Mathematical models for the estimation of leaf chlorophyll content based on RGB colours of contact imaging with smartphones: A pomegranate example

Twelve different pomegranate cv. Wonderful orchards with different cultivation practices were selected for the present study. The orchards were all located within and around the Güzelyurt city in Northern Cyprus. The reason for the selection of different orchards with different cultivation practices is to have different levels of chlorophyll in the leaves. This would have made it possible to obtain different values to be able to correlate the leaf chlorophyll content with RBG colours. One tree was randomly selected from each orchard (representing the average), and three second-year branches were sampled from each selected tree on 1^st of July in 2019. The branches were immediately brought to the laboratory in 1 h for further analysis.

First of all, two closed boxes were developed to capture the contact images of the leaf samples. The dimensions of the closed boxes were 100 mm width × 170 mm length and 100 mm height. The thickness of the material used to make the closed box was 2 mm. A hole was made onto the long side of the box with the dimensions of equalling to the camera dimensions of Samsung S6 Duos. Two different light sources were used in the present study: (1) red LED light (1 Watt/RED, 34 lm, operation voltage: 220–240 V/50–60 Hz) and (2) white LED light (1 Watt, 1,000 lm, operation voltage: 220–240 V/50–60 Hz).

After bringing the samples to the laboratory, a healthy leaf representing the branch was selected from the top-third axis of each branch sample (Figure 1). Then, the leaf samples were washed with pure water to eliminate any dust. Furthermore, the mid-point of the leaf was determined by using a ruler. Thus, the mid-point of the leaf was inserted onto the hole of the developed closed box. Hereafter, capturing the contact image with a smartphone was performed. Image capturing was performed both for red LED light source and white LED light sources separately for each 36 leaf samples. Samsung S6 Duos was used to capture images from the samples with a picture size of 187.4 cm width and 105.41 height (Pixels: 5,312 × 2,988). The picture mode was 8-bit RGB and the resolution was 72 pixels per inch. Pictures were saved as jpeg (joint photographic experts group) format and transferred to a computer by using a portable flash disc (Figure 2). Finally, the images were opened at the Adobe Photoshop 7.0 ME computer program, and the average RGB values of the images were read and noted by using the histogram function.

Figure 1

Figure 2

Chlorophyll (Chl) is vital for plants growth while it absorbs sunlight and enables its usage in photosynthesis. There is more than one type of chlorophyll with unique chemical structures each. The main types are Chl a and Chl b. Chl a is the primary pigment of photosynthesis and Chl b is an accessory pigment. Chl a is the primary electron donor in the electron transfer chain and it absorbs light from the orange-red and violet-blue areas of the electromagnetic spectrum. Chl b absorbs blue light and expands the absorption spectrum of plants. The increase of Chl b is a sign of adaption to shade (Roca et al., 2016).

The chlorophyll contents of the leaf samples were then determined with the method developed by Arnon (1949) as suggested by Sudhakar et al. (2016). For this reason, the same parts of the leaves (which were used to capture images) were used. The image captured parts of the leaves were cut carefully and used to determine the chlorophyll contents of the samples. The fresh weight of the plant samples was determined with a sensitive balance (±0.0001 g) and a grind with 10 mL of 80% acetone in a mortar using a pestle. The sample was then filtered through what man filter paper no. 1. The optical density of the extract is measured at 663 and 645 nm wavelengths using a spectrophotometer. Thus, the absorption coefficients were used to calculate Chl a, Chl b and total Chl contents of the samples by using the following equations (Arnon, 1949; Sudhakar et al., 2016). Chl a(mg⋅g−1)=[12.7(A663)−2.69(A645)]×V1,000×W{\rm{Chl}}\,a\left( {{\rm{mg}} \cdot {{\rm{g}}^{ - 1}}} \right) = {{\left[ {12.7\left( {{\rm{A}}663} \right) - 2.69\left( {{\rm{A}}645} \right)} \right] \times {\rm{V}}} \over {1,000 \times {\rm{W}}}}Chl b(mg⋅g−1)=[22.9(A645)−4.68(A663)]×V1,000×W{\rm{Chl}}\,b\left( {{\rm{mg}} \cdot {{\rm{g}}^{ - 1}}} \right) = {{\left[ {22.9\left( {{\rm{A645}}} \right) - 4.68\left( {{\rm{A663}}} \right)} \right] \times {\rm{V}}} \over {1,000 \times {\rm{W}}}}

In the above-given formula; A = is the absorbance at specific wavelengths, V = final volume of chlorophyll extract and W = fresh weight of tissue extracted. Correlation analysis showed that there is no significant correlation among the RGB values and the leaf Chl content (mg ∙ g⁻¹), but further analysis showed that the RGB values (which are captured from a specific area) are highly related with the Chl content of the sampled areas. Thus, the Chl content of sampled areas (in mg ∙ MW⁻¹, MW: Measured Weight) was calculated by multiplying the Chl contents (mg ∙ g⁻¹) with the W (fresh weight (g) of tissue extracted, which is also equal to the fresh weight of the area used for the image capturing).

After transferring the images to a computer as described earlier in the present study, the images were opened in Adobe Photoshop 7.0 ME software. Using the software histogram function, the whole image was selected and the average values of red (R), green (G) and blue (B) were obtained from each image. In addition to RGB of colour spaces, other combination indices (features) suggested by previous studies (Rorie et al., 2011; Lee and Lee, 2013; Wang et al., 2013) were calculated by using the following equations: NRI (Normalized red)=RR+G+B{\rm{NRI}}\,\,\left( {{\rm{Normalized}}\,\,{\rm{red}}} \right){\rm{ = }}{{\rm{R}} \over {{\rm{R}} + {\rm{G}} +{\rm{ B}}}}NGI (Normalized green)=GR+G+B{\rm{NGI}}\,\,\left( {{\rm{Normalized}}\,\,{\rm{green}}} \right){\rm{ = }}{{\rm{G}} \over {{\rm{R}} + {\rm{G}} +{\rm{ B}}}}NBI (Normalized blue)=BR+G+B{\rm{NBI}}\,\,\left( {{\rm{Normalized}}\,\,{\rm{blue}}} \right){\rm{ = }}{{\rm{B}} \over {{\rm{R}} + {\rm{G}} +{\rm{ B}}}}GMR(Difference between green and red )=G−R{\rm{GMR}}\left( {{\rm{Difference}}\,{\rm{between}}\,{\rm{green}}\,{\rm{and}}\,{\rm{red}}\,} \right) = {\rm{G}} - {\rm{R}}GRRI(Green−Red−Ratio Index)=G/R{\rm{GRRI}}\,\left( {{\rm{Green}} - {\rm{Red\,Ratio\,Index}}} \right) = {\rm{G}}/{\rm{R}}GRVI(Green−Red Vegetation Index )=G−RG+R{\rm{GRVI}}\left( {{\rm{Green}} - {{\rm {Red\,Vegetation\,Index}}}} \right) = {{{\rm{G}} - {\rm{R}}} \over {{\rm{G}} + {\rm{R}}}}DGCI(Dark GreenColour Index)=[(Hue−6060)+(1−S)+(1−Br)]/3{\rm{DGCI}}\left( \matrix{ {\rm{Dark}}\,{\rm{Green}} \hfill \cr {\rm{Colour}}\,{\rm{Index}} \hfill \cr} \right) = \left[ \matrix{ \left( {{{{\rm{Hue}} - 60} \over {60}}} \right) + \hfill \cr \left( {1 - {\rm{S}}} \right) + \left( {1 - {\rm{Br}}} \right) \hfill \cr} \right]/3

For the calculation of the DGCI (dark green colour index) following equations were used to obtain Hue, Saturation (S) and Br (Brightness) values as suggested by Karcher and Richardson (2003). C=max(R,G,B)−min(R,G,B){\rm{C}} = {\rm{max}}\left( {{\rm{R}},{\rm{G}},{\rm{B}}} \right) - \min \left( {{\rm{R}},{\rm{G}},{\rm{B}}} \right)Hue={60×(G−BC),max(R,G,B)=R60×(2+B−RC),max(R,G,B)=G60×(4+G−BC),max(R,G,B)=B{\rm{Hue = }}\left\{ {\matrix{ {60 \times \left( {{{{\rm{G}} - {\rm{B}}} \over {\rm{C}}}} \right),\max \left( {{\rm{R}},{\rm{G}},{\rm{B}}} \right) = {\rm{R}}} \cr {60 \times \left( {2 + {{{\rm{B}} - {\rm{R}}} \over {\rm{C}}}} \right),\max \left( {{\rm{R}},{\rm{G}},{\rm{B}}} \right) = {\rm{G}}} \cr {60 \times \left( {4 + {{{\rm{G}} - {\rm{B}}} \over {\rm{C}}}} \right),\max \left( {{\rm{R}},{\rm{G}},{\rm{B}}} \right) = {\rm{B}}} \cr } } \right.S={0,V=0Cmax(R,G,B),V≠0{\rm{S}} = \left\{ {\matrix{ {0,} & {{\rm{V}} = 0} \cr {{{\rm{C}} \over {{\rm{max}}({\rm{R}},{\rm{G}},{\rm{B}})}},} & {{\rm{V}} \ne 0} \cr } } \right.Br(Brightness)=max(R,G,B)/255{\rm{Br}}\left( {{\rm{Brightness}}} \right) = \max \left( {{\rm{R}},{\rm{G}},{\rm{B}}} \right)/255

Moreover, the following model was developed during the present study based on the uniqueness of the experimental methodology. The use of red LED light behind the leaves during contact imaging is a new method, and it was necessary to develop new models for a better correlation among the leaf chlorophyll content and extracted features.

After the calculation of the above-mentioned indices, dataset was subjected to Pearson’s correlation analysis. The significant data for both red LED and white LED were then subjected to linear regression and the Student’s t-test at 95% confidence by using IBM SPSS 22.0. The correlation and linear regression results for red LED light and white LED light were then discussed to determine any possibility to estimate leaf chlorophyll content (mg ∙ MW⁻¹). The dataset obtained from the red LED method provided a strong correlation with the leaf chlorophyll contents (mg ∙ MW⁻¹). Hereafter, multiple regression analysis was performed to find out the most accurate model for the estimation of the leaf chlorophyll content (mg ∙ MW⁻¹) of pomegranate leaves by using the RGB colours of contact imaging.

The analytical extraction of the pomegranate leaves resulted in an acceptable range of chlorophyll content ranging from 2.07 to 6.66 mg ∙ g⁻¹ for a good correlation and estimation of contents with some indices. The results of the present study showed that neither the RGB values from red LED light nor white LED light have a significant relationship between the leaf Chl content in mg ∙ g⁻¹ (Table 1). Furthermore, it was intended that the RGB values of the contact images might be related to the Chl content of the given areas. Thus, the fresh weight (W), in g, of tissue extracted (contact imaging area), was multiplied with the leaf Chl contents (mg ∙ g⁻¹) to calculate the Chl content of given areas (mg ∙ MW⁻¹, MW: Measured Weight). The leaf Chl in mg ∙ MW⁻¹ was also found to ranging from 0.033 to 0.148, which is useful for a good correlation and estimation of the contents with the RGB indices. The results provided a higher correlation for the RGB values and leaf Chl content in mg ∙ MW⁻¹, and the correlation is high when red LED light passed through the leaf samples.

A negative correlation was observed between R (Red) value and leaf chlorophyll (mg ∙ MW⁻¹) content while a positive correlation was calculated for G (Green) value and leaf Chl content, at both conditions (red LED passed and white LED passed). The negative correlation for R-value was moderate when red LED passed through the leaf, but very weak under white LED light source. Among the three colour values, G value was found to have the strongest correlation with leaf Chl content. The correlations for all colour values and combination indices were higher at the red LED conditions than the white LED conditions. This result suggests that the use of red LED provides a better correlation with leaf Chl content and is much useful for the estimation of leaf Chl content. The extracted indices were also found to have a higher correlation with Chl content in mg ∙ MW⁻¹.

According to the results obtained, the B (Blue) value also found to have a very strong positive correlation with the leaf Chl content (when red LED passed). The correlation between the B value and leaf Chl content (mg ∙ MW⁻¹) was weak and negative when white LED passed through the leaf during contact imaging. The correlation among the normalised colour values (NRI, NGI and NBI) and leaf Chl (mg ∙ MW⁻¹) were calculated as very strong under red LED conditions. The results suggested that raw G and B values and normalised RGB values can be used for the estimation of the leaf Chl content (mg ∙ MW⁻¹) of the pomegranate tree. GMR (Difference between Green and Red) is an extracted feature used for the estimation of the leaf Chl. Due to the nature of the present study (use of red LED), an additional feature was extracted to better estimate the leaf Chl content which is GMB (Difference between Green and Blue). The results showed that GMB has a better correlation (very strong) with leaf Chl content than GMR. The Green-Red Ratio Index (GRRI) and Green-Red Vegetation Index (GRVI) were also found to have a very strong positive correlation with the leaf Chl (mg ∙ MW⁻¹) under the red LED conditions. Lastly, the DGCI (Dark Green Colour Index) was found to have a moderate positive correlation with the leaf Chl (mg ∙ MW⁻¹) under red LED conditions and neutral (no) correlation under white LED conditions.

After the correlation analysis, to determine the best model for the estimation of the leaf Chl content (mg ∙ MW⁻¹) with different colour indices, a stepwise linear regression analysis was performed to formulate models. This classical method resulted in a close relationship for the G and B values with the leaf Chl (mg ∙ MW⁻¹) under red LED conditions (Figure 3). In line with the obtained results from stepwise linear regression, the best indices for the estimation of the leaf Chl (mg ∙ MW⁻¹) were found to be G value with an R² of 0.8355. The calculated linear formula for the leaf Chl content (mg ∙ MW⁻¹) (y) estimation was y = 0.1522 * G − 0.0911.

Figure 3

The G value was found to have a very weak estimation for the leaf Chl content (mg ∙ MW⁻¹) under white LED conditions with an R² of 0.212. According to the obtained results, the B value was also found to provide strong estimation of the leaf Chl content (mg ∙ MW⁻¹) under red LED conditions with a R² of 0.797. The calculated formula for that is y = 0.1915 * G − 0.0565. The B values under white LED light conditions found to have some very high values which damage the regression analysis. The elimination of these extreme values was also resulted with a very weak correlation, and the values were not eliminated in the presented form. The normalised values of RGB provided a better estimation of the leaf Chl (mg ∙ MW⁻¹) with R-value. The Normalised G and B (NGI and NBI) values had similar results with the G and B results. The R-value (under red LED) had a weak relationship with leaf Chl content (mg ∙ MW⁻¹) (R² = 0.3047) but the NRI had a stronger relationship (R² = 0.8366). Estimation of the leaf Chl content (mg ∙ MW⁻¹) was possible with the NRI by using the equation of y = −0.0455 * NRI + 0.9956. According to the results obtained, the best-fit regression model for the single colour values and also for the normalised indices was from green (G).

The GMR (Difference between Green and Red) under red LED was found to have a very weak relationship with the leaf Chl content (mg ∙ MW⁻¹) with an R² of 0.3264. On the other hand, the GMB (Difference between Green and Blue) had a better relationship with leaf Chl content (mg ∙ MW⁻¹) and the equation of y = 1.3272 * GMB + 0.3058 was found to have an R² of 0.5712. The results showed that GMB under red LED has higher correlation (very strong) with leaf Chl content (mg ∙ MW⁻¹) than GMR. There was a good linear relationship (0.8421) between the GRRI under red LED and the leaf Chl content. The equation for the estimation of the leaf Chl content (mg ∙ MW⁻¹) was y = 0.0265 * GRRI − 0.0028. The GRVI under red LED was also calculated to have a very strong positive relationship with leaf Chl content (mg ∙ MW⁻¹) with a formula of y = 0.0524 * GRVI + 0.9944. Finally, the relationship between the DGCI (Dark Green Colour Index) under red LED and leaf Chl content (mg ∙ MW⁻¹) was found to be very low (R² of 0.3285) and not useful for the estimation of the leaf Chl content of pomegranate trees under neither red LED nor white LED.

Results showed that, from the three colour values, the G and B values have a higher direct influence on the leaf Chl content and were selected for further model estimation. Stepwise regression, correlation analysis as suggested by previous literature (Mollazade et al., 2012; Lee and Lee, 2013; Teimouri et al., 2014) was used together for the feature selection to estimate leaf Chl content (mg ∙ MW⁻¹). Thus, multiple regression analysis was performed to estimate the Chl content (mg ∙ MW⁻¹) of pomegranate leaves by using the G and B values together. Results provided a similar R² (0.8355) with a simple regression analysis. The standard error for the model was found to be 0.0126 and the multiple R was calculated as 0.9141. The summary results of the multiple regression analysis were given in Table 2.

According to the obtained results, it was concluded that the estimation of Chl content by using both G and B values has the same efficiency with using only G factor. However, due to the reduced standard error, it is suggested to use both factors together. The calculated formula for the estimation of Chl content (mg ∙ MW⁻¹) is: Chl = (0.1537 * G) + (−0.0019 * B) − 0.0914. Dividing the obtained result to the fresh weight of the sampled area gives the leaf Chl content of the sample is mg ∙ g⁻¹.