Indirect Determination of Basic Tomato Quality Parameters Using Color Digital Images ^†

Abstract

The indirect determination of basic tomato quality parameters using color digital images is presented in the paper. A database of images of tomatoes of the Clarosa variety was formed. The six main chemical parameters, dry matter, ascorbic acid, titratable organic acids, total dyes, lycopene, and beta-carotene, were measured as referent values. Image processing techniques were used for the extraction of the color components, to remove the background, and for color spaces transformation. The values of the color components of four color models, RGB, HSV, XYZ, and Lab, were obtained in the MATLAB environment. Statistical approaches were used for assessing the relation between the main chemical parameters of tomatoes and the color components. The results of the correlation analysis showed that there were the following relationships between the color components and the chemical indicators: the dry substance had a moderate dependence with R(RGB), S(HSV), and b(Lab) and a significant dependence with H(HSV) and a(Lab); the ascorbic acid substance had a moderate dependence with H(HSV), S(HSV), and a(Lab); the titratable organic acids had a moderate dependence with S(HSV) and b(Lab); a significant dependence was found with R(RGB), and a strong dependence was found with V(HSV), L(Lab), a(Lab), X(XYZ), and Y(XYZ); the general dyes had a significant dependence with H(HSV), S(HSV), and a(Lab); the lycopene had a significant dependence with H(HSV), S(HSV),a and a(Lab); the beta-carotene had a significant dependence with R(RGB), G(RGB), B(RGB), V(HSV), L(Lab), X(XYZ), Y(XYZ), and Z(XYZ). The obtained results showed that the chemical composition values of tomatoes could be predicted with polynomial regression models that use color components from the HSV and Lab models: dry matter-H(HSV); ascorbic acid-H(HSV); titratable organic acids-a(Lab); general dyes-H(HSV), S(HSV), and a(Lab); lycopene-H(HSV), S(HSV), and a(Lab). For the determination of beta-carotene, it is necessary to use more than one color component to obtain mathematical models with a higher coefficient of determination. The obtained results are a prerequisite for this approach to be used in the automated systems for evaluating the quality of tomatoes in the harvesting process.

1. Introduction

In the agricultural system, the production of fruits and vegetables is very important, as it provides a significant part of the population’s livelihood and raw materials for the food industry. Assessing the quality of fruits and vegetables takes a large part of production time.

The evaluation is usually performed manually under visual control, relying primarily on the routine and experience of the evaluator. This is one of the reasons to look for ways to partially or fully automate the process of production control and evaluation.

The need for visual quality control combined with increasing automation in all areas of production leads to the demand for the automatic and objective evaluation of visual parameters, such as size, shape, structure, color, etc. Systems made up of video cameras, appropriate lighting, and computers provide a solution to this task.

Grading or sorting objects is dividing them into separate groups according to their quality indicators. All mechanical methods of separation into size groups have a common drawback—a high degree of product trauma in the process of separation, which is due to the very nature of the method.

Mechanical separation uses forces for orientation—these are centrifugal forces, frictional forces, gravity forces, etc. They can be reduced, but they cannot be avoided, since the separation methods themselves are based on them.

This problem is completely avoided with visual methods. A major part of analyzing product quality with visual systems is image analysis. The representation of the image in the computer’s memory is performed by means of a specific description. The description of objects from a given image is analyzed in order to recognize them. The main tasks that are solved in computer image recognition are:

• Presentation of the measured data for the objects that are subject to recognition;
• Pre-processing of the data and separation of characteristic signs for the objects.

Currently, there is a growing interest in qualitative and quantitative increases in the content of beneficial health compounds in tomato fruits [1,2].

Sensory evaluation is used to evaluate taste, which is significantly positively correlated with the soluble solids content, fructose, glucose, citric acid, fumaric acid, and β-ionone (p < 0.01) and significantly negatively correlated with the water content and hardness without peeling [3]. Lab color space is used for the assessment of the tomato surface color.

One of the commonly used methods for the analysis of the quality of tomatoes is spectroscopy [4]. The other applied method is based on liquid chromatography/mass spectroscopy [5]. These techniques require expensive and specialized equipment and highly qualified and trained staff.

In recent years, image processing and computer vision have become the most often used techniques for different purposes in the quality assessment process. Image processing was used for the assessment of maturity and the ripening stages of tomatoes, based on United States standards for the grades of fresh tomatoes [6,7,8]. Image analysis techniques were used for the estimation of the volume of tomatoes, in a cultivar grown in Turkey, using image processing techniques. Five different images of a tomato were captured using high-resolution digital cameras [9]. Fetal volume was calculated by estimating the horizontal and vertical distances of the captured images.

The aim of the paper is to propose an indirect determination of basic tomato quality parameters using color digital images.

2. Materials and Methods

In recent years, there has been an increased interest in tomato varieties with high fruit contents of lycopene, beta-carotene, and anthocyanins, due to their high antioxidant capacities. Lycopene causes the red color, beta-carotene the yellow–orange color, and anthocyanins the violet color of the fruits. The ones with the most powerful antioxidant properties are the varieties with a high content of anthocyanins, followed by those with a high content of lycopene and beta-carotene. Lycopene is a more powerful antioxidant than beta-carotene, and its biological value is higher in processed products.

The object of this study was tomatoes of the Clarosa variety, which have a strong resistance to bronzing. It is a strong plant with well-decorated foliage, balanced internodes, and beautiful bunches. Pollination is very good, even in the summer months, which makes it very suitable for a second harvest. The fruits are round and shiny with a pleasant raspberry-pink color, without traces of a green ring. The weight is 220–250 g and very even. They are hard, with great post-harvest durability.

2.1. Analysis of the Main Chemical Components of Fresh Tomato Fruits

The analysis of the main chemical components of fresh tomato fruits and the evaluation of the technological and sensory properties were carried out in the Quality Laboratory at the Trakia University, Stara Zagora. On average, for the samples of 10 fruits, the content of dry matter was determined by a refractometer, ascorbic acid was determined by the Tillmans reaction, titratable organic acids were determined by the direct titration of juice with 0.1 n NaOH, and total dyes and lycopene were determined. The results are presented in

Table 1. Formatting of the chemical compositions of tomatoes of the Clarosa variety.

№	Weight	Dry Substance	Ascorbic Acid	Titratable Organic Acids	General Dyes	Lycopene	Beta-Carotene
	(g)	Re (%)	(mg %)	(%)	(mg %)	(mg %)	(mg %)
1	134	3.30	17.36	0.16	1.14	0.78	0.28
2	198	3.80	20.32	0.23	1.32	0.90	0.32
3	290	3.50	18.63	0.28	1.67	1.23	0.33
4	228	3.80	18.20	0.31	1.84	1.32	0.40
5	284	4.00	20.32	0.28	2.30	1.94	0.20
6	306	3.90	19.05	0.27	2.49	1.89	0.42
7	288	4.10	18.63	0.30	2.51	2.05	0.29
8	260	4.30	18.63	0.35	2.65	2.11	0.36
9	258	4.20	18.20	0.38	3.73	3.11	0.35
10	196	4.10	17.36	0.35	3.65	3.07	0.33

.

2.2. Image Acquisition of the Tomato Fruits

The images of Clarosa tomatoes were captured with a document camera. The tomato images were captured with a Triumph Board A 405 document camera in daylight. Shooting was performed through a specially installed Nimo Studio software with the ability to set the resolution and image format. The VGA resolution (640 × 480) and the JPEG format of the tomato image files were selected. Color digital images of a tomato fruit were obtained in the primary RGB color space. The images of the tomatoes were obtained from two sides—top and bottom. Images of tomatoes in the RGB color space are presented in Figure 1.

In recent years, there has been an increase in the researches related to the assessment of fruit and vegetable quality using image processing. The analysis showed that color models were successfully used as follows: HSI—citrus maturity evaluation; Lab—strawberry grading based on the external quality; RGB and HIS—apple color classification and grading by color [10]; machine vision with the RGB color model—detecting the color, size, shape, and surface defects of fresh fruits and vegetables [11]; a combination of RGB, HIS, and YIQ—assessment of the tomatoes’ ripeness [12]; RGB and Lab color models—assessment of defective areas in apples, oranges, and tomatoes [13]; and RGB and HSV—sorting and grading of fruits and vegetables [14]. In [15], the authors commented that standard RGB (sRGB; red, green, blue) and L*a*b* are commonly applied in quantifying standard food colors, and they are needed to define the mapping between the RGBs (non-linear signals) from a computer vision system and a device-independent system, such as CIE XYZ. Based on the analysis of the used color spaces for image analysis, HSV, Lab, and XYZ were selected.

The images were transformed into the following color spaces—Lab, HSV, and XYZ.

2.3. Tomato Fruits Image Preprocessing

The image preprocessing started with removing the background. The Toolbox “Color Thresholder” in the MATLAB [16] environment was used for the selection of the informative features for background removing. This tool visualized the object in a selected color model to visualize the histograms by color components from the model. Figure 2 shows the 3 color models integrated into this tool—RGB, HSV, and Lab.

The obtained results from the analysis of the color components of the four color models showed that component b (Lab model) can unambiguously describe the background chosen for the photos well enough in the interval from 0 to 50. For the remaining components, it was necessary to propose a combination of two or three components, which complicated the calculation process.

To separate the object from the background, the component b (Lab) color model was selected, which, in the range of 0 to 50, can be applied as a criterion for separating the background from the object.

2.4. Selection of Color Characters for Tomato Quality

A total of 640 × 480 pixels (307 200 pixels) was obtained for each image and transformed into HSV, Lab, and XYZ color models. The pixels belonging to the background were removed. The other pixels from the object tomato formed the vectors with color components for each tomato fruit. The color components for one fruit consisted of the pixels obtained for the top and bottom images of the tomatoes. The mean value for each color component was calculated from the pixels obtained for the top and bottom images of the tomatoes.

$$C_{Cmean}={\displaystyle \frac{1}{n}}\sum _{i=1}^n{C}_C,$$

(1)

where n is the number of pixels of the tomato fruit obtained from the top and bottom images of the tomatoes; C_C is the color component from the RGB, HSV, Lab, and XYZ color models; and C_Cmean is the mean value of the color component. The image analysis was performed by a specific software application developed using the programming language MATLAB.

The mean values of the color components for the following color models—RGB, HSV, Lab, and XYZ—obtained from the images are presented in

Table 2. Color component values for 10 objects.

№	R	G	B	H	S	V
1	150	159	188	225.79	0.20	0.74
2	150	161	189	223.08	0.21	0.74
3	156	166	193	223.78	0.19	0.76
4	162	169	197	228.00	0.18	0.77
5	154	161	190	228.33	0.19	0.75
6	159	173	202	220.47	0.21	0.79
7	156	163	192	228.33	0.19	0.75
8	163	169	201	230.53	0.19	0.79
9	156	160	189	232.73	0.17	0.74
10	153	158	187	231.18	0.18	0.73
№	L	a	b	X	Y	Z
1	65.68	3.06	−16.02	0.34	0.35	0.53
2	66.25	2.18	−15.72	0.35	0.36	0.53
3	68.16	2.24	−15.01	0.37	0.38	0.56
4	69.53	3.41	−15.11	0.39	0.40	0.58
5	66.58	3.69	−15.75	0.35	0.36	0.54
6	70.54	1.38	−16.37	0.40	0.42	0.62
7	67.33	3.67	−15.71	0.36	0.37	0.55
8	69.74	4.62	−17.00	0.40	0.40	0.61
9	66.43	4.67	−15.40	0.35	0.36	0.53
10	65.60	4.36	−15.56	0.34	0.35	0.52

.

In order to determine significant informative color characters for the indirect determination of tomato quality, it was necessary to analyze the relationship and its significance between each color component and tomato chemical indicators. One of the main tasks of statistics is the study of the relationship between random variables. Correlation analysis was applied to describe the strength and direction of the dependence between variables, including color components and quality parameters of the tomato fruits. In

Table 3. Correlation coefficients between chemical indicators and color components.

	R	G	B	H	S	V
Dry substance	0.446	0.077	0.216	0.608	−0.445	0.216
Ascorbic acid	−0.081	0.154	0.120	−0.385	0.373	0.120
Titratable organic acids	0.568	−0.133	−0.085	−0.191	−0.313	0.972
General dyes	0.257	−0.133	−0.036	0.675	−0.563	−0.036
Lycopene	0.216	−0.186	−0.085	0.699	−0.576	−0.085
Beta-carotene	0.603	0.678	0.644	−0.191	0.040	0.644
	L	a	b	X	Y	Z
Dry substance	0.161	0.617	−0.330	0.257	0.160	0.210
Ascorbic acid	0.113	−0.363	−0.095	0.060	0.108	0.118
Titratable organic acids	0.982	0.989	−0.442	0.980	0.999	−0.265
General dyes	−0.056	0.629	−0.054	0.033	−0.054	−0.037
Lycopene	−0.107	0.655	−0.046	−0.016	−0.106	−0.087
Beta-carotene	0.681	−0.223	−0.092	0.675	0.686	0.651

, the values of the correlation coefficients between the chemical indicators of tomatoes and the color components are presented.

For the purposes of the study, we considered the cases in which the correlation coefficient had moderate, significant, and strong dependences. The dry substance had moderate dependence with R(RGB), S(HSV), and b(Lab) and significant dependence with H(HSV) and a(Lab). The ascorbic acid substance had moderate dependence with H(HSV), S(HSV), and a(Lab). The titratable organic acids had moderate dependence with S(HSV) and b(Lab); significant dependence with R(RGB); and strong dependance with V(HSV), L(Lab), a(Lab), X(XYZ), and Y(XYZ). The general dyes had significant dependence with H(HSV), S(HSV), and a(Lab). The lycopene had significant dependence with H(HSV), S(HSV), and a(Lab). The beta-carotene had significant dependence with R(RGB), G(RGB), B(RGB), V(HSV), L(Lab), X(XYZ), Y(XYZ), and Z(XYZ). The results are presented in

Table 4. Correlation coefficients between chemical indicators and color components.

	Moderate Dependence from 0.3 to 0.5	Significant Dependence from 0.5 to 0.7	Strong Addiction from 0.7 to 0.9
Dry substance	R, S, b	H, a	-
Ascorbic acid	H, S, a	-	-
Titratable organic acids	S, b	R	V, L, a, X, Y
General dyes	-	H, S, a	-
Lycopene	-	H, S, a	-
Beta-carotene	-	R, G, B, V, L, X, Y, Z	-

.

The obtained results showed that the determined color components were informative and could be used to obtain a mathematical model to determine the chemical indicators and the quality of tomatoes.

3. Modeling the Dependencies between Color Components and Chemical Indicators of Tomatoes with Regression Models

If some relationship exists between two random variables, one of the most important tasks of statistics is to estimate this relationship and to determine the nature and form of the relationship. Questions related to the dependence between two random variables are studied from two aspects: from the point of view of correlation and from the point of view of regression. Correlation describes the degree of dependence between two variables. When, in the study of the dependence between two random variables X and Y as a result of the correlation analysis, it is established that the dependence is statistically significant, one can proceed to its mathematical modeling by applying regression analysis. Regression estimates the value of one variable for a given item based on our knowledge of the value of the other variable for the same item. The correlation statistic answers the question of how strong the relationship is between the two variables. Regression statistics provide an answer to the question of what the nature of the dependence between them is. Regression is a widely used technique for analyzing retrospective and experimental data.

In [17], the non-destructive detection of fruit quality parameters using hyperspectral imaging, multiple regression analysis, and artificial intelligence showed that regression models with values higher than 0.9989 achieved better results than artificial neural networks with a feed-forward network structure and an LM training algorithm. The results for the evaluation of the sweetness and firmness of tomatoes by HSI using the PLSR method with Rpred 0.82 and 0.84 are presented in [18]. In [19], the research successfully used NIR-HSI to predict the firmness of strawberries using partial least squares (PLS) regression. The polynomial regression model is useful when there is reason to believe that the relationship between two variables is curvilinear [20]. Polynomial regression is a special case of multiple regression, with only one independent variable, X. The one-variable polynomial regression model can be expressed as:

$${ChP}_i={\beta }_0+{\beta }_1{C}_{Ci}+{\beta }_2{C}_{Ci}^2+{\beta }_3{C}_{Ci}^3+\dots +{\beta }_k{C}_{Ci}^k+e_i, for i=\mathrm{1,2},\dots ,m$$

(2)

where k is the degree of the polynomial. The degree of the polynomial is the order of the model.

Mathematical regression models have been applied to represent the relationship between color components and chemical indicators for its indirect evaluation using tomato color images. Polynomial regression models have been developed to describe the relationship between chemical indicators and the most significant color components for the respective indicator. These are as follows: dry matter and components H and a; ascorbic acid and components H, S, and a; titratable organic acids and components V, L, a, X, and Y; general dyes and components H, S, and a; lycopene and components H, S, and a; and beta-carotene and components R, G, B, V, L, X, Y, and Z. The paper presents part of the developed models.

In Figure 3, the regression models of the polynomial type (dry matter and color components H and a) are presented. In Figure 4, the regression models of the polynomial type (ascorbic acid and components H and S) are presented. In Figure 5, the regression models of the polynomial type (titratable organic acids and components V and L) are presented. In Figure 6, the regression models of the polynomial type (general dyes and components H and S) are presented. In Figure 7, the regression models of the polynomial type (lycopene H and S components) are presented. In Figure 8, the regression models of the polynomial type (beta-carotene and components R and G) are presented.

A coefficient of determination or a test for the existence of a linear relationship between variables has the meaning of a correlation coefficient: the closer it is to unity, the more “deterministic” the model is.

The R-squared R² (coefficient of determination) of the multiple regression is similar to the simple regression, where the coefficient of determination R² is defined as:

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^m{\left({ChP}_i-\widehat{{ChP}_i}\right)}^2}{{\sum }_{i=1}^m{\left({ChP}_i-\overline{ChP}\right)}^2}},$$

(3)

where $\overline{ChP}$is the arithmetic mean of the ChP variable. R² measures the percentage of variation in the response variable ChP, explained by the explanatory variable C_C.

Thus, it is an important measure of how well the regression model fits the data. The value of R² is always between zero and one, where 0 ≤ R² ≤ 1. An R² value of 0.9 or above is very good, a value above 0.8 is good, and a value of 0.6 or above may be satisfactory in some applications. The highest values of the coefficient of determination for the corresponding mathematical model are presented in

Table 5. Coefficient of determination between the respective quality parameter and the color component.

Model	Dry Substance = f(H(HSV))	Ascorbic Acid = f(H(HSV))	Titratable Organic Acids = f(a(Lab))	General Dyes = f(H(HSV))	General Dyes = f(S(HSV))	General Dyes = f(a(Lab))	Lycopene = f(H(HSV))	Lycopene = f(S(HSV))	Lycopene = f(a(Lab))
$R^2$	0.7161	0.7495	0.8054	0.9065	0.9308	0.9067	0.8864	0.9329	0.9199

.

The obtained results showed that tomato chemical indicator values could be predicted with models that use components from HSV and Lab color models from color tomato images as follows:

• Dry matter—H(HSV);
• Ascorbic acid—H (HSV);
• Titratable organic acids—a(Lab);
• General dyes—H(HSV), S(HSV), and a(Lab);
• Lycopene—H(HSV), S(HSV), and a(Lab).

For the determination of beta-carotene, it was necessary to use more than one color component to obtain mathematical models with a higher coefficient of determination.

4. Conclusions

The article proposed an approach to indirectly determine the quality of Clarosa tomatoes by analyzing their color digital images. The following databases were formed: the values of six main chemical indicators for the quality of tomatoes, which were dry substance, ascorbic acid, titratable organic acids, general dyes, lycopene, and beta-carotene, obtained from laboratory reference measurements; top and bottom images of tomato fruits; and the values of 12 color components, obtained from four color models (RGB, HSV, Lab, and XYZ) from the tomato fruit images.

The results of the correlation analysis showed that there were the following relationships between the color components and the chemical indicators:

• The dry substance had moderate dependence with R(RGB), S(HSV), and b(Lab) and significant dependence with H(HSV) and a(Lab);
• The ascorbic acid substance had moderate dependence with H(HSV), S(HSV), and a(Lab);
• The titratable organic acids had moderate dependence with S(HSV) and b(Lab); significant dependence with R(RGB); and strong dependance with V(HSV), L(Lab), a(Lab), X(XYZ), and Y(XYZ);
• The general dyes had significant dependence with H(HSV), S(HSV), and a(Lab);
• The lycopene had significant dependence with H(HSV), S(HSV) and a(Lab);
• The beta-carotene had significant dependence with R(RGB), G(RGB), B(RGB), V(HSV), L(Lab), X(XYZ), Y(XYZ), and Z(XYZ).

Regression models of the polynomial type can be used to determine the chemical indicators of tomatoes using the color components, due to the high coefficient of determination obtained. The obtained results show that tomato chemical indicator values can be predicted with models that use components from HSV and Lab color models of color tomato images as follows: dry matter—H(HSV); ascorbic acid—H (HSV); titratable organic acids—a(Lab); general dyes—H(HSV), S(HSV), and a(Lab); and lycopene—H(HSV), S(HSV), and a(Lab). For the determination of beta-carotene, it is necessary to use more than one color component to obtain mathematical models with a higher coefficient of determination.

Future research is aimed at increasing the experimental sample of images of tomato fruits, validating the developed models, and evaluating the position of the tomato when it is photographed and the difference between the obtained value of the corresponding chemical indicator according to the developed models and the reference laboratory studies.