Introduction

Bayberry (Myrica rubra Siebold and Zuccarini), which belongs to the genus Myrica in the family Myricaceae, is cultivated in Southeast China since more than 2000 years. It is an important economic Asian fruit crop that produces luscious fruit with appealing flavor (Perkins et al. 2017). The fresh fruit can be processed into a variety of forms, including jam, juice, wine, preserved and canned in syrup (Li et al. 2018). It is highly regarded by consumers, which is abundant with high nutritional components such as anthocyanins, carbohydrates, organic acids, flavonoids, and vitamins (Cheng et al. 2016). Soluble solids content (SSC) and pH, two of the internal quality indices, play an important role in determining fruit maturity and harvest time (Huang et al. 2018). During red bayberry ripening, SSC increased and the acidity decreased (Zhang et al. 2005). The SSC reflects sugar content such as glucose, fructose, and sucrose which is related to fruit taste (Jordan et al. 2000). The pH value of red bayberry, to some extent, is due to organic acids including citric acid, malic acid, oxalic acid and tartaric acid. It is not only related to fruit taste, but also affects the stability of anthocyanins which provides colors ranging from salmon-pink through red and from violet to nearly black of red bayberry. In addition, the attractive colors and the sugar/acid ratios are likely to be the primary attributes contributing to consumer preference. Therefore, the measurements of SSC and pH of red bayberry are important in fruit quality issue.

In recent years, several methods have been developed for detecting the fruit SSC for apples and other fruits, such as infrared spectroscopy technology (Guo et al. 2015; Pu et al. 2016; Guo et al. 2016; Cen et al. 2006; Paz et al. 2008; Fan et al. 2009; Moghimi et al. 2010; Ma et al. 2018), hyperspectral scattering technology (Peng and Lu 2008; Mendoza et al. 2011), and electronic nose sensors (Xu et al. 2018). However, there is no information available on using color space to detect the SSC and pH of red bayberry. Color as an important component of food quality relevant to market acceptance, can be used to quantify the distribution of ingredients for quality evaluation using computer vision. Researches showed that color has been successfully tested for detecting the quality of various food products, such as bruises detection on red bayberry (Lu et al. 2011), color measurements and pattern recognition of paprika (Palacios-Morillo et al. 2016), color quantification of processed ginger (Zhou et al. 2016), evaluation of acrylamide contents in biscuit (Lu and Zheng 2012), prediction of anthocyanins, ascorbic acid, total phenols, flavonoids and antioxidant activity in red bayberry juice (Zheng et al. 2011), maturity evaluation of date (Zhang et al. 2014), and prediction of color and firmness in banana (Xie et al. 2018). In addition, the image processing software, the lowering cost of digital camera and computational technique have made color image processing more versatile and less expensive. With a digital camera, color images can be obtained and saved in three color sensors per pixel in which each sensor captures the intensity of the light in the red (R), green (G) or blue (B) spectrum. Other color spaces such as CMY (Cyan, Magenta and Yellow), HSI (Hue, Saturation and Intensity), I1I2I3 (I1, I2 and I3 in Ohta color space), YCbCr (luminance, blue and red) and CIELAB (L*a*b*) can be transformed by RGB color space. Generally speaking, different color spaces have different characteristics and we should select a suitable color space for a specific visual task. Thus, it is important to choose an appropriate color space for achieving a best result.

In this paper, different color spaces coupled with partial least square regression (PLSR) models and least square-support vector machine (LS-SVM) models were used for detecting the SSC and pH values of red bayberry. The aim of this research is (1) to evaluate the effectiveness of models on inspecting the SSC and pH values originated from red bayberry image analysis, (2) to compare the performance of PLSR and LS-SVM models combined with different color spaces, (3) to lay a foundation for evaluation of other nutrient contents (phenols, flavonoids, anthocyanins) and choosing optimal red bayberry to fruits processing (bayberry juice, dried bayberry or canned bayberry).

Materials and methods

Fruit materials and image acquisition

Red bayberry (M. rubra Sieb. & Zucc. cv. ‘Biqi’) was hand-harvested from an orchard in Cixi (Ningbo, China), and transported by refrigeration at 5 °C for 3 h to the laboratory. After transporting to our laboratory, a total of 50 fruits were selected according to its uniform size, while the physically damaged or diseased ones were removed. Then, a Canon EOS 50D camera with a Canon EF-S 18–55 mm f/3.5–5.6 IS lens was used to acquire red bayberry images, and all image acquisitions were carried out at least in triplicate under the same condition. After acquisition of images, SSC measurement was made with a portable refractometer (Shanghai Tianlei Instrument Co. Ltd., Shanghai, China) with accuracy of 0.002 Brix, and pH value of bayberry samples was measured by a pH meter (Mettler-Toledo Delta 320) with accuracy of 0.01 pH unit. Both of these measurements were performed immediately after image acquisition.

Color spaces

A color space is a method by which we can specify, create and visualize color (Ford and Roberts 1998). Generally, there are three types of color spaces, namely hardware-orientated space, human-orientated space, and instrumental space (Wu and Sun 2013). However, there is no any color space which is better than others and suitable to all kinds of images yet. To study the effect of different color spaces on the prediction performance of SSC and pH value of red bayberry, six different color spaces were evaluated, i.e., NRGB (normalized RGB), CIELAB, CMY, HSI, I1I2I3, and YCbCr. 3D demonstration of these color space images is illustrated in Fig. 1 (Wu and Sun 2013).

Fig. 1
figure 1

3D demonstration of six different color space images. a RGB, b CIELAB, c CMY, d HSI, e I1I2I3, f YCbCr

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RGB corresponds to the three primary colors: red, green and blue, respectively. To reduce the dependence on lighting, the RGB color components are normalized by the following equation (García-Mateos et al. 2015):

$$\left\{\begin{array}{c} {{n}_{r}}=R/\left(R+G+B \right) \\ {{n}_{g}}=G/\left(R+G+B \right) \\ {{n}_{b}}=B/\left(R+G+B \right) \\ \end{array} \right.$$
(1)

where nr, ng and nb are the normalized values between 0 and 1, and the sum of these components is 1.

CIELAB is an international standard for color measurement developed by the Commission International Eclairage (CIE) in 1976. It consists of a lightness component (L* value, from 0 to 100), along with two chromatic components (a* value and b* value, from − 120 to 120), in which a* extends from green to red and b* from blue to yellow as illustrated in Fig. 1b. The CIELAB values were obtained using the formulas as follows (Wu and Sun 2013):

$$\left\{\begin{array}{l} X=0.607\times R+0.174\times G+0.201\times B \\ Y=0.299\times R+0.587\times G+0.114\times B \\ Z=0.000\times R+0.066\times G+1.117\times B \\ \end{array} \right.$$
(2)
$$\left\{\begin{array}{*{35}{l}} L*=116\times {{\left(\frac{Y}{{{Y}_{0}}} \right)}^{\frac{1}{3}}}-16 \\ a*=500\times \left[{{\left(\frac{X}{{{X}_{0}}} \right)}^{\frac{1}{3}}}-{{\left(\frac{Y}{{{Y}_{0}}} \right)}^{\frac{1}{3}}} \right] \\ b*=200\times \left[{{\left(\frac{Y}{{{Y}_{0}}} \right)}^{\frac{1}{3}}}-{{\left(\frac{Z}{{{Z}_{0}}} \right)}^{\frac{1}{3}}} \right] \\ \end{array} \right.$$
(3)

where X/X0 > 0.01, Y/Y0 > 0.01 and Z/Z0 > 0.01. (X0, Y0, Z0) are X, Y, Z values for the standard white.

The CMY color model stands for Cyan, Magenta and Yellow which are the complements of Red, Green and Blue respectively as shown in Fig. 1c. The values can be achieved by the following equation (Dahat and Chavan 2016):

$$\left\{\begin{array}{c} C=255-R \\ M=255-G \\ Y=255-B \\ \end{array} \right.$$
(4)

HSI color space (see Fig. 1d) is intuitive, which are motivated by the human vision system in a sense. It can be separated into three components, i.e. hue, saturation and intensity. They were calculated as Eq. (5) (Deb et al. 2009):

$$\left\{ {\begin{array}{*{20}c} {H = cos^{{\left( { - 1} \right)}} \left\{ {\frac{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}\left[ {\left( {R - G} \right) + \left( {R - B} \right)} \right]}}{{\left[ {\left( {R - G} \right)^{2}+ \left( {R - B} \right)\left( {G - B} \right)} \right]^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} }}} \right\}} \\ {S = 1 - 3\left[ {min\left( {R,G,B} \right)} \right]/\left( {R + G + B} \right)} \\ {I = \left( {R + G + B} \right)/3} \\ \end{array} } \right.$$
(5)

where H represents the dominant color of an area, S measures the colorfulness of an area in proportion to its brightness, and I is related to the color luminance.

As shown in Fig. 1e, I1I2I3 color space can be achieved by a linear transformation of RGB (García-Mateos et al. 2015):

$$\left\{\begin{array}{*{35}{l}} I1=\frac{1}{3}(R+G+B) \\ I2=\frac{1}{2}(R-B) \\ I3=\frac{1}{4}(2G-R-B) \\\end{array} \right.$$
(6)

And for YCbCr color space, it can be seen in Fig. 1f. that Cb represents the difference between the blue channel and a reference value and Cr is between red and a reference value. The values can be achieved by Eq. (7) (García-Mateos et al. 2015):

$$\left\{\begin{array}{l}Y=0.299\times R+0.587\times G+0.114\times B \\ Cb=0.564\left(B-Y \right)+128 \\ Cr=0.713\left(R-Y \right)+128 \\ \end{array} \right.$$
(7)

Partial least square regression (PLSR)

PLSR is a linear algorithm for modeling the relationship between two data sets (Wold et al., 2001). In this study, the color space values and the quality indicators (SSC and pH value) were used to form the explanatory matrix (X) and dependent matrix (Y), respectively. The development of PLSR prediction models involves two basic steps: training and test phases. In the training phase, 70% of the data were randomly selected to generate the model. In this phase, tenfold cross validation (10-CV) was used to choose the optimum number of PLSR components with the smallest prediction error, which avoids overfitting of the model. After training models, an independent data set (30% of the total data) was utilized to test the prediction performance. The PLSR was performed using the software MATLAB (R2010a, the MathWorks Inc., USA). Conventional analysis of linear regression was carried out using OriginLab (OriginPro, version 7.5).

Least square-support vector machine (LS-SVM)

The least-squares support vector machine (LS-SVM) is a variant of the standard SVM that can address linear and nonlinear multivariable calibration and solve multivariable calibration problems relatively quickly (Yu et al. 2016). And proper kernel function and optimal kernel parameters are the crucial elements for LS-SVM. In this study, radial basis function (RBF) kernel was used as the kernel function due to its effectiveness and speed in training process. A grid-search technique and leave one out (LOO) cross-validation was applied to find out the optimal parameter values including regularization parameter gam (γ) and RBF kernel function parameter sig2 (σ2). All LS-SVM algorithms were implemented with MATLAB (R2010a, the MathWorks Inc., USA) and a LS-SVM toolbox for MATLAB (LS-SVM v1.7, Suykens, Leuven, Belgium) under Windows XP.

Cluster analysis

Cluster analysis is one of the most useful statistical tools used in chemometrics for classifying a given population into groups (clusters), based on similarity or closeness measures. Hierarchical clustering, as a common used clustering algorithm, has different agglomerative cluster methods: Ward’s minimum variance method, weighted pair-group method using centroids (WPGMC), the single linkage method, the complete linkage method, the average linkage method (UPGMA) and a maximum likelihood estimate algorithm (Berge et al. 2003). It calculates the distances between all samples using a defined metric such as Euclidean, Manhattan, Camberra and Pearson distances (Ragno et al. 2007). In this study, cluster analysis was displayed in order to find out similarities among the prediction models. UPGMA and the squared Euclidean distance were applied as the hierarchic agglomerative cluster algorithm and distance elaboration, respectively. The cluster analysis was conducted using PAST software (Version 2.17c) (Hammer et al. 2001).

Results and discussion

Prediction of SSC and PH value using PLSR models based on color space

In this study, the mean value and standard deviation of pH and SSC in red bayberry were 3.36 ± 0.20 and 12.57 Brix ± 1.42, respectively. The average values of six different color spaces (NRGB, CIELAB, CMY, HSI, I1I2I3, and YCbCr) were evaluated as the inputs for the prediction models. As seen in Tables 1 and 2, the number of components in the PLSR to predict pH and SSC is 3 for all of the color spaces. To test the performance of models, several parameters between experimental and predicted values were calculated (Tables 1 and 2): correlation coefficient (r), root mean squared error (RMSE), mean absolute error (MAE), mean relative error (MRE). For predicting SSC (in Table 1), the PLSR models based on CIELAB color space could get the highest r value (r = 0.90) and lowest errors (RMSE = 0.91 Brix, MAE = 0.69 Brix and MRE = 0.12). From Table 2, it can be observed that the r value for PLSR models based on NRGB, CIELAB, CMY, HSI, I1I2I3 and YCbCr color spaces to detect pH value is higher than 0.95, and the error is lower than 0.10. Figure 2 shows the correlation between the experimental and the model-predicted values. It indicated that the predictive capacity for detecting pH value was better than SSC.

Table 1 The results of partial least square regression (PLSR) and least square-support vector machine (LS-SVM) models of soluble solids content (SSC) using different color spaces
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Table 2 The results of partial least square regression (PLSR) and least square-support vector machine (LS-SVM) models of pH using different color spaces
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Fig. 2
figure 2

Correlation of experimental values (○) and predicted values (●) for pH and SSC in red bayberry from PLSR models based on a RGB, b CIELAB, c CMY, d HSI, e I1I2I3, f YCbCr

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Prediction of SSC and pH value using LS-SVM models based on color space

LS-SVM as a variant of SVM was applied to building SSC and pH value prediction models in this study. In the training phase, 70% of the data were randomly selected to develop the models. To obtain a good prediction performance, the optimal parameters (γ and σ2) were optimized by grid-search and LOO cross-validation. As seen in Tables 1 and 2, the selected optimal value of γ and σ2 for pH and SSC prediction models are 70.77 and 163.19 for NRGB, 27.21 and 43.21 for CIELAB, 2.6 × 104 and 1.0 × 105 for CMY, 1.9 × 105 and 3.7 × 103 for HSI, 2.1 × 103 and 368.47 for I1I2I3, and 529.27 and 456.06 for YCbCr, respectively.

After training the LS-SVM models, prediction performance was tested using an independent data set. Examining the agreement between the experimental data and the prediction values are presented in Fig. 3, and the r, RMSE, MAE and MRE are given in Tables 1 and 2. According to Table 1, the LS-SVM models based on NRGB, CIELAB, CMY, HSI, I1I2I3 and YCbCr could predict SSC in red bayberry with the RMSE of 1.06, 1.36, 1.22, 1.10, 1.07, and 1.14 Brix, and r values of 0.91, 0.73, 0.82, 0.91, 0.90, and 0.88, respectively. For the prediction of pH, the r value is more than 0.9, and the range of RMSE, MAE and MRE are 0.10–0.12, 0.08–0.09, and 0.06, respectively.

Fig. 3
figure 3

Correlation of experimental values (○) and predicted values (●) for pH and SSC in red bayberry from LS-SVM models based on a RGB, b CIELAB, c CMY, d HSI, e I1I2I3, f YCbCr

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Comparison of the results

Figure 4 shows the dendrogram representing the relationships between the models clustered by hierarchical cluster analysis on the basis of r, RMSE, MAE, MRE. Prediction models divided into the same cluster, meaning that the prediction ability of these models is approximately equal. According to Table 1 and Fig. 4a, the results showed that the optimal models for predicting SSC were PLSR models based on CIELAB (r = 0.90, RMSE = 0.91 Brix, MAE = 0.69 Brix, and MRE = 0.12) and HSI color spaces (r = 0.89, RMSE = 0.95 Brix, MAE = 0.73 Brix, and MRE = 0.13). The results were better than Shao and He (2007) using Vis/NIR spectroscopy techniques for nondestructive measurement of SSC and pH of bayberry juice. The values of correlation coefficient of SSC obtained in this research was slightly better than those obtained by Peirs et al. (2001) with apple of 0.84 and those obtained by Lu (2001) with sweet cherries of 0.89, and was similar with the results obtained by Shao et al. (2007) with tomatoes of 0.90. Although the results in our study were worse than those obtained by Moghimi et al. (2010) with kiwifruit of 0.93, they were still better than many other fruits above. So, the PLSR models based on CIELAB and HSI color space were good methods to predict SSC. For predicting pH (in Table 2 and Fig. 4b), the minimum errors (RMSE = 0.09, MAE = 0.07, and MRE = 0.04) and maximum r value (r = 0.96) were found with PLSR model based on CMY, I1I2I3, and YCbCr color spaces. However, it is worthy to notice that both PLSR and LS-SVM models based on all of color space could get a high r value (r = 0.93–0.96) and low errors (RMSE = 0.09–0.12, MAE = 0.07–0.09, and MRE = 0.04–0.06). In addition, the performance of these models to predict pH in red bayberry fruit was better than those obtained by Gómez et al. (2006) using Satsuma mandarin fruit with r = 0.8 and RMSEP = 0.18; and by Moghimi et al. (2010) in kiwifruit with r = 0.943 and RMSEP = 0.076. Therefore, color space combined with chemometrics could be an appropriate method to predict SSC and pH value in fruit.

Fig. 4
figure 4

Dendrogram representing the relationships between the prediction models clustered by hierarchical cluster analysis on the basis of r, RMSE, MAE, and MRE, a SSC, b pH value

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Conclusion

This paper proposes the application of PLSR and LS-SVM to develop a non-destructive technique to predict soluble solids content and pH value in red bayberry based on six different color spaces (NRGB, CIELAB, CMY, HSI, I1I2I3, and YCbCr). The results showed that PLSR and LS-SVM models combined with color space (r = 0.93–0.96, RMSE = 0.09–0.12, MAE = 0.07–0.09, and MRE = 0.04–0.06) as a potential tool can be used to predict pH value in red bayberry, and the PLSR models based on CIELAB and HSI color space (r = 0.89–0.90, RMSE = 0.91–0.95, MAE = 0.73–0.77, and MRE = 0.13–0.14) is adequate for the prediction of SSC in this study. It indicates the possibility of developing a potentially non-destructive and cost-effective technique using color space and chemometrics for facilitating quality detection of red bayberry. And we consider it available for detecting other fruits as well in further study.