Diversity of Plum Stones Based on Image Texture Parameters and Machine Learning Algorithms

Abstract

The objective of this study was to evaluate the usefulness of machine learning based on image texture parameters to discriminate plum stone cultivars. The plums of cultivars ‘Emper’, ‘Kalipso’, and ‘Polinka’ were sampled. For each cultivar, one hundred images of plum stones were acquired using a digital camera. Processing of the plum stone images included the conversion of the images to individual color channels, image segmentation, region of interest (ROI) determination, and texture parameter extraction. Then, the discriminant analysis, including the texture selection and building discriminative models for the evaluation of the diversity of the plum stone cultivars, was carried out. The obtained results of discrimination of plum stone cultivars were very accurate and confirmed the effectiveness of image processing to evaluate the cultivar diversity. The most satisfactory results, reaching 96.67% for the average accuracy for three cultivars (97% for ‘Emper’, ‘Kalipso’, and 96% for ‘Polinka’), were obtained for the models built based on combined textures selected from all the color channels using the IBk classifier. The developed procedure can be of practical importance for the correct identification of plum stone cultivars and avoiding their mixing to preserve cultivar uniformity.

1. Introduction

Plum is a stone fruit with an edible fleshy mesocarp and is included in the genus Prunus (Rosaceae). The cultivars belonging to the species Prunus domestica (European plum) and Prunus salicina (Asian or Japanese plum) are the most important. The cultivars of the European plum cultivated traditionally by farmers are intended for local fresh markets or processing. Some traditional cultivars are especially appreciated due to their flavor and taste. The cultivar differentiation is also important for farming due to its adaptation to climatic conditions and disease resistance. The evaluation of plum diversity may be essential; for example, for on-farm conservation schemes and the utilization of genetic resources for sustainable agriculture [1]. Plums are one of the major fruit crops worldwide. The plum is considered a health-promoting fruit [2]. Plums, apart from their diversity in terms of size, shape, taste, and appearance, may be characterized by cultivar differentiation in terms of chemical properties. Plums are rich, e.g., in polyphenols, among others, and flavonoids, proanthocyanidins, coumarins, and hydroxycinnamic acids that may be associated with health benefits [3]. Plums are characterized by a short postharvest life. Due to their high respiration rate, fragile structure, fungal infection, and high water content, the fruit quality declines after harvesting, storage for longer times, and the long-distance transport of plums without an edible coating on the surface are limited [4,5]. Plums are seasonal with short periods of harvest and a supply of fresh fruit. Therefore, plums are also commercially available in processed forms, e.g., as dried plum powders, prunes, jams, juices, and plums in cans [6,7]. Stone fruits consist of an epicarp (outer layer), a mesocarp (flesh), and an endocarp (stone) [8]. During plum processing, the flesh and skin are the main raw materials, and the stones are generated as by-products [9]. The stone of a plum consists of the seed covered with a hull. The seed may be a source of useful substances for food, cosmetics (e.g., personal care products), and pharmaceutical industries [10,11]. Plum seeds have a high content of proteins and lipids, but also amygdalin [10,12,13]. The cultivar affects the properties of plum stones and kernels and, thus, the quality of their products [9]. Therefore, the correct cultivar recognition of plum stones previously extracted from the fruit is important before their further processing.

The application of machine learning (ML) algorithms may be useful to carry out the discrimination of samples based on the texture, color, and shape parameters extracted from digital images. Due to this, the analysis is performed in a non-destructive, quick, inexpensive, reliable, and objective way [14]. Machine learning enables quantifying and understanding data-intensive processes due to learning machines without being strictly programmed. A learning process aims to learn from training data to perform a task. After the end of this process, the trained model can predict, classify, or cluster new testing data using the obtained experience [15]. The use of machine learning algorithms can provide many benefits to agriculture. It can help to maximize yields and minimize input costs. Machine learning can allow the enhancement of the selection and crop yield prediction, weather forecasting, crop diseases predictions, and smart irrigation system [16]. Classification in machine learning separates the data and refers to a predictive modeling problem, as well [17]. Machine learning algorithms, combined with imaging technologies or non-imaging spectroscopy, can provide successful results [18]. Therefore, image analysis with machine learning can be widely used for the classification of different plant materials, including seeds [19,20], grain [21,22,23], fruit [24,25], or other parts of plants, e.g., leaves [26].

The objective of this study was to evaluate the usefulness of a machine learning approach based on texture parameters selected from a set of about 1600 textures extracted from images color converted to the color channels R, G, B, L, a, b, X, Y, and Z to discriminate the plum stone cultivars. The criteria considered for evaluating the discrimination were accuracies and the values of other performance metrics, such as the precision, MCC (Matthews Correlation Coefficient), F-measure, Kappa statistic, mean absolute error, and root mean squared error. The available literature lacks information on the use of such a large data set (1600 attributes), including textures from the individual color channels of the images and machine learning algorithms from different groups (‘Bayes’, ‘Lazy’, ‘Trees’, ‘Meta’, ‘Functions’, and ‘Rules’) used for developing models for the evaluation of plum stone cultivar diversity, which is a great novelty of the present study. The innovation of the study involving developing models for the textures selected from a set included textures from all the color channels R, G, B, L, a, b, X, Y, and Z (about 1600 textures), as well as separately for each color channel (about 180 textures for each of the nine color channels).

2. Materials and Methods

2.1. Materials

The plum stones belonging to the ‘Emper’, ‘Kalipso’, and ‘Polinka’ cultivars were obtained manually from the mature fruits harvested from an orchard in central Poland. The plums were cut in half to extract the stones. The removed stones were washed and cleaned of their flesh. After air-drying, the undamaged stones were subjected to imaging.

2.2. Image Processing

The whole plum stones were imaged using a digital camera placed on a tripod, LED illumination, and a black box. Images were acquired under room conditions. Color calibration of the digital camera was carried out. The stones were positioned against a black background. This facilitated the segmentation of the images. In the case of each cultivar, ‘Emper’, ‘Kalipso’, and ‘Polinka’, one hundred imaged stones were obtained. Ten images were taken for each cultivar. There were ten plum stones in each image. In total, the obtained set consisted of images for three hundred plum stones. For the acquired images, a traditional image processing approach was applied. The image segmentation and texture determination were performed with the use of MaZda software (Łódź University of Technology, Institute of Electronics, Łódź, Poland) [27]. The procedure of image acquisition and processing is presented in Figure 1. The lighter plum stones were separated from the black background using the segmentation of the images into brightness regions. For each plum stone considered as a set of pixels, the region of interest (ROI) was overlaid. The image textures were considered as a function of the spatial variation of the pixel brightness intensity. The images can have repeated subpatterns of the distribution of pixel brightness. Textures can provide information about the structure of the objects. The quantitative texture analysis can provide important insights about object quality [19]. The texture parameters were calculated for stone images converted to color channels R, G, B, L, a, b, X, Y, and Z. The examples of original plum stone images and images converted to randomly selected color channels, for which significant differences between H Mean textures were determined based on the results performed using a one-way ANOVA in Statistica (StatSoft Inc., Tulsa, OK, USA) software at a significance level of p ≤ 0.05, are shown in Figure 2.

In the case of each ROI (each plum stone) in each of the nine color channels, about 180 textures, based on the co-occurrence matrix (132 texture parameters, including 11 features computed for 4 various directions and 3 between-pixels distances), run-length matrix (20 texture parameters, including 5 features computed for 4 various directions), histogram (9 texture parameters), Haar wavelet transform (10 texture parameters), gradient map (5 texture parameters), and autoregressive model (5 texture parameters), were computed [27]. In total, about 1600 image textures were determined for each stone. These textures were used first for the selection step and then for the development of models to distinguish plum stone cultivars.

2.3. Plum Stone Cultivar Discrimination Using Machine Learning Algorithms

The plum stones were discriminated into ‘Emper’, ‘Kalipso’, and ‘Polinka’ cultivars with the use of the WEKA (Machine Learning Group, University of Waikato, Hamilton and Tauranga, New Zealand) machine learning software [28,29]. The analysis included attribute selection and building the models for the discrimination of the plum stone cultivars (Figure 3). The textures with the highest discriminative power were selected using the Best–first algorithm. The texture selection step was performed for a set of textures from color channels R, G, B, L, a, b, X, Y, and Z, and separately for individual color channels R, G, and B from the color space RGB, color channels L, a, and b from the color space Lab, and the color channels X, Y, and Z from the color space XYZ. Then, the models were developed for each set of selected textures using the machine learning algorithms (classifiers) [30]. The algorithms from different groups (‘Bayes’, ‘Lazy’, ‘Trees’, ‘Meta’, ‘Functions’, and ‘Rules’) were tested. The classification was performed using a 10-fold cross-validation mode. The dataset was randomly divided into 10 parts. The learning was performed a total of 10 times using different training sets. Each of the 10 parts was used as the test set, and the remaining 9 parts as the training sets, in turn. The results were the average of 10 estimates [30]. The discriminant analysis allowed the determination of the confusion matrices with the discrimination accuracies, as well as the values of the precision, MCC (Matthews Correlation Coefficient), and F-measure. The equations for the computation of these metrics are presented in Equations (1)–(4). The range of values for accuracy was 0–100%, and for the precision, MCC, and F-measure—0.000–1.000. The decision on the effectiveness of the model was made based on the highest performance metrics. The higher the values of the metrics, the more correct the classifications are. Additionally, the values of the Kappa statistic, mean absolute error, and root mean squared error (range of 0.000–1.000) were determined. The high value of the Kappa statistic was considered desirable, whereas the values of the errors should be as low as possible. Based on the most successful values of the metrics obtained for the IBk (Instance-Based Learning with parameter, k) (‘Lazy’), QDA (Quadratic Discriminant Analysis) (‘Functions’), LDA (Linear Discriminant Analysis) (‘Functions’) and Random Forest (‘Trees’), the results for these algorithms were chosen to be presented in this paper. The parameters of these selected algorithms were the following: for IBk—do Not Check Capabilities: False, batch Size: 100, KNN: 1, debug: False, mean Squared: False, window Size: 0, nearest Neighbour Search Algorithm: Linear NN Search (distance Function: Euclidean Distance-R first-last); for QDA and LDA—do Not Check Capabilities: False, ridge: 1 × 10⁻⁶, batch Size: 100, debug: False; for Random Forest—bag Size Percent: 100, batch Size: 100, break Ties Randomly: False, debug: False, do Not Check Capabilities: False, num Excecution Slots: 1, num Interactions: 100, seed: 1.

$$\mathit{Accuracy}=\frac{\mathit{TP}+\mathit{TN}}{\mathit{TP}+\mathit{FP}+\mathit{TN}+\mathit{FN}}\times 100$$

(1)

$$\mathit{Precision}=\frac{TP}{\mathit{TP}+\mathit{FP}}$$

(2)

$$\mathit{MCC}=\frac{\left(\mathit{TP}\times \mathit{TN}\right)-\left(\mathit{FN}\times \mathit{FP}\right)}{\sqrt{\left(\mathit{TP}+\mathit{FN}\right)\times \left(\mathit{TN}+\mathit{FP}\right)\times \left(\mathit{TP}+\mathit{FP}\right)\times \left(\mathit{TN}+\mathit{FN}\right)}}$$

(3)

$$F1-\mathit{Measure}=\frac{2\mathit{TP}}{2\mathit{TP}+\mathit{FP}+\mathit{FN}}$$

(4)

TP: True Positive; TN: True Negative; FP: False Positive; FN: False Negative.

In order to verify the correctness of the approach used, the automatic General Discriminant Analysis (GDA) model involving the progressive discrimination was tested in STATISTICA (StatSoft Inc., Tulsa, OK, USA) software at suggested parameters. Different software and a different procedure for building the model than in WEKA were chosen to ensure the independence of the analysis. The verification was used for models including textures selected from color channels R, G, B, L, a, b, X, Y, and Z and built into WEKA using various machine learning algorithms.

3. Results

Firstly, the discriminative models were built based on the combined textures selected from the color channels R, G, B, L, a, b, X, Y, and Z (

Table 1. The confusion matrices, average accuracies, and values of precision, MCC, F-measure, Kappa statistic, mean absolute error, and root mean squared error of discrimination of plum stones belonging to different cultivars based on models including textures selected from color channels R, G, B, L, a, b, X, Y, and Z.

Classifier	Predicted Class (%)			Actual Class	Average Accuracy (%)	Precision	MCC	F-Measure	Kappa Statistic	Mean Absolute Error	Root Mean Squared Error
	‘Emper’	‘Kalipso’	‘Polinka’
Lazy. IBk	97	3	0	‘Emper’	96.67	0.933	0.926	0.951	0.95	0.0247	0.1369
	3	97	0	‘Kalipso’		0.970	0.955	0.970
	4	0	96	‘Polinka’		1.000	0.970	0.980
Functions. QDA	96	1	3	‘Emper’	95.33	0.906	0.897	0.932	0.93	0.031	0.1756
	3	97	0	‘Kalipso’		0.990	0.970	0.980
	7	0	93	‘Polinka’		0.969	0.925	0.949
Functions. LDA	93	1	6	‘Emper’	95	0.930	0.895	0.930	0.925	0.0378	0.1692
	2	98	0	‘Kalipso’		0.980	0.970	0.980
	5	1	94	‘Polinka’		0.940	0.910	0.940
Trees. Random Forest	93	2	5	‘Emper’	94.67	0.912	0.881	0.921	0.92	0.1136	0.1918
	1	99	0	‘Kalipso’		0.980	0.978	0.985
	8	0	92	‘Polinka’		0.948	0.902	0.934

MCC—Matthews Correlation Coefficient.

). The textures contributing most to the accuracy of the models were from the color channels G and B. They were characterized by the highest discriminative power. Examples of these textures are GS5SH5SumOfSqs, GS5SV1SumVarnc, BS5SZ1SumOfSqs, BS5SV1SumOfSqs, GHPerc10, GHKurtosis, and BHPerc10. The obtained results were very satisfactory. The ‘Emper’, ‘Kalipso’, and ‘Polinka’ plum stones were discriminated with a high average accuracy of up to 96.67% for the model developed using the IBk classifier. The individual cultivars were distinguished in 97% for ‘Emper’ and ‘Kalipso’, and 96% for ‘Polinka’. None of the cases belonging to the other cultivars were incorrectly included in the class ‘Polinka’. In the case of the predicted class ‘Emper’, 3% of the stones, ‘Kalipso’, and 4% of the stones, ‘Polinka’, were incorrectly classified as ‘Emper’. Additionally, 3% of the ‘Emper’ stones were incorrectly included in the class ‘Kalipso’. The values of the precision, MCC, and F-measure were the highest for ‘Polinka’ and were equal to 1.000, 0.970, and 0.980, respectively. Additionally, the Kappa statistic, equal to 0.95, was high, whereas the values of mean absolute error (0.0247) and root mean squared error (0.1369) were low.

In the case of the other classifiers, the average accuracies of the discrimination of ‘Emper’, ‘Kalipso’, and ‘Polinka’ plum stones, based on models including the textures selected from the color channels R, G, B, L, a, b, X, Y, and Z, reached 95.33% for QDA, 95% for LDA, and 94.67% for ‘Random Forest’ (Table 1). Based on the confusion matrices, it was observed that the stones, ‘Kalipso’, were discriminated with the highest accuracies of up to 97% (QDA), 98% (LDA), and 99% (Random Forest). The models built with the use of the QDA and ‘Random Forest’ algorithms allowed for the complete differentiation of the ‘Kalipso’ and ‘Polinka’ plum stones, whereas the greatest mixing of cases occurred between the ‘Emper’ and ‘Polinka’ stones. In the case of the ‘Random Forest’, 8% of the cases belonging to the class ‘Polinka’ were incorrectly included in the class ‘Emper’, and 5% of the stones, ‘Polinka’, were incorrectly classified as ‘Emper’. The ‘Kalipso’ plum stones were characterized by a very high precision (0.990) for the model built using the QDA algorithm, whereas the values of the MCC (0.978) and F-measure (0.985) were the most satisfactory for the ‘Kalipso’ cultivar and ‘Random Forest’ algorithm. The values of the Kappa statistic were high for QDA (0.93), LDA (0.925), and ‘Random Forest’ (0.92). In the case of each classifier, the mean absolute error and root mean squared error were low, up to 0.1136 and 0.1918 (Random Forest), respectively. The verification of these models built based on the textures selected from the color channels R, G, B, L, a, b, X, Y, and Z (Table 1) and carried out using automatic General Discriminant Analysis (GDA), proved the high accuracy of discrimination. The plum stones were correctly discriminated in 96.67%. The accuracies for the stones belonging to individual cultivar were equal to 96% for ‘Emper’ and ‘Polinka’ and 98% for ‘Kalipso’.

The mean values of some of the image textures from the selected color channels are presented in Figure 4. The differences between the plum stone cultivars were visible. The most noticeable differentiation was observed between ‘Kalipso’ and ‘Polinka’. This confirmed the high correctness of the discrimination between these cultivars and the lack, or slight mixing of cases, between them (Table 1). The results of a one-way ANOVA revealed that the differences in the means of the GH Mean, LH Mean, XH Mean, and BH Mean, between the ‘Emper’, ‘Kalipso’, and ‘Polinka’ plum stones, were statistically significant and that each cultivar formed the separate homogenous group. The values of the GH Mean were equal to 140.34 for ‘Polinka’, 160.60 for ‘Emper’, and 170.02 for ‘Kalipso’. The LH Mean variable was characterized by the values of 172.97 for ‘Polinka’, 188.15 for ‘Emper’, and 195.12 for ‘Kalipso’. The values of the XH Mean were equal to 91.56 for ‘Polinka’, 111.65 for ‘Emper’, 121.46 for ‘Kalipso’. The determined BH Mean values were equal to 84.21 for ‘Polinka’, 105.05 for ‘Emper’, and 111.12 for ‘Kalipso’.

In the next steps of the analysis, the models were built based on the textures selected from individual color channels from the color spaces RGB, Lab, and XYZ, using two selected classifiers (QDA and LDA) and providing the most satisfactory results. Among the individual color channels from the color space RGB (

Table 2. The results of cultivar discrimination of plum stones based on textures selected from individual color channels R, G, and B.

Classifier	Predicted Class (%)			Actual Class	Average Accuracy (%)	Precision	MCC	F-Measure	Kappa Statistic	Mean Absolute Error	Root Mean Squared Error
	‘Emper’	‘Kalipso’	‘Polinka’
Color channel R
Functions. QDA	88	5	7	‘Emper’	90.67	0.863	0.806	0.871	0.86	0.0617	0.2302
	4	94	2	‘Kalipso’		0.949	0.917	0.945
	10	0	90	‘Polinka’		0.909	0.857	0.905
Functions. LDA	86	11	3	‘Emper’	88	0.804	0.743	0.831	0.82	0.0921	0.2350
	3	97	0	‘Kalipso’		0.890	0.892	0.928
	18	1	81	‘Polinka’		0.964	0.835	0.880
Color channel G
Functions. QDA	96	1	3	‘Emper’	94.67	0.889	0.884	0.923	0.92	0.0373	0.1747
	3	97	0	‘Kalipso’		0.990	0.970	0.980
	9	0	91	‘Polinka’		0.968	0.910	0.938
Functions. LDA	88	4	8	‘Emper’	90.67	0.854	0.799	0.867	0.86	0.0710	0.2103
	5	95	0	‘Kalipso’		0.950	0.925	0.950
	10	1	89	‘Polinka’		0.918	0.857	0.904
Color channel B
Functions. QDA	96	1	3	‘Emper’	93.33	0.857	0.858	0.906	0.90	0.0489	0.2012
	4	96	0	‘Kalipso’		0.990	0.962	0.975
	12	0	88	‘Polinka’		0.967	0.887	0.921
Functions. LDA	83	7	10	‘Emper’	90.67	0.883	0.788	0.856	0.86	0.0700	0.2126
	3	97	0	‘Kalipso’		0.933	0.926	0.951
	8	0	92	‘Polinka’		0.902	0.866	0.911

MCC—Matthews Correlation Coefficient.

), the highest average accuracy, equal to 94.67%, was obtained in the case of the model built based on the textures selected from images converted to the color channel G, using the QDA classifier. The stones ‘Emper’, ‘Kalipso’, and ‘Polinka’ were discriminated with very high accuracies up to 96%, 97%, and 91%, respectively. The values of the other metrics were the highest for ‘Kalipso’, were equal to 0.990 for the precision, were 0.970 for the MCC, and were 0.980 for the F-measure. For the analysis performed for the color channel G and the LDA classifier, the accuracies were lower, reaching 90.67% in the case of average accuracy, and 88% for ‘Emper’, 95% for ‘Kalipso’, and 89% for ‘Polinka’. The results for the other performance metrics were also the highest for the ‘Kalipso’ plum stones (with the precision at 0.950, the MCC at 0.925, and the F-measure at 0.950). Slightly lower results were observed for the models developed based on the textures selected from channel B. The average accuracies were equal to 93.33% in the case of the QDA classifier and 90.67% for the LDA classifier. The stones, ‘Kalipso’, were discriminated with the highest performance metrics. In the case of the textures from the color channel R, the average accuracy reached 90.67% for the QDA and 88% for the LDA classifier. The Kappa statistic was in the range of 0.82 to 0.92, with the mean absolute error from 0.0921 to 0.0373 and the root mean squared error from 0.2350 to 0.1747. The lowest values were obtained for the model developed based on the selected image textures from the color channel R using the LDA algorithm. The highest values were determined in the case of the color channel G and QDA.

The metrics of the discrimination analysis performed for the color channels L, a, and b from the color space Lab are presented in

Table 3. The metrics of cultivar discrimination of plum stones based on textures selected from individual color channels L, a, b.

Classifier	Predicted Class (%)			Actual Class	Average Accuracy (%)	Precision	MCC	F-Measure	Kappa Statistic	Mean Absolute Error	Root Mean Squared Error
	‘Emper’	‘Kalipso’	‘Polinka’
Color channel L
functions. QDA	94	2	4	‘Emper’	93.67	0.879	0.861	0.908	0.905	0.0423	0.1933
	7	93	0	‘Kalipso’		0.979	0.932	0.954
	6	0	94	‘Polinka’		0.959	0.925	0.949
functions. LDA	89	5	6	‘Emper’	93.33	0.918	0.857	0.904	0.90	0.0587	0.1884
	2	98	0	‘Kalipso’		0.942	0.941	0.961
	6	1	93	‘Polinka’		0.939	0.902	0.935
Color channel a
functions. QDA	87	4	9	‘Emper’	88.67	0.813	0.758	0.841	0.83	0.0797	0.2432
	10	89	1	‘Kalipso’		0.957	0.887	0.922
	10	0	90	‘Polinka’		0.900	0.850	0.900
functions. LDA	88	9	3	‘Emper’	88.67	0.830	0.779	0.854	0.83	0.1034	0.2376
	5	95	0	‘Kalipso’		0.880	0.869	0.913
	13	4	83	‘Polinka’		0.965	0.850	0.892
Color channel b
functions. QDA	89	7	4	‘Emper’	81	0.712	0.679	0.791	0.715	0.1251	0.3142
	13	85	2	‘Kalipso’		0.850	0.775	0.850
	23	8	69	‘Polinka’		0.920	0.719	0.789
functions. LDA	75	12	13	‘Emper’	79.67	0.815	0.680	0.781	0.695	0.1575	0.2967
	8	85	7	‘Kalipso’		0.780	0.715	0.813
	9	12	79	‘Polinka’		0.798	0.692	0.794

MCC—Matthews Correlation Coefficient.

. The plum stones were distinguished with lower average accuracies in the range of 79.67% (75% for ‘Emper’, 85% for ‘Kalipso’, 79% for ‘Polinka’) for color channel b and the LDA classifier to 93.67% (94% for ‘Emper’, 93% for ‘Kalipso’, 94% for ‘Polinka’) for color channel L and the QDA classifier. In the case of the model built for textures from the color channels L using the LDA classifier, the average accuracy was quite high and reached 93.33%. For textures selected from color channel a, the average accuracy was equal to 88.67% for both the QDA and LDA classifiers. The highest Precision equal to 0.979 was found for the ‘Kalipso’, the color channels L and QDA. The highest MCC (0.941) and F-measure (0.961) were determined for the ‘Kalipso’, the color channels L and LDA. The model built for textures selected from the color channels L using QDA was characterized by the highest Kappa statistic (0.905) and the lowest mean absolute error (0.0423). The lowest root mean squared error was observed for the color channels L and LDA. Whereas the highest mean absolute error (0.1575, LDA) and root mean squared error (0.3142, QDA), as well as the lowest Kappa statistic (0.695, LDA), were found in the case of classification performed based on textures selected from color channel b.

In the case of models built for individual color channels from color space XYZ (

Table 4. The cultivar discrimination of plum stones based on textures selected from individual color channels X, Y, and Z.

Classifier	Predicted Class (%)			Actual Class	Average Accuracy (%)	Precision	MCC	F-Measure	Kappa Statistic	Mean Absolute Error	Root Mean Squared Error
	‘Emper’	‘Kalipso’	‘Polinka’
Color channel X
Functions. QDA	95	1	4	‘Emper’	92	0.833	0.830	0.888	0.88	0.0561	0.2063
	5	95	0	‘Kalipso’		0.990	0.955	0.969
	14	0	86	‘Polinka’		0.956	0.864	0.905
Functions. LDA	85	8	7	‘Emper’	88.67	0.825	0.755	0.837	0.83	0.0924	0.2335
	7	93	0	‘Kalipso’		0.912	0.881	0.921
	11	1	88	‘Polinka’		0.926	0.856	0.903
Color channel Y
Functions. QDA	90	2	8	‘Emper’	90	0.818	0.783	0.857	0.85	0.0683	0.2267
	7	93	0	‘Kalipso’		0.979	0.932	0.954
	13	0	87	‘Polinka’		0.916	0.841	0.892
Functions. LDA	83	8	9	‘Emper’	89.67	0.856	0.766	0.843	0.845	0.0856	0.2340
	5	95	0	‘Kalipso’		0.922	0.903	0.936
	9	0	91	‘Polinka’		0.910	0.865	0.910
Color channel Z
Functions. QDA	84	6	10	‘Emper’	89	0.832	0.753	0.836	0.835	0.0770	0.2198
	7	93	0	‘Kalipso’		0.939	0.902	0.935
	10	0	90	‘Polinka’		0.900	0.850	0.900
Functions. LDA	91	3	6	‘Emper’	87.67	0.765	0.742	0.831	0.815	0.0784	0.2650
	8	92	0	‘Kalipso’		0.968	0.917	0.944
	20	0	80	‘Polinka’		0.930	0.803	0.860

MCC—Matthews Correlation Coefficient.

), the cultivar discrimination of plum stones reached 92% for channel X and the QDA classifier. For the stones ‘Emper’ and ’Kalipso’, the discrimination accuracy was equal to 95%, and for the class ‘Polinka’, the accuracy reached 86%. In the case of the LDA classifier, the cultivar discrimination of the plum stones based on the textures selected from the color channel X was characterized by an average accuracy of 88.67%. The models developed using the textures selected from images from the color channel Y provided average accuracies of up to 90% and 89.67% for the QDA and LDA classifiers, respectively, whereas the average accuracies for the models built based on the textures selected from the color channel Z were equal to 89% (QDA) and 87.67% (LDA). The most satisfactory precision (0.990MCC (0.955) and F-measure (0.969) were obtained for the ‘Kalipso’ color channel X and QDA. The Kappa statistic (0.88) was the highest, and the values of the mean absolute error (0.0561) and root mean squared error (0.2063) were the lowest in the case of the model built for the textures selected from the color channel X using QDA. In the case of the color channel Z and LDA, the Kappa statistic, equal to 0.815, was the lowest, and the root mean squared error of 0.2650 was the highest. The highest mean absolute error equal to 0.0924 was observed for the color channel X and LDA.

4. Discussion

The obtained results proved the usefulness of machine learning algorithms to discriminate the plum stone cultivars based on selected image texture parameters. The machine learning algorithms were also successively applied to discriminate the stones or pits of other species in previous studies, which confirms the usefulness of this approach. For example, in the case of sour cherry pits, machine learning was used for the discrimination based on geometric parameters, reaching the average accuracy of 96% for two cultivars and 75% for four cultivars for the logistic classifier [31]. The discrimination accuracy of two cultivars of peach stone equal to 100% based on seed textures was observed for the BayesNet algorithm [32]. The selected machine learning algorithms allowed, also, for the successful discrimination of two different cultivars of sweet cherry pits were based on selected textures (accuracy of 100%) and combined selected textures and geometric features (100%) for the BayesNet, logistic classifier, multi-class classifier, PART, LMT, as well as the geometric features (99%) for the BayesNet and LMT. Three sweet cherry cultivars were discriminated with the average accuracies of 95% for selected textures and the LMT classifier, 93% for selected geometric features and the LMT classifier, and 98% for combined textures and geometric features and the logistic classifier [33]. The average discrimination accuracy of 96.25% was obtained for four cultivars of sour cherry pits for the models built based on texture parameters using the multilayer perceptron classifier and 100% for two cultivars for all the applied algorithms (BayesNet, multilayer perceptron, multi-class classifier, and ‘Random Forest’) [34]. In the case of the discrimination of plum kernels using models developed using textures and machine learning algorithms, the average accuracy reached 98% for the set of textures selected from the color space Lab and the KStar algorithm [35]. The developed models can be of great practical use. They may allow the detection of adulteration in a set of stones and the identification of a cultivar of unknown cases. The prediction of the classes of examined objects using the constructed classifiers is the aim of the classification analysis. It can be useful for both binary and multiclass classifications. The categorization of future objects can be performed using their known vectors of features included in the training data set with the known correct classifications. Classification methods may be used for the categorization to classify new objects automatically [36]. The discriminative models can model the posterior probabilities. A large training set may allow the tuning of the parameters of an adaptive model using a machine learning approach. Training the model enables the identification of new cases included in a test set [37]. It is important to train the model correctly using as many cases as possible to recognize the cultivar of unknown cases. Therefore, future research may be expanded to other cultivars and other species of stone fruit to evaluate the diversity and identify and confirm the authenticity of the stone cultivar and species based on texture, as well as color and geometric features.

5. Conclusions

The application of machine learning allowed us to obtain satisfactory results with the use of a non-destructive, inexpensive, and objective approach. The average accuracy of the discrimination of plum stones belonging to the cultivars ‘Emper’, ‘Kalipso’, and ‘Polinka’ reached 96.67%. This result was obtained for the model, including the selected textures extracted from the images from all the color channels R, G, B, L, a, b, X, Y, and Z. This proved that it is possible to distinguish the cultivars of fruit stone with a very high probability using image textures and machine learning algorithms. Future research may be expanded to other species and cultivars of stone fruit. An increase of correctness and, also, other features, such as color and geometric features, can be included in the discriminative models. These models can be useful in practice to evaluate the diversity and identify and confirm the authenticity of the stone cultivar.