During 2014, 2016, and 2017, images were acquired from Virginia and Georgia runner types planted at the Edisto Research and Education Center of Clemson University. Pod sample size were roughly 100 pods. The pods were blasted with a pressure washer of 1500 psi and then counted manually to determine the observed percentage of OBB_obs and BL_obs. The 323 images of peanut were randomly selected for photography with a conventional RGB camera (MOTOROLA XT1030) at a distance of approximately 30 cm from cardboard. The images were captured as a resolution 6000 × 4000. The peanut maturity profile board ( Figure 1 ) and twenty-eight representative peanut pod images proposed by William and Drexler [10] ( Figure 2 ) were selected to classify 6 maturity color groups and train software for estimating different colors of mesocarp (%), color saturation, brightness, and two maturity target OBB and BL (%) ( Figure 1 and Figure 2 ). The 323 images were used to develop the peanut maturity model of the OBB_est and BL_est (%). The images taken in 2017 were used to test peanut maturity model and compared the results of estimated OBB_est, BL_est and actual pod counts of OBB and BL.

Mahalanobis distance is an adequate classification method for analyzing pods color. The Mahalanobis distance (Equation (1)) measures the similarity between an unknown sample group and a known one. It accounts for the fact that the variances in each direction are different as well as for the covariance between variables [23] . The Mahalanobis distance between two random vectors (X, Y) with the same distribution, and covariance matrix S, can be defined as:

$\text{Mahalanobis}\text{distance}=\sqrt{{\left(X-Y\right)}^{\text{T}}{S}^{-1}\left(X-Y\right)}$(1)

The Mahalanobis color distance standardizes the influence of the distribution of each feature considering the correlation between each pair of terms. In the case of RGB color images, S is computed as (Equation (2)):

$S=\left[\begin{array}{ccc}{\sigma }_{R_{ref}{R}_{ref}}& {\sigma }_{R_{ref}{G}_{ref}}& {\sigma }_{R_{ref}{B}_{ref}}\\ {\sigma }_{G_{ref}{R}_{ref}}& {\sigma }_{G_{ref}{G}_{ref}}& {\sigma }_{G_{ref}{B}_{ref}}\\ {\sigma }_{B_{ref}{R}_{ref}}& {\sigma }_{B_{ref}{G}_{ref}}& {\sigma }_{B_{ref}{B}_{ref}}\end{array}\right]$(2)

and the element of S is calculated as:

${\sigma }_{G_{ref}{R}_{ref}}={\sigma }_{R_{ref}{G}_{ref}}=\frac{{{\displaystyle \sum }}_{i=1}^n\left(R_i-\bar{R}\right)\left(G_i-\bar{G}\right)}{n-1}$(3)

where R_i, G_i, B_i are the values of the i^th match ( $i=1,2,3,\cdots ,n$), and $\bar{R}$, $\bar{G}$, $\bar{B}$ are the mean color values for R, G, B in the given images, respectively.

X was a three-dimensional vector (R, G, B), which represented pixels from the image to be processed. Y was also a three dimensional vector ( $\bar{R}$, $\bar{G}$, $\bar{B}$), which represented the reference pixels (reference group) for each class to be identified.

In the proposed methodology of this work, 9 reference groups of pixels were selected to generate the classification, in which every group represented relevant characteristics of peanut pods and background classes. The 9 groups identified were: peanut pods (white, pale yellow, deep yellow, orange, brown, and black pods groups) and background (red, blue, and green cardboard). If any group was not present, or a new color group appeared on the image, the number and/or the group labels could be modified in the program.

Each reference group of peanut pods was manually selected from peanut maturity profile board ( Figure 1 ) and a set of 28 representative images ( Figure 2 ) proposed by William and Drexler and a set of 20 colors in each reference group was chosen [10] . Mahalanobis distance was computed over a set of 323 images in our developed software to obtain the percentage of each color group, OBB_est and BL_est. To implement the classification and provide graphical interface to the user, the software was developed based on Visual Basic 2017. These images were used to train the model for the OBB_est and BL_est. Details of the identified peanut pods were shown original color in the output figures and background in the output figures were transformed to pink color ( Figure 3 ). All selected group colors, including pod and background classes, were also analyzed for the images without using classification method.

Two parameters are used to determine maturity target: one is the percentage of pods in the orange, brown, and black categories combined (OBB); the other is the percentage of pods in black (BL). The representative images mentioned above were selected to classify 6 maturity color groups (white, pale yellow, deep yellow, orange, brown, black) and train software for estimating different colors of mesocarp (%) and two maturity targets (OBB and BL) (%). The selected pod colors were defined as: C1 (white), C2 (pale yellow), C3 (deep yellow), C4 (orange), C5 (brown) and C6 (black); each image was analyzed by the software program and pixels were classified accordingly. After analysis, individual pixel number for each color class (C1 through C6) were mathematically calculated. Equations (4) and (5) were used to compute OBB and BL pods percentage for 323 images. The actual number of OBB_obs and BL_obs pods were also counted for 323 images. These actual pod counts were performed by experienced county educators and peanut specialists.

$OB{B}_{est}\left(\%\right)=\frac{\sum C4,C5,C6pixelnumber}{\sum TotalC1,C2,C3,C4,C5,C6pixelnumber}\times 100$(4)

$B{L}_{est}\left(\%\right)=\frac{\sum C6pixelnumber}{\sum C1,C2,C3,C4,C5,C6pixelnumber}\times 100$(5)

A linear relationship was found between the OBB_est percentage obtained from image analysis and the OBB percentage from OBB_obs. Empirical models for OBB_est percentage were developed to evaluate statistical trends in the data. The trends were studied by conducting percentage of 6 color group, and OBB_obs using SAS (SAS, 2017, Institute SAS Inc., Cary, NC). The correlations between the OBB_est and OBB_obs were analyzed, and the R², error, and root mean square error (RMSE) were calculated (Equation (6) and Equation (7)).

$\text{Error}\left(\%\right)=r_{est}-r_{obs}$(6)

$\text{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(r_{est}-r_{obs}\right)}_i^2}{n}}$(7)

where n is number of photos; and r_est and r_obs are modeled and observed OBB percentage, respectively. The hypothesis is that the total pixel number of OBB can be applied to estimate the actual OBB percentage.

Based on the data and images collected in 2014, 2016, and 2017, a comprehensive and predictive OBB and BL model was developed for estimating peanut maturity. To validate this model, additional data were collected in 2017 from studies conducted at the Edisto Research Station of Clemson University on August 28th, and in Orange County, SC on September 14th and October 20th. The 27 pod samples were randomly selected for photography using a conventional RGB camera or digital cell phone at a distance of approximately 30 cm on a green cardboard background. The number of pods in each color class was then counted. The data and images obtained in 2017 were used to test the peanut maturity model and compare the results with the actual pods categorized as OBB_obs and BL_obs. These actual pod counts were performed by experienced county educators and peanut specialists.

Six peanut cultivars, Bell, Emery, Sullivan, GA-06G, GA-16H0, and AU-17, were planted at Edisto Research Station of Clemson University. To determine the optimal pod blasting time for image analysis, 100 pod samples were randomly selected with three replicates and poured into a picker basket, and the basket is placed in a five-gallon bucket. The pods were blasted with a lightweight pressure washer at 1500 psi each minute, then laid on the cardboard and photographed. Each image was taken with a conventional RGB camera (MOTOROLA XT1030) at a distance of approximately 30 cm on a green cardboard. Pods numbers were also counted according to color classes.

The reference pixels of 6 pods color group selected from Williams and Drexler [10] for calculating Y and S (Equations (1)-(3)) were shown in Figure 1 and Figure 2 to generate classification ( Figure 4 ). Mahalanobis distance method identified more surface area of pods from an image (6000 × 4000 pixels) when evaluating algorithms for pattern recognition ( Figure 4 ). For unknown color pixels (not selected in the reference groups), Mahalanobis distance computed for each reference group and determined whether unknown pixels were classified as pods color or background. The classifiers for 9 reference groups performed well without any adjustments to contrast, brightness, or color ( Figure 5(c) ). Manual validation showed 73% and 94% of correct classification for pods or background with the unclassified image and Mahalanobis distance processing, respectively ( Figure 5(b) , Figure 5(c) ). Most of the misclassifications were due to the shadow of black pods, which exhibited similar color as black pods group. Figure 5(a) was taken from author’s experiment.

The OBB_obs ( Figure 3(a) ) and a processed photo ( Figure 3(b) ) using Mahalanobis distance showed that OBB_est was positively influenced by the sum of orange (r = 0.30, p < 0.001), brown (r = 0.61, p < 0.001), and black (r = 0.69, p < 0.001) percentage based on image analysis ( Figure 6 ). Actual counts showed negatively relationships with brightness (r = −0.23, p < 0001) and saturation (r = −0.21, p < 0.001). The most dominant direct effects on OBB_est were brightness, saturation, and 6 color pixel (%) from image analysis. Multiple linear regression analysis (SAS procedure PROC REG) was used to generate linear equation (Equation (8)). However, saturation and brightness exhibited multicollinearity based on a VIF (variance inflation factor) test. Therefore, only brightness was selected as an independent parameter, which had a greater effect on OBB. Adding saturation on top of brightness didn’t improve the model based on Cp, AIC, BIC, and adjusted R². The residual plot showed no linearity violation and constant variances, and QQ plot depicted the data is normally distributed. Statistical interactions were also introduced (Equation (8)) to perform better estimation.

$\begin{array}{l}OB{B}_{est}=50.88-0.01Brightness-0.83PaleY-1.86DeepY\\ +0.04Orange+1.18Brown+0.80Black+0.03PaleY\times DeepY\\ +0.03DeepY\times Orange+0.01Brown\times Black{R}^2=0.93\end{array}$(8)

where 15.2 < OBB_est < 86.2%; 311 < Brightness < 730; 0 < PaleY < 38.2%; 3.8 < DeepY < 44.6%; 6.6 < Orange < 47.6%; 8.7 < Brown < 36.9%; and 0 < Black < 48.6%.

The validation curves for the estimated and observed OBB using linear equations indicated that the correlation between the observed and predicted defoliation were both close to the 1:1 line and the values of R² of linear regression was 0.93 ( Figure 7 ). Plot of correlation curve of OBB_est and OBB_obs ( Figure 7 ) showed the RMSE produced by linear equation at 4.1%.

The BL_est ( Figure 3(a) ) and a processed photo ( Figure 3(b) ) using Mahalanobis distance showed that BL_est was influenced by the sum of orange (r = −0.42, p < 0.001), and black (r = 0.86, p < 0.001) percentage based on image analysis. The most dominant direct effects on BL_est were orange and black pixel (%) from image analysis. Multiple linear regression analysis (SAS procedure PROC REG) was also used to generate linear equation (Equation (9)). The residual plot also showed no linearity violation and constant variances, and QQ plot depicted the data is normally distributed. Statistical interactions were also introduced (Equation (9) to perform better estimation.

$B{L}_{est}=-3.00+0.09Orange+0.74Black-0.02Orange\times Black{R}^2=0.88$(9)

where 6.6 < Orange < 47.6%, and 0 < Black < 48.6%.

The validation curves for the BL_est and BL_obs using linear equations indicated that the correlation between the observed and predicted values were both close to the 1:1 line and the values of R² of linear regression was 0.88 ( Figure 8 ). Plot of correlation curve of BL_est and BL_obs ( Figure 8 ) showed the RMSE produced by linear equation at 1.8%.

To validate the maturity model, the images taken on August 28^th, September 4^th, and October 15^th, 2017 were selected for photography with a conventional RGB camera (MOTOROLA XT1030) at a distance of approximately 30 cm. The ability of the developed maturity model to predict OBB and BL as computed image in 2017 was evaluated and compared ( Table 1 ). The validation of OBB using other images from field provided reasonable estimation (R² = 0.98 and RMSE = 2.73%). The average error between OBB_est and OBB_obs was 2.37% ( Table 1 ). The average error between BL_est and BL_obs was 0.76% ( Table 1 ). The peanut maturity model provided reasonable estimation compared to OBB_obs and BL_obs obtained in 2017 images for validation. This maturity model currently only can be used in images with resolution (1000 × 750 pixels) or above, which can provide reasonable estimation. When the resolution is under 1000 × 750 pixels, the OBB_est is underestimated due to the insensitivity of color detection. To make the model more suitable for use in the field, future work can focus on making the proposed software more robust against different weather conditions of pod color classification.

Note: ¹Error = OBB_est − OBB_obs; ²Error = BL_est − BL_obs.

To determine the optimal pod blasting time for image analysis, six peanut cultivars—Bell, Emery, Sullivan, GA-06G, GA-16H0, and AU-17 were selected. Approximately 100 pods from each cultivar were randomly chosen and photographed at one-minute intervals during pod blasting. Figure 9 illustrates the peanut pod images of the AU-17 variety at different blasting times. The OBB_est values increased with pod blasting time, eventually plateauing for several minutes before decreasing due to mesocarp damage from the pressure washer, as shown in Figure 10 and Figure 11 . The red frame in Figure 9(i) highlights the white kernels. The optimal pod blasting times for each cultivar are summarized in Table 2 . On average, Runner type peanuts required 1 - 2 minutes longer than Virginia type peanuts to achieve thorough pod blasting. When the optimal pod blasting time was reached, the average error between the estimated OBB_est and the observed OBB_obs was only 1.18%.

Although various studies have estimated peanut pod maturity [8] [10] [12] [17] [18] [24] , they employed a range of methods, most of which were manual and relied on scanners or hyperspectral sensors. These methods can be time-consuming and costly for growers to implement. Therefore, this study has developed an accurate, fast, and non-destructive method for estimating peanut maturity, which can significantly enhance the efficiency of scouting for color classification, making it more practical for widespread use.