Optimizing maize germination forecasts with random forest and data fusion techniques

Materials

The Zhengdan-958 maize seed variety utilized experimentally was purchased from Zhengzhou, Henan Province, in 2023. The germination rate of the Zhengdan-958 variety was about 91%. The 600 undamaged seeds were randomly chosen as samples to experiment.

Image acquisition

The maize seed images were obtained using two different methods: top lighting to get the appearance image and bottom lighting to attain the internal crack image.

Appearance image acquisition

The sample images of maize seeds were captured using a PSSX60HS digital camera. The acquisition of maize appearance images was completed in a lighting room to avoid the influence of external light. The diffuse reflective circular LED light was utilized as the light source for indoor illumination. A black, non-reflective paper was chosen as a background to discriminate maize seeds from the background. The light source was placed above the maize, and the seeds with the embryo facing upwards were placed sequentially on black paper.

The 600 seeds are randomly distributed in 12 groups, with 50 maize seeds in each image. After smoothing, the image was uniformly cropped to 1,130 × 700 pixels, as shown in Fig. 1, which was the appearance image of the first group of maize seeds.

Internal crack image acquisition

The internal crack image collection of maize was also completed in a lighting room. The seeds with the embryo facing downwards were placed sequentially on a white paper. Internal cracks inside seeds were difficult to identify and needed to be exposed to light source illumination (Li et al., 2024). Therefore, the light sources were placed under a white paper. Cracked seeds promoted germination (46%) with a mean germination time of 146 days (Iralu & Upadhaya, 2018). Like the process of capturing appearance images, internal crack images were also composed of a 50-seed image. Figure 2 shows the internal crack image of the first maize group.

Dielectric constant—voltage score acquisition

The dielectric constant of a maize seed can be employed to characterize a seed’s internal quality, and differences in seed moisture content, thickness, protein, fatty acid content, etc. can all affect the dielectric constant. Two electrically connected metal plates are employed to form a parallel plate capacitance sensor, and the output capacitance score will change with alterations in the plate area, plate spacing, or the medium between the plates. When the area and spacing of the plates remain unchanged, but the dielectric constant between the plates changes, the dielectric constant will change accordingly, thereby altering the capacitance score. By converting the amplification circuit, capacitance alterations are converted into voltage changes.

Each maize seed was placed between two flat electrodes to obtain the corresponding voltage score. Figure 3 shows the normalized voltage scores of the first group of maize seeds between the flat electrodes.

Germination experiment

Before running a standard germination test on Zhengdan 958 variety seeds, the seeds were soaked in a germination dish disinfected with alcohol for 12 h. Then, the seeds were covered with sprouting paper and cling film, and the seeds were watered regularly every day to replenish moisture, allowing them to grow in a moist environment. The incubator temperature was 25 °C, and the germination dishes were placed in it. The process of seed germination is shown in Fig. 4.

The germinated seeds on the 7th day were recorded utilizing the samples’ germination and rooting criteria. A consistent germination rate of 91% was found, with the same rate in large samples. Therefore, a certain representation for the 600 samples was shown.

The segmentation of a maize image

To facilitate the feature extraction of single corn seeds, the background of each maize needs to be blackened. So, maize images can be better seen when the background turns black. In other words, the target area of the maize seed had a large grey difference from the background. Then, the histogram method was implemented to pick the optimal threshold, and the segmentation outcome is presented in Fig. 5.

In the maize internal crack images, the background was white, and there was a slight difference in color between the maize and the background. So, the segmentation method based on grayscale histograms was not very suitable (Xu, Li & Chen, 2022). The commonly used image segmentation algorithms include Sobel’s edge detection, Prewitt’s edge detection, Roberts’s edge detection, and Canny’s edge detection algorithms. A background segmentation needs to separate individual maize grains and reflect the crack information inside the maize. Figure 6 shows the maize images obtained by implementing distinct edge detection methods, and the segmentation impact is not ideal.

A maize crack image was first processed by mathematical morphology and Sobel operator and then refused through multi-scale decomposition of the wavelet transform. The new image is shown in Fig. 7. The edges of the image are clear, complete, and continuous. The image not only retains internal crack information but also removes unnecessary noise (Qiu et al., 2022).

The feature extraction of the appearance image

Color feature

Color attributes are the most intuitive and obvious physical variables of an image. Compared to geometric features, color features have a certain degree of stability and are insensitive to size and direction. The images captured by the camera are RGB representations, and the HSI model is consistent with the human eye’s observation mode. Therefore, the RGB and HSI representations were employed in the manuscript to extract color features.

In RGB, representations are superimposed to obtain colors that can be perceived visually. Due to the fusion of red and green resulting in yellow, R and G components were selected for maize color feature extraction.

In the HIS representation, the I component is independent of color information. The light source and intensity that affect the S component remain unchanged in actual shooting, so the S’s component score is determined. Thus, only the H component must be considered in maize color recognition.

R, G, and H components were derived from the preprocessed sample images and normalized for subsequent model training. Figure 8 shows the color characteristic scores of the first group of 50 maize seeds.

Shape feature

(a) Length-width ratio

Each maize seed was divided and a bounding rectangle’s length and width were employed to represent the length and width of a seed, as shown in Fig. 9.

(b) Area and perimeter

The area of a maize is the pixels’ total number in the seed area, and the area score can be obtained by summing up the pixels’ actual numbers in the area of the maize seed. The perimeter is the total number of pixels at the boundary of the maize seed area.

(c) Rectangularity and circularity

Rectangularity represents the degree to which a corn seed is close to a rectangle. Equation (1) is used to calculate rectangularity.

(1) $$Re={\displaystyle \frac{A}{LW}}$$where Re, A, L, and W represent the rectangle, seed area, seed length, and seed width, respectively.

Circularity represents the degree to which the shape of a corn seed is close to a circle. Equation (2) is utilized to compute the circularity score.

(2) $$C={\displaystyle \frac{4\pi A}{P^2}}$$where C, A, and P represent the circularity, the area of the seed, and the circumference of the seed, respectively.

(d) Embryo area ratio

There are apparent indentations on the embryonic surface of corn seeds, which is the boundary between the embryonic area (white part) and the nonembryonic area (yellow part), as shown in Fig. 10. The ratio of embryo bud area can be utilized to distinguish maize seeds. Equation (3) is employed to calculate the embryo area ratio.

(3) $$E={\displaystyle \frac{Em}{A}}$$where E, A, and Em represent the embryo area, the area of the seed, and the area of the embryo bud, respectively.

Figure 11 illustrates the six shape features extracted from 50 seeds of the first maize samples.

Texture feature

The texture is locally irregular and is composed of macroscopic characteristics in an image, which is a natural attribute of the surface of an object and one of the commonly utilized image features. The methods extracting texture features mainly include structural, statistical, and spectral approaches. The grey level co-occurrence matrix (GLCM), a broadly implemented statistical method, is employed to analyze image texture features proposed by Haralick.

The GLCM was implemented to extract texture features. The energy, contrast, correlation, and homogeneity of the image were computed from four directions, namely, 0°, 45°, 90°, and 135° to represent the texture features. The expressions are shown in Eqs. (4) to (7).

(a) Energy

(4) $$ENR=\sum _{i=0}^{L-1}\sum _{j=0}^{L-1}P{(i,j|d,\theta )}^2$$

(b) Contrast

(5) $$CON=\sum _{i=0}^{L-1}\sum _{j=0}^{L-1}{(i-j)}^{2}P(i,j|d,\theta )$$

(c) Correlation

(6) $$COR=\sum _{i=0}^{L-1}\sum _{j=0}^{L-1}{\displaystyle \frac{ijP(i,j|d,\theta )-{\mu }_1{\mu }_2}{{\sigma }_1{\sigma }_2}}$$where ${\mu }_1,{\mu }_2,{\sigma }_1,{\sigma }_2$ are expressed by

${\mu }_1=\sum _{i=0}^{L-1}i\sum _{j=0}^{L-1}P(i,j|d,\theta )$, ${\mu }_2=\sum _{i=0}^{L-1}j\sum _{j=0}^{L-1}P(i,j|d,\theta )$

${\sigma }_1=\sum _{i=0}^{L-1}{(i-{\mu }_1)}^2\sum _{j=0}^{L-1}P(i,j|d,\theta )$, ${\sigma }_2=\sum _{i=0}^{L-1}{(j-{\mu }_2)}^2\sum _{j=0}^{L-1}P(i,j|d,\theta )$

(d) Homogeneity

(7) $$HOM=\sum _{i=0}^{L-1}\sum _{j=0}^{L-1}{\displaystyle \frac{P(i,j|d,\theta )}{1+{(i-j)}^2}}.$$

From Eqs. (4) to (7), $P(i,j|d,\theta )$ represent the probabilities of two pixels i and j in the image with a distance of d, and θ represents the four directions of 0°, 45°, 90°, and 135°, respectively.

As mentioned above, the same feature extraction process was performed on all maize seed samples. Figure 12 shows the texture features of 50 maize seeds used as training samples in the first group.

Internal crack feature

Single-grain maize needed to be segmented, and the number of internal cracks also needed to be counted for image processing of internal cracks. According to the number of cracks in a maize seed, the one containing one crack, two cracks, and three or more cracks were called a single crack, a double, and a turtle crack, respectively.

Each crack had only one starting and ending point for single and double-cracked maize. The starting and ending points of the cracks are found to compute the crack numbers. There were at least turtle cracks or many single cracks for turtle-cracked maize. For statistical convenience, the branch of the turtle crack was also treated as a crack. To search for the two-dimensional logical matrix of a maize crack image, the number of cracks could be counted. Figure 13 shows the first class's internal crack numbers in 50 corn seeds.

Multi-source feature fusion

The multi-source heterogeneous data can be fused by dividing it into layers, such as the data, feature, and decision layers. The fusion of the feature layer utilizes a greater amount of information and results in higher accuracy when compared to the fusion of the decision layer. Compared to data layer fusion, it eliminates redundant information and reduces computational complexity. Therefore, the fusion of the feature layers was chosen in the experiment. The data fusion method based on multi-core learning can flexibly employ distinct kernel functions to process data from different sources and has been widely applied in classification and prediction tasks. The weighted polynomial extension was implemented to fuse the extracted features mentioned above.

Random forest regression

The RF employs an ensemble learning proposed by Beriman (2001) to reduce overfitting risk and improve overall model performance by constructing multiple decision trees. The RF employs the bootstrap sampling method to randomly generate multiple training sets and produce corresponding decision trees for each training set. Each decision tree is predicted once, and the average of the predicted scores from numerous decision trees is combined to generate the result. The RF adds additional randomness to the model while growing the trees. Instead of searching for the most critical feature while splitting a node, it searches for the best feature among a random subset of features. This results in a wide diversity that generally results in a better model.

Figure 14 depicts the schema of the RF.

(a) A training set is generated for each decision tree by randomly selecting data from the original dataset with no duplicates or replacements.

(b) Each training set could be implemented to construct a decision tree where no pruning is required.

(c) An RF was composed of multiple decision trees. The RF’s prediction is the mean of the results of all decision trees. Also, the steps of the RF are presented as follows:

Step 1: Pick random samples from a given dataset.

Step 2: Construct a decision tree for each training data.

Step 3: Vote by averaging the decision tree.

Step 4: Eventually, pick the most voted estimation outcome as the outcome.

The numbers of decision trees and leaves represent the key parameters affecting the RF model’s predictive capability.

Evaluation index

MAE and RMSE are implemented to assess the RF model’s prediction accuracy (Özen, 2024). The closer the MAE and RMSE scores near 0, the higher the model’s accuracy. The scores of MAE and RMSE can be calculated by Eqs. (8) and (9).

(8) $$MAE={\displaystyle \frac{1}{N}\sum _{i=1}^N\left|y_i-{\hat{y}}_i\right|}$$

(9) $$RMSE=\sqrt{{\displaystyle \frac{1}{N}\sum _{i=1}^N{\left(y_i-{\hat{y}}_i\right)}^2}}.$$

The accuracy is calculated by Eq. (10),

(10) $$ACC=\left(1-\sum _{i=1}^N{\displaystyle \frac{\left|y_i-{\hat{y}}_i\right|}{\left|y_i\right|}}\right)\times 100\mathrm{\%}$$where the number of samples is represented by N, $y_i$ and ${\hat{y}}_i$ the true and estimated scores are designated, respectively.

The implementation of the RF prediction model

The 600 Zheng Dan-958 variety maize seeds were split into 12 classes, containing 50 in each. The split courses of 1–10 are allocated for the training and 11–12 for the testing.

In the RF regression model, two parameters must be adjusted: decision tree numbers and feature numbers when each node is split. The cross-validation is employed to determine the number of optimal parameters.

The grid search method was implemented to compute the cross-validation performance of various parameters on the new sample training set. When the numbers of the decision trees and the maximum features are assigned to 80 and 2, respectively, the minimum error would be obtained.

The predicted output scores and corresponding prediction errors of corn germination rate are shown in Fig. 15. MAE and RMSE are 0.913 and 1.163, respectively.

The comparison results of the different strategies

When comparing the prediction results of the RF with those of the radial basis function (RBF), support vector machine (SVM), and extreme learning machine (ELM) through experiments. Table 1 presents the optimal prediction outcomes of the germination rate obtained by several distinct prediction models by implementing the same training and testing sets.

Table 1 depicts that the RF excels the RBF, SVM, and ELM when the prediction accuracy is used. The RF’s runtime is second after the ELM for model efficiency. Overall, the RF prediction model has a simple structure, easy parameter adjustment, and effectively resolves the problem of overfitting, while also improving training efficiency.

Discussion

In the research, Zheng Dan958 variety maize seeds are utilized. A digital camera and a parallel plate capacitor are employed to attain the appearance and intrinsic information of maize seeds non-destructively. To extract features and fuse distinct source information, the germination rate of maize seed is predicted by the RF with a 5.18-s running time. The accuracy reached 92.88%, the average absolute error of the prediction results was 0.913, the RMSE was 1.163. The RF provides significant advantages when compared with the RBF, SVM, and ELM. To predict the germination rate of maize, the proposed nondestructive approach employing multi-source information fusion has strong practicality and becomes a reference.