classifiers are applied for comparison in terms of accuracy and computational cost by using data from a representative batch of herring roe. The final tuning parameters of the classifier are obtained by an optimization of an objective function that is based on representative processing factors. II. GRADING

AND

CLASSIFICATION

In food processing industries, grading (or rating) is an operation to classify a product according to quality specifications. This quality assessment may be based on “subjective” specifications. For this reason, we define two types of grading according to the “subjectivity” of specifications, namely, hard grading and soft (or fuzzy) grading. With hard grading, each class can be clearly determined by some “well defined” (or “hard” or “crisp”) specifications and criteria (for example, apple grading according to weight or size range). On the contrary, soft grading is subjective and the grading specifications are usually determined based on the perception of a

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HU et al.: APPLICATION OF FUZZY CLASSIFICATION TECHNIQUE IN GRADING FISH PRODUCTS

APPLICATIONS

OF

TABLE I COMPUTER GRADING

human expert grader. The typical cases are grading based on evaluation of shape, color, texture or firmness, flavor, odor, freshness, defects, and their combinations. Usually, different human graders classify differently and an expert grader may have a great difficulty in articulating the grading criteria. The present application of herring roe is a good example of soft grading. Fig. 1 shows three different grades of processed herring roe. Human graders look for well formed, firm, and golden yellow roe skeins as requirements for a good-quality product. A poor-quality product can result from factors such as poor handling of the raw product (e.g., broken roe) or irregularities in the extraction and processing (e.g., curing) operations. A marginal-quality product may be due to a slight crack of the skin or minor deformation. Different grading specifications may be grouped into two primary purposes, namely, defect grading and value grading. In defect grading, the purpose is to exclude defective or abnormal items within a batch of processed (or produced) items. Examples are spoiled meat or poultry products and contaminated fish products. This is usually considered a twoclass classification problem. Two types of misclassification are defined as false negative and false positive. In practice, false negative grading (abnormal product not detected) must be zero or minimal, while false positive grading (normal product detected as abnormal) is more tolerable. The task in value grading, which is usually a multiclass problem, is to grade a product according to the degree of goodness, customer acceptance, or commercial value. Examples are apple grading according to maturity and the herring-roe grading according to shape, color, and texture. Similar to the case of defect-grading, we define two types of classification errors, namely, upgrading (product assigned a higher grade or value than the true one)

TO

145

FOOD PRODUCTS

(a)

(b)

(c) Fig. 1. Examples of processed herring roe skeins. (a) Good. (b) Marginal. (c) Poor.

and downgrading (product assigned a grade lower than the true one) in value-grading. In fact, we can consider defect grading as a special case of value grading with respect to multiclass classification. Moreover, value grading may assign a “value” to a product based on the severity of a defect. When considering grading-type problems, it is necessary to distinguish the differences between the operations of “grading” and “sorting.” Both are regarded as separation operations and are sometimes used interchangeably in food industries. For example, separation of apples according to size can be called either sorting or grading. While grading is considered

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TABLE II THE DIFFERENCES BETWEEN GRADING AND SORTING

a separation operation carried out on a single kind of product, such as herring roe, sorting may deal with several different items, like sorting a mixed batch of several species of salmon. Sorting will also include the separation of items according to naturally distinguished characteristics—like sex sorting of fish. The difference between grading and sorting, as shown in Table II, is of particularly interest in classification due to the data feature. The data of grading-type problems generally occur with overlapping or at least with touching clusters. This is due to the nature of continuous distribution of data for food products. The data will not be as well separated as those that occur in sorting of a product according to naturally distinguishable characteristics. Since touching or overlapping clusters lead to poorer classification accuracy than well-separated clusters, a classifier designed for grading-type problems will be suitable for sorting-type problems as well. In food processing, optimization will be necessary for a classifier to reduce the overall loss for two reasons: misclassification and cost of manual grading. Some misclassification is inevitable in practical applications. The effect of misclassification will depend on the associated error type. One type of error may lead to a larger loss than another. We have proposed an automated grading system, which includes regrading by expert graders or the computer system in a second pass operated at a lower speed and with higher accuracy and resolution levels. Due to the high level of uncertainty in classification within a batch of rejected items, the classification error can be reduced by regrading on the product rejected by the firstpass computer grading. Hence, by optimizing a classifier with respect to the error types and rejection rate, a tradeoff between the accuracy of computer grading and the cost of regrading, either manual or computer, may be reached. The same issue should be considered in the selection of sample size if a training procedure is used in classification. III. CLASSIFICATION METHOD A classification method is presented based on the generalized K-nearest neighbor rules [4] that incorporates the fuzzy C-means and fuzzy K-nearest neighbor methods. In addition, we employ optimization to tune the system performance according to the primary process parameters, thereby minimizing the processing loss (i.e., cost of yield loss and labor cost). The classification procedure is implemented as a four-level hierarchical system illustrated in Fig. 2. The details of the four levels are given below.

Fig. 2. A four-level hierarchy of the classification algorithm.

Level 1—Fuzzy C-Means: The labeled observation data of classes are the input to this level where is the feature space, is a feature vector, is the th (measured) feature or characteristic of observation , is the number of features, and is the number of observations. The task of this level is to determine prototypes for each labeled class. The method we use is based on fuzzy C-means [3], which determines the cluster centers by the following optimization procedure: minimize (1a) subject to (1b) is a scalar, , the Euclidean where distance between point and prototype vector , is the fuzzy grade of membership of pattern with class , is a matrix, and is an matrix. Since we obtain sets of prototypes within each class, we have total prototypes for the all classes and, finally, becomes a matrix and becomes an matrix. Level 2—Fuzzy Nearest Prototype: In this level of the hierarchy, with the labeled prototypes as inputs, we have implemented a modified form of the fuzzy nearest prototype classifier proposed by Keller et al. [14]. Here we have included cost weightings for error types in classification. If some errors

HU et al.: APPLICATION OF FUZZY CLASSIFICATION TECHNIQUE IN GRADING FISH PRODUCTS

are more costly than others, this scheme minimizes the overall cost. The procedures for the modifications are as follows. First, input weighting set by . Then, make a weighting set satisfying by a mapping of if corresponds to the th class. The are calculated as components of

6) The overall error

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is given by (6)

7) Evaluate the rejection rate (7)

(2)

for the th sample will Any labeled observation data be tested in this level and a membership vector is obtained, which satisfies the conditions of (1b). A threshold of fuzziness will be given for a crisp decision for each set of measurement data by the following steps. 1) Determine the maximum grade of membership by (3). If a tie is found in the argument between the different classes, choose the class that is associated with the lowest loss due to misclassification maximum

(3)

, corresponds to the th prototype, then 2) If the known labeled prototype will map onto the known class set accordingly. , will be classified into a “rejected” class 3) If set due to a lack of confidence in the classification result. matrix. Note 4) Evaluate the confusion matrix —a since one more class, the “rejected” that class, is added. The term is the number classified correctly, the number of misclassifications from the th class into , the number of samples the th class, and is in the following rejected by computer. The matrix form:

(4)

5) Evaluate the error matrix in the form of equation—a matrix. The terms correspond to the error of misclassification from the th class into the th class. is the total number of detected (or nonrejected) samples. The matrix has the following form:

(5)

is the number of total processing samples. where The output data at this level are a set of and and the corresponding tuning parameters and . Level 3—Minimization of Processing Loss: In this level, a minimization of the total processing loss is implemented. The optimization problem may be expressed as minimize subject to:

(8) where mean grade of membership with respect to total number of prototypes; specified maximum error ( ) for ; specified maximum rejection rate ( ). The loss function will be evaluated using processing cost data such as product prices, loss due to processing errors, and manual processing cost. The details of this function are given in the Appendix. The constraints on and are set by and , respectively, according to the specific requirements in processing. Any one of the last two constraints can be removed by assigning either or . A quasi-Newton method within the MATLAB Optimization Toolbox [29], is used for optimization. We have noticed that is a noncontinuous function and has multiple local minimums. Therefore, a certain perturbation length of variables should be chosen for calculation of the Hessian matrix and different starting points should be performed to verify a global minimum. In applications related to food production, a computer grading system should be capable of adjusting the parameters automatically or interactively by process operators. Since classification errors and the rejection rate are the functions of and , the final form of the loss function can be written as . The classification accuracy can be improved by increasing the threshold of fuzziness ( ) although this may increase the rejection rate. The cost weighting ( ) can change the percentage of a given type of error in the overall classification error. Level 3 of the hierarchy serves as an automatic controller of the system performance. The implementation of the level also serves to provide for the evaluation of for any given set of parameters ( ). The information is useful for manual interactive control of the system performance.

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Fig. 3. Automatic grading/sorting system for herring roe.

Level 4—Fuzzy Nearest Prototype: The fuzzy nearest prototype algorithm is also employed in Level 4 as a classifier for the unlabeled observation data. The control data sets, prototypes ( ), threshold of fuzziness ( ), and cost weighting ( ) for error types (which are obtained from the learning stage) are utilized for classification. When an item from an unlabeled observation data set is supplied to the system for grading, the output of the classifier will be the classified data. In this manner, if accepted, the grade of the sample is labeled. If it is not accepted, the sample is assigned to a rejected class for regrading. IV. CLASSIFICATION RESULTS In this section, results from grading experiments carried out using a laboratory prototype system are presented. An automated grading system (as shown in Fig. 3) may be conveniently integrated into existing herring roe processing lines. The four components of the automated roe grading system shown in Fig. 3 include a mechanism for handling bulk roe, the visual sensing system—a sorting mechanism which extracts acceptable roe skeins within grade categories accordingly—and a switch mechanism, which directs the rejected roe either to a manual grading line or to a second computer grading system that is operated at a lower speed and at higher accuracy and resolution levels. In principle, this system demonstrates a general scheme for computer grading of other kinds of food products as well. In a manual processing, herring roe is assigned a grade based on the evaluation of color, shape, firmness, maturity, and general appearance. In the present study, we use only two-dimensional (2-D) shape information for grading. A total of 219 samples of herring roe were processed by the computer grading system. The shape of each sample was assessed by the expert graders from a collaborating fish processing company, as being either “good” (Class 1, 126 in total) or “poor” (Class 2, 93 in total). A CCD camera is used for image acquisition. After the raw image is smoothed to remove spurious noise, the image is binarized and the largest object in the image that corresponds to the roe is extracted. A contour tracing algorithm is used to extract boundary from the object shape.

Fig. 4. Critical points: dorsal and ventral curves in roe boundary.

The extraction of features describing the shape of the roe is based on the detection of two critical points at the anterior and posterior ends of the roe as shown in Fig. 4. The roe boundary is segmented into the dorsal and ventral curves, connected at these critical points. This approach to boundary segmentation was carried out based on discussions of roe shape with grading experts from industry. A curvature function is then estimated that uniquely specifies a curve independent of translation and rotation [5]. After the curvature function is obtained, the mean and deviation of the function are calculated as the features for both dorsal and ventral curves. In this manner, four shape features are extracted for each sample. Before classification, the structure of the data is examined for a better understanding in a selection of the classification method. Table III gives the estimated means and standard deviation for the herring roe data. In order to visualize the nature of the four-variable data, we transform the data into a 2-D space by the following relations:

and covariance where covariance matrix of ; the th eigenvalue and eigenvector of , respectively. For the herring roe data, the following normalized eigenvalues were obtained: . According to the Karhunen–Lo´eve expansion method [9], we and , the eigenvectors corresponding to the maxiselect mum and near maximum eigenvalues and , respectively,

HU et al.: APPLICATION OF FUZZY CLASSIFICATION TECHNIQUE IN GRADING FISH PRODUCTS

m

THE ESTIMATED MEAN ( ^ i )

TABLE III STANDARD DEVIATION ( ^i )

AND

OF THE

DATA

Fig. 5. Scatter plot in two-principal component projections using the Karhunen–Lo´eveve expansion method.

to be the principal components in the projection. Since the ratio calculated by

is close to 1.0, it is concluded that the variance has been significantly retained in the new space. It follows that the data in 2-D projections reasonably represent the features of the original data. Fig. 5 shows the scatter plot of the transformed data. Three characteristics of the data may be identified from the present data analysis: 1) two classes are overlapping in the feature space (Fig. 5); 2) the data for the two classes are linearly nonseparable (Fig. 5); 3) the “poor” class (Class 2) has a higher level of diversified data than those for “good” class (Class 1) (comparing the standard deviations between two classes in Table III). The first characteristic listed above indicates that classification would be a difficult task due to the overlapping of the classes. It is understandable that the data corresponding to both “good” and “poor” classes for fish quality would not be well separated. Naturally, they are overlapping or at least touching clusters. Since this is the case, a fuzzy classifier is an appropriate means of dealing with such overlapping features in which each pattern is allowed to belong to two classes with

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a measure of “belongingness” or membership in each one. The nonlinear separability of the data is another important feature that has to be taken into account, making it necessary to employ a nonlinear partition method. The higher value of in comparing with indicates that Class 2 would be more difficult to classify than Class 1. Due to the higher level of diversity of the data in the “poor” class, it was found that upgrading errors occurred more frequently than downgrading errors. Since the present classification method is based on a framework of “generalized K-nearest neighbor rules,” various hard (conventional) and fuzzy classifiers can be utilized. In this work, we have tested several classification methods on herring roe data in order to select a classifier that performs best for the given task. A comparison of the results using different classifiers is shown in Table IV. The errors and correspond to the “downgrading” and “upgrading” errors with . We have used the “leave-one-out” technique for calculation of classification errors. In this technique, a ) samples and tested on the classifier is trained by using ( remaining sample. The procedure is repeated until all samples in the data set have been tested for classification. In using the generalized fuzzy classifier, each class maintains the same number of prototypes. In the fuzzy nearest prototype method ( ), we take the prototypes as the class means of the labeled sample set. In this situation, this method would be identical to the generalized fuzzy classifier ( ). The fuzzy C-means and hard C-means (which are unsupervised clustering analyses) appear to have higher errors than the other methods. A comparison between computational costs is based on number of floating point operations (or FLOPS). The FLOPS for learning, not including optimization of processing loss, is based on all sample data. The FLOPS for classification is based only on one observation data. Note that the required FLOPS may change if the error setting is changed in some classifiers. The comparison indicates that the generalized fuzzy classifier has the best classification accuracy. In this method, the FLOPS increases dramatically with prototype number for learning while it has a linear relationship for classification. The memory cost is small because only a few prototypes are stored. While the learning cost is significantly higher than the other methods, this is not as crucial as for a real-time classification. The best classifier was achieved using the generalized ), with 89% classification accuracy fuzzy classifier ( (Table IV). Compared with the fuzzy rule-based classifier [5] with 83% accuracy, this classifier is automatically built by training from known labeled samples, rather than by constructing the rules from the expert graders and engineers and assigning the fuzziness to the rules manually. Table V lists the classification errors and rejection rates for the generalized fuzzy classifier ( ) for several values of the threshold of fuzziness ( ). As expected, increases. This the classification error decreases as the occurs, however, at the expense of an increased rejection rate. Table VI lists the classification error and cost weighting for each error type using the same classifier with . It is evident that the upgrading error decreases and downgrading

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TABLE IV A COMPARISON OF DATA CLASSIFICATION METHODS. (TOTAL 219 OBSERVATIONS: 126

TABLE V CLASSIFICATION ERROR, REJECTION RATE, AND THE THRESHOLD OF FUZZINESS. A GENERALIZED FUZZY CLASSIFIER (ctp = 4; w1 = w2 = 0:5)

TABLE VI CLASSIFICATION ERROR AND THE COST WEIGHTING. A GENERALIZED FUZZY CLASSIFIER (ctp = 4; T F = 0)

FOR

CLASS 1; 93

FOR

CLASS 2;

TF

=0

; w1

= w2 = 0:5)

Table VII shows the minimization results for the loss function defined in the Appendix. The best method, with respect to minimization of the processing loss, is the generalized fuzzy classifier ( ) with /lb. While the classification accuracy is increased to 93.8% by the tuning parameters, this is achieved at the expense of an increased rejection rate of 26.5%. If that the same method is employed without optimization ( ), we obtain /lb. Optimization, therefore, results in a 12% decrease in process loss, which is significant in terms of implementing an industrial system. V. SUMMARY

error increases as the weighing is decreased. The total error also changes as the weighting is changed. From Tables V and and , which are functions of tuning VI, we can see both parameters, control the performance of the overall system. For the most cost-effective utilization of the system in food processing, the tuning parameters should be obtained with respect to a specific optimization function. As an example, we give the following processing data: lb lb lb lb

lb

The natural variation in the quality of food products leads to a corresponding variation in appearance and poses considerable challenges in manual grading to maintain a high level of grading consistency. This is particularly true in soft grading of food products. In this paper, we have studied automated grading of herring roe for the fish processing industry. A generalized fuzzy classifier [4] is applied to provide a soft boundary, which allows modeling of overlapping pattern classes in a soft grading problem. In addition, a simple tuning parameter, a threshold of fuzziness, is used to adjust the processing system to achieve higher classification accuracy. The number of prototypes, which controls the degree of accommodation to piecewise linear separability in the data, is determined by optimization. We have proposed optimization for minimizing the total loss due to misclassification in both computer grading and manual regrading. A cost weighting for error types is added to the tuning parameters, which can de-emphasize specific errors. Several other advantages of the technique may be identified. The approach is nonparametric with respect to the feature space, and does not rely on the underlying statistical properties of the grading criteria. It can be simply implemented via labeled samples learned through the computer grading system,

HU et al.: APPLICATION OF FUZZY CLASSIFICATION TECHNIQUE IN GRADING FISH PRODUCTS

(1)

Le

151

TABLE VII THE OPTIMIZATION RESULTS OF Lmin (T F; w ). [P1 = $10:00/lb, P2 = $4:00/lb, = $6:00/lb, Le(2) = $4:00/lb, Cm = $0:10/lb, em12 = 0:05; em21 = 0:15; em = 0:2]

without requiring a priori knowledge of the relationships between the process variables under investigation. The system automatically builds up the decision rules for classification. Using the data from a representative batch of herring roe, we first conducted a data analysis. The results have provided us some insight into the nature of the original data, including overlapping classes, nonlinearly separable boundary, and diversified data of a “poor” class. Then, both hard (conventional) and fuzzy versions of classifiers were used. The classification results show a generalized fuzzy classifier provides the best accuracy of 89% without using the tuning parameters. A full benefit of cost savings has been achieved by tuning the two of the parameters, which has resulted in a 12% decrease in process loss for a given set of process data.

total ( ), computer ( ), and manual ( ) grading loss ($/lb). A two-class grading problem is considered here. The total loss ($/lb) is given by (A.1) where (A.2) (A.3) In a value-grading problem, the loss error is determined by

due to downgrading (A.4)

FOR

APPENDIX LOSS FUNCTION IN PROCESSING A TWO-CLASS GRADING PROBLEM

Notations:

There is no simple rule, however, to calculate the loss due to upgrading error . ACKNOWLEDGMENT

prices ($/lb) of Class 1 (good class) and Class 2 (poor class) products, respectively; classification error for computer grading corresponding to downgrading ( ) and upgrading ( ) of rejected samples; the total error is given by ; classification error for manual grading corresponding to downgrading ( ) ); note that and upgrading ( ; loss ($/lb) associated with downgrading ] and upgrading [ ] errors; [ rejection rate of total samples due to computer grading; cost ($/lb) of using computer ( ) and manual ( ) processing;

The authors would like to thank Ms. P. LeFeuvre and Ms. E. Nesbitt for their editorial assistance and proofreading of the manuscript. The authors would also like to thank Dr. S. Li for enlightening discussions of classification methods. REFERENCES [1] “Food processing automation—I, II, III,” Amer. Soc. Agricultural Eng., St. Joseph, MI, 1990, 1992, and 1994, respectively. [2] U. Ben-Hanan, K. Peleg, and P. Gutman, “Classification of fruits by a Boltzmann perceptron neural network,” Automatica, vol. 28, pp. 961–968, 1992. [3] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum, 1981. [4] J. C. Bezdek, S. K. Chuah, and D. Leep, “Generalized K-nearest neighbor rules,” Fuzzy Sets Syst., vol. 18, pp. 237–256, 1986. [5] L. X. Cao, C. W. de Silva, and R. G. Gosine, “A knowledge-based fuzzy classification system for herring roe grading,” in Amer. Soc. Mech. Eng. Winter Annu. Meet., New Orleans, LA, DSC-vol. 48; Nov. 1993, pp. 47–56. [6] Y. R. Chen and T. P. McDonald, “Application of artificial intelligence in carcass beef grading automation,” Proc. Amer. Soc. Agricultural

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